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from typing import List, Tuple, Dict, Union, Optional, Any, overload, Literal, Callable
from typing_extensions import Unpack
import numpy as numpy_
import torch as torch_
import nvdiffrast.torch
import numbers
from . import numpy, torch
import utils3d.numpy, utils3d.torch
__all__ = ["sliding_window",
"pooling",
"max_pool_2d",
"lookup",
"lookup_get",
"lookup_set",
"group",
"csr_matrix_from_dense_indices",
"reverse_permutation",
"vector_outer",
"perspective_from_fov",
"perspective_from_window",
"intrinsics_from_fov",
"intrinsics_from_focal_center",
"fov_to_focal",
"focal_to_fov",
"intrinsics_to_fov",
"view_look_at",
"extrinsics_look_at",
"perspective_to_intrinsics",
"perspective_to_near_far",
"intrinsics_to_perspective",
"extrinsics_to_view",
"view_to_extrinsics",
"normalize_intrinsics",
"denormalize_intrinsics",
"crop_intrinsics",
"pixel_to_uv",
"pixel_to_ndc",
"uv_to_pixel",
"depth_linear_to_buffer",
"depth_buffer_to_linear",
"unproject_cv",
"unproject_gl",
"project_cv",
"project_gl",
"project",
"unproject",
"screen_coord_to_view_coord",
"quaternion_to_matrix",
"quaternion_multiply",
"quaternion_inverse",
"quaternion_normalize",
"axis_angle_to_matrix",
"matrix_to_quaternion",
"extrinsics_to_essential",
"axis_angle_to_quaternion",
"euler_axis_angle_rotation",
"euler_angles_to_matrix",
"matrix_to_axis_angle",
"matrix_to_euler_angles",
"quaternion_to_axis_angle",
"skew_symmetric",
"rotation_matrix_from_vectors",
"ray_intersection",
"make_affine_matrix",
"random_rotation_matrix",
"lerp",
"slerp",
"slerp_rotation_matrix",
"interpolate_se3_matrix",
"piecewise_lerp",
"piecewise_interpolate_se3_matrix",
"transform_points",
"angle_between",
"kabasch",
"umeyama",
"affine_umeyama",
"solve_pose",
"segment_solve_pose",
"solve_poses_sequential",
"segment_solve_poses_sequential",
"segment_roll",
"segment_take",
"segment_argmax",
"segment_argmin",
"segment_concatenate",
"segment_concat",
"segment_chain",
"group_as_segments",
"triangulate_mesh",
"compute_face_corner_angles",
"compute_face_corner_normals",
"compute_face_corner_tangents",
"compute_face_normals",
"compute_face_tangents",
"compute_vertex_normals",
"remove_corrupted_faces",
"merge_duplicate_vertices",
"remove_unused_vertices",
"subdivide_mesh",
"mesh_edges",
"mesh_half_edges",
"mesh_connected_components",
"graph_connected_components",
"mesh_adjacency_graph",
"flatten_mesh_indices",
"create_cube_mesh",
"create_icosahedron_mesh",
"create_square_mesh",
"create_camera_frustum_mesh",
"merge_meshes",
"uv_map",
"pixel_coord_map",
"screen_coord_map",
"build_grid_mesh",
"build_mesh_from_map",
"build_mesh_from_depth_map",
"depth_map_edge",
"depth_map_aliasing",
"normal_map_edge",
"point_map_to_normal_map",
"depth_map_to_point_map",
"depth_map_to_normal_map",
"chessboard",
"masked_nearest_resize",
"masked_area_resize",
"colorize_depth_map",
"colorize_normal_map",
"colorize_segmentation_map",
"colorize_probability_map",
"flood_fill",
"perlin_noise",
"perlin_noise_map",
"fractal_perlin_noise_map",
"RastContext",
"rasterize_triangles",
"rasterize_triangles_peeling",
"rasterize_lines",
"rasterize_point_cloud",
"sample_texture",
"test_rasterization",
"read_extrinsics_from_colmap",
"read_intrinsics_from_colmap",
"write_extrinsics_as_colmap",
"write_intrinsics_as_colmap",
"read_obj",
"write_obj",
"read_ply",
"write_ply",
"masked_min",
"masked_max",
"csr_eliminate_zeros",
"lexsort",
"index_reduce",
"index_reduce_",
"scatter_argmax",
"scatter_argmin",
"large_multinomial",
"matrix_trace",
"rotation_matrix_2d",
"rotate_2d",
"translate_2d",
"scale_2d",
"pose_graph_optimization",
"segment_median",
"segment_sum",
"segment_cumsum",
"segment_sort",
"segment_argsort",
"segment_topk",
"stack_segments",
"segment_multinomial",
"segment_combinations",
"segment_searchsorted",
"mesh_dual_graph",
"compute_boundaries",
"remove_isolated_pieces",
"compute_mesh_laplacian",
"laplacian_smooth_mesh",
"taubin_smooth_mesh",
"laplacian_hc_smooth_mesh",
"bounding_rect_from_mask",
"texture_composite"]
@overload
def sliding_window(x: numpy_.ndarray, window_size: Union[int, Tuple[int, ...]], stride: Union[int, Tuple[int, ...], NoneType] = None, dilation: Union[int, Tuple[int, ...], NoneType] = None, pad_size: Union[int, Tuple[int, int], Tuple[Tuple[int, int]], NoneType] = None, pad_mode: str = 'constant', pad_value: numbers.Number = 0, axis: Optional[Tuple[int, ...]] = None) -> numpy_.ndarray:
"""Get a sliding window of the input array. Window axis(axes) will be appended as the last dimension(s).
This function is a wrapper of `numpy.lib.stride_tricks.sliding_window_view` with additional support for padding and stride.
## Parameters
- `x` (ndarray): Input array.
- `window_size` (int or Tuple[int,...]): Size of the sliding window. If int
is provided, the same size is used for all specified axes.
- `stride` (Optional[Tuple[int,...]]): Stride between the sliding windows. If None,
no stride is applied. If int is provided, the same stride is used for all specified axes.
- `dilation` (Optional[Tuple[int,...]]): Dilation in each sliding window. If None,
no dilation is applied. If int is provided, the same dilation is used for all specified axes.
- `pad_size` (Optional[Union[int, Tuple[int, int], Tuple[Tuple[int, int]]]]): Size of padding to apply before sliding window.
Corresponding to `axis`.
- General format is `((before_1, after_1), (before_2, after_2), ...)`.
- Shortcut formats:
- `int` -> same padding before and after for all axes;
- `(int, int)` -> same padding before and after for each axis;
- `((int,), (int,) ...)` -> specify padding for each axis, same before and after.
- `pad_mode` (str): Padding mode to use. Refer to `numpy.pad` for more details.
- `pad_value` (Union[int, float]): Value to use for constant padding. Only used
when `pad_mode` is 'constant'.
- `axis` (Optional[Tuple[int,...]]): Axes to apply the sliding window. If None, all axes are used.
## Returns
- (ndarray): Sliding window of the input array.
- If no padding, the output is a view of the input array with zero copy.
- Otherwise, the output is no longer a view but a copy of the padded array."""
utils3d.numpy.utils.sliding_window
@overload
def pooling(x: numpy_.ndarray, kernel_size: Union[int, Tuple[int, ...]], stride: Union[int, Tuple[int, ...], NoneType] = None, padding: Union[int, Tuple[int, int], Tuple[Tuple[int, int]], NoneType] = None, axis: Union[int, Tuple[int, ...], NoneType] = None, mode: Literal['min', 'max', 'sum', 'mean'] = 'max') -> numpy_.ndarray:
"""Compute the pooling of the input array.
NOTE: NaNs will be ignored.
## Parameters
- `x` (ndarray): Input array.
- `kernel_size` (int or Tuple[int,...]): Size of the pooling window.
- `stride` (Optional[Tuple[int,...]]): Stride of the pooling window. If None,
no stride is applied. If int is provided, the same stride is used for all specified axes.
- `padding` (Optional[Union[int, Tuple[int, int], Tuple[Tuple[int, int]]]]): Size of padding to apply before pooling.
Corresponding to `axis`.
- General format is `((before_1, after_1), (before_2, after_2), ...)`.
- Shortcut formats:
- `int` -> same padding before and after for all axes;
- `(int, int)` -> same padding before and after for each axis;
- `((int,), (int,) ...)` -> specify padding for each axis, same before and after.
- `axis` (Optional[Tuple[int,...]]): Axes to apply the pooling. If None, all axes are used.
- `mode` (str): Pooling mode. One of 'min', 'max', 'sum', 'mean'.
## Returns
- (ndarray): Pooled array with the same number of dimensions as input array."""
utils3d.numpy.utils.pooling
@overload
def max_pool_2d(x: numpy_.ndarray, kernel_size: Union[int, Tuple[int, int]], stride: Union[int, Tuple[int, int]], padding: Union[int, Tuple[int, int]], axis: Tuple[int, int] = (-2, -1)):
utils3d.numpy.utils.max_pool_2d
@overload
def lookup(key: numpy_.ndarray, query: numpy_.ndarray) -> numpy_.ndarray:
"""Look up `query` in `key` like a dictionary. Useful for COO indexing.
Parameters
----
- `key` (ndarray): shape `(num_keys, *key_shape)`, the array to search in
- `query` (ndarray): shape `(..., *key_shape)`, the array to search for. `...` represents any number of batch dimensions.
Returns
----
- `indices` (ndarray): shape `(...,)` indices in `key` for each `query`. If a query is not found in key, the corresponding index will be -1.
Notes
----
`O((Q + K) * log(Q + K))` complexity, where `Q` is the number of queries and `K` is the number of keys."""
utils3d.numpy.utils.lookup
@overload
def lookup_get(key: numpy_.ndarray, value: numpy_.ndarray, get_key: numpy_.ndarray, default_value: Union[numbers.Number, numpy_.ndarray] = 0) -> numpy_.ndarray:
"""Dictionary-like get for arrays
## Parameters
- `key` (ndarray): shape `(N, *key_shape)`, the key array of the dictionary to get from
- `value` (ndarray): shape `(N, *value_shape)`, the value array of the dictionary to get from
- `get_key` (ndarray): shape `(..., *key_shape)`, the key array to get for. `...` represents any number of batch dimensions.
- `default_value` (Union[Number, ndarray]): a scalar or an array broadcastable to shape `(..., *value_shape)`. Value to return if a key in `get_key` is not found in `key`.
## Returns
`get_value` (ndarray): shape `(..., *value_shape)`, result values corresponding to `get_key`"""
utils3d.numpy.utils.lookup_get
@overload
def lookup_set(key: numpy_.ndarray, value: numpy_.ndarray, set_key: numpy_.ndarray, set_value: numpy_.ndarray, append: bool = False, inplace: bool = False) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
"""Dictionary-like set for arrays.
## Parameters
- `key` (ndarray): shape `(N, *key_shape)`, the key array of the dictionary to set
- `value` (ndarray): shape `(N, *value_shape)`, the value array of the dictionary to set
- `set_key` (ndarray): shape `(M, *key_shape)`, the key array to set for
- `set_value` (ndarray): shape `(M, *value_shape)`, the value array to set as
- `append` (bool): If True, append the (key, value) pairs in (set_key, set_value) that are not in (key, value) to the result.
- `inplace` (bool): If True, modify the input `value` array
## Returns
- `result_key` (ndarray): shape `(N_new, *value_shape)`. N_new = N + number of new keys added if append is True, else N.
- `result_value (ndarray): shape `(N_new, *value_shape)` """
utils3d.numpy.utils.lookup_set
@overload
def group(labels: numpy_.ndarray, data: Optional[numpy_.ndarray] = None) -> List[Tuple[numpy_.ndarray, numpy_.ndarray]]:
"""Split the data into groups based on the provided labels.
## Parameters
- `labels` `(ndarray)` shape `(N, *label_dims)` array of labels for each data point. Labels can be multi-dimensional.
- `data`: `(ndarray, optional)` shape `(N, *data_dims)` dense tensor. Each one in `N` has `D` features.
If None, return the indices in each group instead.
## Returns
- `groups` `(List[Tuple[ndarray, ndarray]])`: List of each group, a tuple of `(label, data_in_group)`.
- `label` (ndarray): shape `(*label_dims,)` the label of the group.
- `data_in_group` (ndarray): shape `(length_of_group, *data_dims)` the data points in the group.
If `data` is None, `data_in_group` will be the indices of the data points in the original array."""
utils3d.numpy.utils.group
@overload
def csr_matrix_from_dense_indices(indices: numpy_.ndarray, n_cols: int) -> 'csr_array':
"""Convert a regular indices array to a sparse CSR adjacency matrix format
## Parameters
- `indices` (ndarray): shape (N, M) dense tensor. Each one in `N` has `M` connections.
- `n_cols` (int): total number of columns in the adjacency matrix
## Returns
Tensor: shape `(N, n_cols)` sparse CSR adjacency matrix"""
utils3d.numpy.utils.csr_matrix_from_dense_indices
@overload
def reverse_permutation(perm: numpy_.ndarray, axis: int = 0) -> numpy_.ndarray:
"""Compute the reverse of a permutation array.
Parameters
----
- `perm` (ndarray): shape `(..., N, ...)` permutation array.
- `axis` (int): axis of the permutation array. Other axes are treated as batch dimensions.
Returns
----
- `rev_perm` (ndarray): shape `(N,)` reverse permutation array.
Notes
-----
Equivalent to `np.argsort(perm, axis=axis)`, but more efficient."""
utils3d.numpy.utils.reverse_permutation
@overload
def vector_outer(x: numpy_.ndarray, y: Optional[numpy_.ndarray] = None) -> numpy_.ndarray:
"""Compute the outer product of two arrays.
Parameters
----
- `x` (ndarray): shape `(..., M)` first array.
- `y` (ndarray, optional): shape `(..., N)` second array. If None, compute the outer product of `x` with itself.
Returns
----
- `outer` (ndarray): shape `(..., M, N)` outer product of `x` and `y`."""
utils3d.numpy.utils.vector_outer
@overload
def perspective_from_fov(*, fov_x: Union[float, numpy_.ndarray, NoneType] = None, fov_y: Union[float, numpy_.ndarray, NoneType] = None, fov_min: Union[float, numpy_.ndarray, NoneType] = None, fov_max: Union[float, numpy_.ndarray, NoneType] = None, aspect_ratio: Union[float, numpy_.ndarray, NoneType] = None, near: Union[float, numpy_.ndarray, NoneType], far: Union[float, numpy_.ndarray, NoneType]) -> numpy_.ndarray:
"""Get OpenGL perspective matrix from field of view
## Returns
(ndarray): [..., 4, 4] perspective matrix"""
utils3d.numpy.transforms.perspective_from_fov
@overload
def perspective_from_window(left: Union[float, numpy_.ndarray], right: Union[float, numpy_.ndarray], bottom: Union[float, numpy_.ndarray], top: Union[float, numpy_.ndarray], near: Union[float, numpy_.ndarray], far: Union[float, numpy_.ndarray]) -> numpy_.ndarray:
"""Get OpenGL perspective matrix from the window of z=-1 projection plane
## Returns
(ndarray): [..., 4, 4] perspective matrix"""
utils3d.numpy.transforms.perspective_from_window
@overload
def intrinsics_from_fov(*, fov_x: Union[float, numpy_.ndarray, NoneType] = None, fov_y: Union[float, numpy_.ndarray, NoneType] = None, fov_max: Union[float, numpy_.ndarray, NoneType] = None, fov_min: Union[float, numpy_.ndarray, NoneType] = None, cx: Union[float, numpy_.ndarray] = 0.5, cy: Union[float, numpy_.ndarray] = 0.5, aspect_ratio: Union[float, numpy_.ndarray, NoneType] = None) -> numpy_.ndarray:
"""Get normalized OpenCV intrinsics matrix from given field of view.
You can provide either fov_x, fov_y, fov_max or fov_min and aspect_ratio
Parameters
----
fov_x (float | ndarray): field of view in x axis
fov_y (float | ndarray): field of view in y axis
fov_max (float | ndarray): field of view in largest dimension
fov_min (float | ndarray): field of view in smallest dimension
cx (float | ndarray): principal point x coordinate
cy (float | ndarray): principal point y coordinate
aspect_ratio (float | ndarray): aspect ratio of the image
Returns
----
(ndarray): [..., 3, 3] OpenCV intrinsics matrix"""
utils3d.numpy.transforms.intrinsics_from_fov
@overload
def intrinsics_from_focal_center(fx: Union[float, numpy_.ndarray], fy: Union[float, numpy_.ndarray], cx: Union[float, numpy_.ndarray], cy: Union[float, numpy_.ndarray]) -> numpy_.ndarray:
"""Get OpenCV intrinsics matrix
## Returns
(ndarray): [..., 3, 3] OpenCV intrinsics matrix"""
utils3d.numpy.transforms.intrinsics_from_focal_center
@overload
def fov_to_focal(fov: numpy_.ndarray):
utils3d.numpy.transforms.fov_to_focal
@overload
def focal_to_fov(focal: numpy_.ndarray):
utils3d.numpy.transforms.focal_to_fov
@overload
def intrinsics_to_fov(intrinsics: numpy_.ndarray) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
utils3d.numpy.transforms.intrinsics_to_fov
@overload
def view_look_at(eye: numpy_.ndarray, look_at: numpy_.ndarray, up: numpy_.ndarray) -> numpy_.ndarray:
"""Get OpenGL view matrix looking at something
## Parameters
eye (ndarray): [..., 3] the eye position
look_at (ndarray): [..., 3] the position to look at
up (ndarray): [..., 3] head up direction (y axis in screen space). Not necessarily othogonal to view direction
## Returns
(ndarray): [..., 4, 4], view matrix"""
utils3d.numpy.transforms.view_look_at
@overload
def extrinsics_look_at(eye: numpy_.ndarray, look_at: numpy_.ndarray, up: numpy_.ndarray) -> numpy_.ndarray:
"""Get OpenCV extrinsics matrix looking at something
## Parameters
eye (ndarray): [..., 3] the eye position
look_at (ndarray): [..., 3] the position to look at
up (ndarray): [..., 3] head up direction (-y axis in screen space). Not necessarily othogonal to view direction
## Returns
(ndarray): [..., 4, 4], extrinsics matrix"""
utils3d.numpy.transforms.extrinsics_look_at
@overload
def perspective_to_intrinsics(perspective: numpy_.ndarray) -> numpy_.ndarray:
"""OpenGL perspective matrix to OpenCV intrinsics
## Parameters
perspective (ndarray): [..., 4, 4] OpenGL perspective matrix
## Returns
(ndarray): shape [..., 3, 3] OpenCV intrinsics"""
utils3d.numpy.transforms.perspective_to_intrinsics
@overload
def perspective_to_near_far(perspective: numpy_.ndarray) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
"""Get near and far planes from OpenGL perspective matrix
## Parameters"""
utils3d.numpy.transforms.perspective_to_near_far
@overload
def intrinsics_to_perspective(intrinsics: numpy_.ndarray, near: Union[float, numpy_.ndarray], far: Union[float, numpy_.ndarray]) -> numpy_.ndarray:
"""OpenCV intrinsics to OpenGL perspective matrix
## Parameters
intrinsics (ndarray): [..., 3, 3] OpenCV intrinsics matrix
near (float | ndarray): [...] near plane to clip
far (float | ndarray): [...] far plane to clip
## Returns
(ndarray): [..., 4, 4] OpenGL perspective matrix"""
utils3d.numpy.transforms.intrinsics_to_perspective
@overload
def extrinsics_to_view(extrinsics: numpy_.ndarray) -> numpy_.ndarray:
"""OpenCV camera extrinsics to OpenGL view matrix
## Parameters
extrinsics (ndarray): [..., 4, 4] OpenCV camera extrinsics matrix
## Returns
(ndarray): [..., 4, 4] OpenGL view matrix"""
utils3d.numpy.transforms.extrinsics_to_view
@overload
def view_to_extrinsics(view: numpy_.ndarray) -> numpy_.ndarray:
"""OpenGL view matrix to OpenCV camera extrinsics
## Parameters
view (ndarray): [..., 4, 4] OpenGL view matrix
## Returns
(ndarray): [..., 4, 4] OpenCV camera extrinsics matrix"""
utils3d.numpy.transforms.view_to_extrinsics
@overload
def normalize_intrinsics(intrinsics: numpy_.ndarray, size: Union[Tuple[numbers.Number, numbers.Number], numpy_.ndarray], pixel_convention: Literal['integer-center', 'integer-corner'] = 'integer-center') -> numpy_.ndarray:
"""Normalize intrinsics from pixel cooridnates to uv coordinates
## Parameters
- `intrinsics` (ndarray): `(..., 3, 3)` camera intrinsics to normalize
- `size` (tuple | ndarray): A tuple `(height, width)` of the image size,
or an array of shape `(..., 2)` corresponding to the multiple image size(s)
- `pixel_convention`: `str`, optional `'integer-center'` or `'integer-corner'`, whether integer coordinates correspond to pixel centers or corners. Defaults to 'integer-center'.
- For more definitions, please refer to `pixel_coord_map()`
## Returns
`(ndarray)`: `(..., 3, 3)` normalized camera intrinsics(s)"""
utils3d.numpy.transforms.normalize_intrinsics
@overload
def denormalize_intrinsics(intrinsics: numpy_.ndarray, size: Union[Tuple[numbers.Number, numbers.Number], numpy_.ndarray], pixel_convention: Literal['integer-center', 'integer-corner'] = 'integer-center') -> numpy_.ndarray:
"""Denormalize intrinsics from uv cooridnates to pixel coordinates
## Parameters
- `intrinsics` (ndarray): `(..., 3, 3)` camera intrinsics to denormalize
- `size` (tuple | ndarray): A tuple `(height, width)` of the image size,
or an array of shape `(..., 2)` corresponding to the multiple image size(s)
- `pixel_convention`: `str`, optional `'integer-center'` or `'integer-corner'`, whether integer coordinates correspond to pixel centers or corners. Defaults to 'integer-center'.
- For more definitions, please refer to `pixel_coord_map()`
## Returns
`(ndarray)`: `(..., 3, 3)` denormalized camera intrinsics in pixel coordinates"""
utils3d.numpy.transforms.denormalize_intrinsics
@overload
def crop_intrinsics(intrinsics: numpy_.ndarray, size: Union[Tuple[numbers.Number, numbers.Number], numpy_.ndarray], cropped_top: Union[numbers.Number, numpy_.ndarray], cropped_left: Union[numbers.Number, numpy_.ndarray], cropped_height: Union[numbers.Number, numpy_.ndarray], cropped_width: Union[numbers.Number, numpy_.ndarray]) -> numpy_.ndarray:
"""Evaluate the new intrinsics after cropping the image
## Parameters
- `intrinsics` (ndarray): (..., 3, 3) camera intrinsics(s) to crop
- `size` (tuple | ndarray): A tuple `(height, width)` of the image size,
or an array of shape `(..., 2)` corresponding to the multiple image size(s)
- `cropped_top` (int | ndarray): (...) top pixel index of the cropped image(s)
- `cropped_left` (int | ndarray): (...) left pixel index of the cropped image(s)
- `cropped_height` (int | ndarray): (...) height of the cropped image(s)
- `cropped_width` (int | ndarray): (...) width of the cropped image(s)
## Returns
(ndarray): (..., 3, 3) cropped camera intrinsics"""
utils3d.numpy.transforms.crop_intrinsics
@overload
def pixel_to_uv(pixel: numpy_.ndarray, size: Union[Tuple[numbers.Number, numbers.Number], numpy_.ndarray], pixel_convention: Literal['integer-center', 'integer-corner'] = 'integer-center') -> numpy_.ndarray:
"""Convert pixel space coordiantes to UV space coordinates.
## Parameters
- `pixel` (ndarray): `(..., 2)` pixel coordinrates
- `size` (tuple | ndarray): A tuple `(height, width)` of the image size,
or an array of shape `(..., 2)` corresponding to the multiple image size(s)
- `pixel_convention`: `str`, optional `'integer-center'` or `'integer-corner'`, whether integer coordinates correspond to pixel centers or corners. Defaults to 'integer-center'.
- For more definitions, please refer to `pixel_coord_map()`
## Returns
(ndarray): `(..., 2)` uv coordinrates"""
utils3d.numpy.transforms.pixel_to_uv
@overload
def pixel_to_ndc(pixel: numpy_.ndarray, size: Union[Tuple[numbers.Number, numbers.Number], numpy_.ndarray], pixel_convention: Literal['integer-center', 'integer-corner'] = 'integer-center') -> numpy_.ndarray:
"""Convert pixel coordinates to NDC (Normalized Device Coordinates).
## Parameters
- `pixel` (ndarray): `(..., 2)` pixel coordinrates.
- `size` (tuple | ndarray): A tuple `(height, width)` of the image size,
or an array of shape `(..., 2)` corresponding to the multiple image size(s)
- `pixel_convention`: `str`, optional `'integer-center'` or `'integer-corner'`, whether integer coordinates represent pixel centers or corners. Defaults to 'integer-center'.
- For more definitions, please refer to `pixel_coord_map()`
## Returns
(ndarray): `(..., 2)` ndc coordinrates, the range is (-1, 1)"""
utils3d.numpy.transforms.pixel_to_ndc
@overload
def uv_to_pixel(uv: numpy_.ndarray, size: Union[Tuple[numbers.Number, numbers.Number], numpy_.ndarray], pixel_convention: Literal['integer-center', 'integer-corner'] = 'integer-center') -> numpy_.ndarray:
"""Convert UV space coordinates to pixel space coordinates.
## Parameters
- `uv` (ndarray): `(..., 2)` uv coordinrates.
- `size` (tuple | ndarray): A tuple `(height, width)` of the image size,
or an array of shape `(..., 2)` corresponding to the multiple image size(s)
- `pixel_convention`: `str`, optional `'integer-center'` or `'integer-corner'`, whether integer coordinates correspond to pixel centers or corners. Defaults to 'integer-center'.
- For more definitions, please refer to `pixel_coord_map()`
## Returns
(ndarray): `(..., 2)` pixel coordinrates"""
utils3d.numpy.transforms.uv_to_pixel
@overload
def depth_linear_to_buffer(depth: numpy_.ndarray, near: Union[float, numpy_.ndarray], far: Union[float, numpy_.ndarray]) -> numpy_.ndarray:
"""Project linear depth to depth value in screen space
## Parameters
depth (ndarray): [...] depth value
near (float | ndarray): [...] near plane to clip
far (float | ndarray): [...] far plane to clip
## Returns
(ndarray): [..., 1] depth value in screen space, value ranging in [0, 1]"""
utils3d.numpy.transforms.depth_linear_to_buffer
@overload
def depth_buffer_to_linear(depth_buffer: numpy_.ndarray, near: Union[float, numpy_.ndarray], far: Union[float, numpy_.ndarray]) -> numpy_.ndarray:
"""OpenGL depth buffer to linear depth
## Parameters
depth_buffer (ndarray): [...] depth value
near (float | ndarray): [...] near plane to clip
far (float | ndarray): [...] far plane to clip
## Returns
(ndarray): [..., 1] linear depth"""
utils3d.numpy.transforms.depth_buffer_to_linear
@overload
def unproject_cv(uv: numpy_.ndarray, depth: numpy_.ndarray, intrinsics: numpy_.ndarray, extrinsics: numpy_.ndarray = None) -> numpy_.ndarray:
"""Unproject uv coordinates to 3D view space following the OpenCV convention
## Parameters
uv (ndarray): [..., N, 2] uv coordinates, value ranging in [0, 1].
The origin (0., 0.) is corresponding to the left & top
depth (ndarray): [..., N] depth value
extrinsics (ndarray): [..., 4, 4] extrinsics matrix
intrinsics (ndarray): [..., 3, 3] intrinsics matrix
## Returns
points (ndarray): [..., N, 3] 3d points"""
utils3d.numpy.transforms.unproject_cv
@overload
def unproject_gl(uv: numpy_.ndarray, depth: numpy_.ndarray, projection: numpy_.ndarray, view: Optional[numpy_.ndarray] = None) -> numpy_.ndarray:
"""Unproject screen space coordinates to 3D view space following the OpenGL convention (except for row major matrices)
## Parameters
uv (ndarray): (..., N, 2) screen space XY coordinates, value ranging in [0, 1].
The origin (0., 0.) is corresponding to the left & bottom
depth (ndarray): (..., N) linear depth values
projection (ndarray): (..., 4, 4) projection matrix
view (ndarray): (..., 4, 4) view matrix
## Returns
points (ndarray): (..., N, 3) 3d points"""
utils3d.numpy.transforms.unproject_gl
@overload
def project_cv(points: numpy_.ndarray, intrinsics: numpy_.ndarray, extrinsics: Optional[numpy_.ndarray] = None) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
"""Project 3D points to 2D following the OpenCV convention
## Parameters
points (ndarray): [..., N, 3]
extrinsics (ndarray): [..., 4, 4] extrinsics matrix
intrinsics (ndarray): [..., 3, 3] intrinsics matrix
## Returns
uv_coord (ndarray): [..., N, 2] uv coordinates, value ranging in [0, 1].
The origin (0., 0.) is corresponding to the left & top
linear_depth (ndarray): [..., N] linear depth"""
utils3d.numpy.transforms.project_cv
@overload
def project_gl(points: numpy_.ndarray, projection: numpy_.ndarray, view: numpy_.ndarray = None) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
"""Project 3D points to 2D following the OpenGL convention (except for row major matrices)
## Parameters
points (ndarray): [..., N, 3] or [..., N, 4] 3D points to project, if the last
dimension is 4, the points are assumed to be in homogeneous coordinates
view (ndarray): [..., 4, 4] view matrix
projection (ndarray): [..., 4, 4] projection matrix
## Returns
scr_coord (ndarray): [..., N, 2] OpenGL screen space XY coordinates, value ranging in [0, 1].
The origin (0., 0.) is corresponding to the left & bottom
linear_depth (ndarray): [..., N] linear depth"""
utils3d.numpy.transforms.project_gl
@overload
def project(points: numpy_.ndarray, *, intrinsics: Optional[numpy_.ndarray] = None, extrinsics: Optional[numpy_.ndarray] = None, view: Optional[numpy_.ndarray] = None, projection: Optional[numpy_.ndarray] = None) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
"""Calculate projection.
- For OpenCV convention, use `intrinsics` and `extrinsics` matrices.
- For OpenGL convention, use `view` and `projection` matrices.
## Parameters
- `points`: (..., N, 3) 3D world-space points
- `intrinsics`: (..., 3, 3) intrinsics matrix
- `extrinsics`: (..., 4, 4) extrinsics matrix
- `view`: (..., 4, 4) view matrix
- `projection`: (..., 4, 4) projection matrix
## Returns
- `uv`: (..., N, 2) 2D coordinates.
- For OpenCV convention, it is the normalized image coordinate where (0, 0) is the top left corner.
- For OpenGL convention, it is the screen space XY coordinate where (0, 0) is the bottom left corner.
- `depth`: (..., N) linear depth values, where `depth > 0` is visible.
- For OpenCV convention, it is the Z coordinate in camera space.
- For OpenGL convention, it is the -Z coordinate in camera space."""
utils3d.numpy.transforms.project
@overload
def unproject(uv: numpy_.ndarray, depth: Optional[numpy_.ndarray], *, intrinsics: Optional[numpy_.ndarray] = None, extrinsics: Optional[numpy_.ndarray] = None, projection: Optional[numpy_.ndarray] = None, view: Optional[numpy_.ndarray] = None) -> numpy_.ndarray:
"""Calculate inverse projection.
- For OpenCV convention, use `intrinsics` and `extrinsics` matrices.
- For OpenGL convention, use `view` and `projection` matrices.
## Parameters
- `uv`: (..., N, 2) 2D coordinates.
- For OpenCV convention, it is the normalized image coordinate where (0, 0) is the top left corner.
- For OpenGL convention, it is the screen space XY coordinate where (0, 0) is the bottom left corner.
- `depth`: (..., N) linear depth values, where `depth > 0` is visible.
- For OpenCV convention, it is the Z coordinate in camera space.
- For OpenGL convention, it is the -Z coordinate in camera space.
- `intrinsics`: (..., 3, 3) intrinsics matrix
- `extrinsics`: (..., 4, 4) extrinsics matrix
- `view`: (..., 4, 4) view matrix
- `projection`: (..., 4, 4) projection matrix
## Returns
- `points`: (..., N, 3) 3D world-space points"""
utils3d.numpy.transforms.unproject
@overload
def screen_coord_to_view_coord(screen_coord: numpy_.ndarray, projection: numpy_.ndarray) -> numpy_.ndarray:
"""Unproject screen space coordinates to 3D view space following the OpenGL convention (except for row major matrices)
## Parameters
screen_coord (ndarray): (..., N, 3) screen space XYZ coordinates, value ranging in [0, 1]
The origin (0., 0.) is corresponding to the left & bottom
projection (ndarray): (..., 4, 4) projection matrix
## Returns
points (ndarray): [..., N, 3] 3d points in view space"""
utils3d.numpy.transforms.screen_coord_to_view_coord
@overload
def quaternion_to_matrix(quaternion: numpy_.ndarray) -> numpy_.ndarray:
"""Converts a batch of quaternions (w, x, y, z) to rotation matrices
## Parameters
quaternion (ndarray): shape (..., 4), the quaternions to convert
## Returns
ndarray: shape (..., 3, 3), the rotation matrices corresponding to the given quaternions"""
utils3d.numpy.transforms.quaternion_to_matrix
@overload
def quaternion_multiply(q1: numpy_.ndarray, q2: numpy_.ndarray) -> numpy_.ndarray:
"""Multiplies two quaternions (w, x, y, z)
Parameters
----
q1 (ndarray): shape (..., 4), the first quaternion
q2 (ndarray): shape (..., 4), the second quaternion
Returns
----
ndarray: shape (..., 4), the product of the two quaternions"""
utils3d.numpy.transforms.quaternion_multiply
@overload
def quaternion_inverse(quaternion: numpy_.ndarray) -> numpy_.ndarray:
"""Calculate the inverse of a batch of quaternions (w, x, y, z)
Parameters
----
quaternion (ndarray): shape (..., 4), the quaternions to invert
Returns
----
ndarray: shape (..., 4)"""
utils3d.numpy.transforms.quaternion_inverse
@overload
def quaternion_normalize(quaternion: numpy_.ndarray) -> numpy_.ndarray:
"""Normalize quaternions (w, x, y, z) to unit length and positive w component
Parameters
----
quaternion (ndarray): shape (..., 4), the quaternions to normalize
Returns
----
ndarray: shape (..., 4), the normalized quaternions with unit length and positive w component"""
utils3d.numpy.transforms.quaternion_normalize
@overload
def axis_angle_to_matrix(axis_angle: numpy_.ndarray) -> numpy_.ndarray:
"""Convert axis-angle representation (rotation vector) to rotation matrix, whose direction is the axis of rotation and length is the angle of rotation
## Parameters
axis_angle (ndarray): shape (..., 3), axis-angle vcetors
## Returns
ndarray: shape (..., 3, 3) The rotation matrices for the given axis-angle parameters"""
utils3d.numpy.transforms.axis_angle_to_matrix
@overload
def matrix_to_quaternion(rot_mat: numpy_.ndarray) -> numpy_.ndarray:
"""Convert 3x3 rotation matrix to quaternion (w, x, y, z)
## Parameters
rot_mat (ndarray): shape (..., 3, 3), the rotation matrices to convert
## Returns
ndarray: shape (..., 4), the quaternions corresponding to the given rotation matrices"""
utils3d.numpy.transforms.matrix_to_quaternion
@overload
def extrinsics_to_essential(extrinsics: numpy_.ndarray):
"""extrinsics matrix `[[R, t] [0, 0, 0, 1]]` such that `x' = R (x - t)` to essential matrix such that `x' E x = 0`
## Parameters
extrinsics (np.ndaray): [..., 4, 4] extrinsics matrix
## Returns
(np.ndaray): [..., 3, 3] essential matrix"""
utils3d.numpy.transforms.extrinsics_to_essential
@overload
def axis_angle_to_quaternion(axis_angle: numpy_.ndarray) -> numpy_.ndarray:
"""Convert axis-angle representation (rotation vector) to quaternion (w, x, y, z)
## Parameters
axis_angle (ndarray): shape (..., 3), axis-angle vcetors
## Returns
ndarray: shape (..., 4) The quaternions for the given axis-angle parameters"""
utils3d.numpy.transforms.axis_angle_to_quaternion
@overload
def euler_axis_angle_rotation(axis: str, angle: numpy_.ndarray) -> numpy_.ndarray:
"""Return the rotation matrices for one of the rotations about an axis
of which Euler angles describe, for each value of the angle given.
## Parameters
axis: Axis label "X" or "Y or "Z".
angle: any shape ndarray of Euler angles in radians
## Returns
Rotation matrices as ndarray of shape (..., 3, 3)."""
utils3d.numpy.transforms.euler_axis_angle_rotation
@overload
def euler_angles_to_matrix(euler_angles: numpy_.ndarray, convention: str = 'XYZ') -> numpy_.ndarray:
"""Convert rotations given as Euler angles in radians to rotation matrices.
## Parameters
euler_angles: Euler angles in radians as ndarray of shape (..., 3), XYZ
convention: permutation of "X", "Y" or "Z", representing the order of Euler rotations to apply.
## Returns
Rotation matrices as ndarray of shape (..., 3, 3)."""
utils3d.numpy.transforms.euler_angles_to_matrix
@overload
def matrix_to_axis_angle(rot_mat: numpy_.ndarray) -> numpy_.ndarray:
"""Convert a batch of 3x3 rotation matrices to axis-angle representation (rotation vector)
## Parameters
rot_mat (ndarray): shape (..., 3, 3), the rotation matrices to convert
## Returns
ndarray: shape (..., 3), the axis-angle vectors corresponding to the given rotation matrices"""
utils3d.numpy.transforms.matrix_to_axis_angle
@overload
def matrix_to_euler_angles(matrix: numpy_.ndarray, convention: str) -> numpy_.ndarray:
"""Convert rotations given as rotation matrices to Euler angles in radians.
NOTE: The composition order eg. `XYZ` means `Rz * Ry * Rx` (like blender), instead of `Rx * Ry * Rz` (like pytorch3d)
## Parameters
matrix: Rotation matrices as ndarray of shape (..., 3, 3).
convention: Convention string of three uppercase letters.
## Returns
Euler angles in radians as ndarray of shape (..., 3), in the order of XYZ (like blender), instead of convention (like pytorch3d)"""
utils3d.numpy.transforms.matrix_to_euler_angles
@overload
def quaternion_to_axis_angle(quaternion: numpy_.ndarray) -> numpy_.ndarray:
"""Convert a batch of quaternions (w, x, y, z) to axis-angle representation (rotation vector)
## Parameters
quaternion (ndarray): shape (..., 4), the quaternions to convert
## Returns
ndarray: shape (..., 3), the axis-angle vectors corresponding to the given quaternions"""
utils3d.numpy.transforms.quaternion_to_axis_angle
@overload
def skew_symmetric(v: numpy_.ndarray):
"""Skew symmetric matrix from a 3D vector"""
utils3d.numpy.transforms.skew_symmetric
@overload
def rotation_matrix_from_vectors(v1: numpy_.ndarray, v2: numpy_.ndarray):
"""Rotation matrix that rotates v1 to v2"""
utils3d.numpy.transforms.rotation_matrix_from_vectors
@overload
def ray_intersection(p1: numpy_.ndarray, d1: numpy_.ndarray, p2: numpy_.ndarray, d2: numpy_.ndarray):
"""Compute the intersection/closest point of two D-dimensional rays
If the rays are intersecting, the closest point is the intersection point.
## Parameters
p1 (ndarray): (..., D) origin of ray 1
d1 (ndarray): (..., D) direction of ray 1
p2 (ndarray): (..., D) origin of ray 2
d2 (ndarray): (..., D) direction of ray 2
## Returns
(ndarray): (..., N) intersection point"""
utils3d.numpy.transforms.ray_intersection
@overload
def make_affine_matrix(M: numpy_.ndarray, t: numpy_.ndarray) -> numpy_.ndarray:
"""Make an affine transformation matrix from a linear matrix and a translation vector.
## Parameters
M (ndarray): [..., D, D] linear matrix (rotation, scaling or general deformation)
t (ndarray): [..., D] translation vector
## Returns
ndarray: [..., D + 1, D + 1] affine transformation matrix"""
utils3d.numpy.transforms.make_affine_matrix
@overload
def random_rotation_matrix(*size: int, dtype=numpy_.float32) -> numpy_.ndarray:
"""Generate random 3D rotation matrix.
## Parameters
dtype: The data type of the output rotation matrix.
## Returns
ndarray: `(*size, 3, 3)` random rotation matrix."""
utils3d.numpy.transforms.random_rotation_matrix
@overload
def lerp(x1: numpy_.ndarray, x2: numpy_.ndarray, t: numpy_.ndarray) -> numpy_.ndarray:
"""Linear interpolation between two vectors.
## Parameters
x1 (ndarray): [..., D] vector 1
x2 (ndarray): [..., D] vector 2
t (ndarray): [..., N] interpolation parameter. [0, 1] for interpolation between x1 and x2, otherwise for extrapolation.
## Returns
ndarray: [..., N, D] interpolated vector"""
utils3d.numpy.transforms.lerp
@overload
def slerp(v1: numpy_.ndarray, v2: numpy_.ndarray, t: numpy_.ndarray) -> numpy_.ndarray:
"""Spherical linear interpolation between two (unit) vectors.
## Parameters
- `v1` (ndarray): `(..., D)` (unit) vector 1
- `v2` (ndarray): `(..., D)` (unit) vector 2
- `t` (ndarray): `(..., N)` interpolation parameter in [0, 1]
## Returns
ndarray: `(..., N, D)` interpolated unit vector"""
utils3d.numpy.transforms.slerp
@overload
def slerp_rotation_matrix(R1: numpy_.ndarray, R2: numpy_.ndarray, t: numpy_.ndarray) -> numpy_.ndarray:
"""Spherical linear interpolation between two rotation matrices.
## Parameters
- `R1` (ndarray): [..., 3, 3] rotation matrix 1
- `R2` (ndarray): [..., 3, 3] rotation matrix 2
- `t` (ndarray): [..., N] interpolation parameter in [0, 1]
## Returns
ndarray: [...,N, 3, 3] interpolated rotation matrix"""
utils3d.numpy.transforms.slerp_rotation_matrix
@overload
def interpolate_se3_matrix(T1: numpy_.ndarray, T2: numpy_.ndarray, t: numpy_.ndarray) -> numpy_.ndarray:
"""Linear interpolation between two SE(3) matrices.
## Parameters
- `T1` (ndarray): [..., 4, 4] SE(3) matrix 1
- `T2` (ndarray): [..., 4, 4] SE(3) matrix 2
- `t` (ndarray): [..., N] interpolation parameter in [0, 1]
## Returns
ndarray: [..., N, 4, 4] interpolated SE(3) matrix"""
utils3d.numpy.transforms.interpolate_se3_matrix
@overload
def piecewise_lerp(x: numpy_.ndarray, t: numpy_.ndarray, s: numpy_.ndarray, extrapolation_mode: Literal['constant', 'linear'] = 'constant') -> numpy_.ndarray:
"""Linear spline interpolation.
## Parameters
- `x`: ndarray, shape (n, d): the values of data points.
- `t`: ndarray, shape (n,): the times of the data points.
- `s`: ndarray, shape (m,): the times to be interpolated.
- `extrapolation_mode`: str, the mode of extrapolation. 'constant' means extrapolate the boundary values, 'linear' means extrapolate linearly.
## Returns
- `y`: ndarray, shape (..., m, d): the interpolated values."""
utils3d.numpy.transforms.piecewise_lerp
@overload
def piecewise_interpolate_se3_matrix(T: numpy_.ndarray, t: numpy_.ndarray, s: numpy_.ndarray, extrapolation_mode: Literal['constant', 'linear'] = 'constant') -> numpy_.ndarray:
"""Linear spline interpolation for SE(3) matrices.
## Parameters
- `T`: ndarray, shape (n, 4, 4): the SE(3) matrices.
- `t`: ndarray, shape (n,): the times of the data points.
- `s`: ndarray, shape (m,): the times to be interpolated.
- `extrapolation_mode`: str, the mode of extrapolation. 'constant' means extrapolate the boundary values, 'linear' means extrapolate linearly.
## Returns
- `T_interp`: ndarray, shape (..., m, 4, 4): the interpolated SE(3) matrices."""
utils3d.numpy.transforms.piecewise_interpolate_se3_matrix
@overload
def transform_points(x: numpy_.ndarray, *Ts: numpy_.ndarray) -> numpy_.ndarray:
"""Apply transformation(s) to a point or a set of points.
It is like `(Tn @ ... @ T2 @ T1 @ x[:, None]).squeeze(0)`, but:
1. Automatically handle the homogeneous coordinate;
- x will be padded with homogeneous coordinate 1.
- Each T will be padded by identity matrix to match the dimension.
2. Using efficient contraction path when array sizes are large, based on `einsum`.
## Parameters
- `x`: ndarray, shape `(..., D)`: the points to be transformed.
- `Ts`: ndarray, shape `(..., D1, D2)`: the affine transformation matrix (matrices)
If more than one transformation is given, they will be applied in corresponding order.
## Returns
- `y`: ndarray, shape `(..., D)`: the transformed point or a set of points.
## Example Usage
- Just linear transformation
```
y = transform(x_3, mat_3x3)
```
- Affine transformation
```
y = transform(x_3, mat_3x4)
```
- Chain multiple transformations
```
y = transform(x_3, T1_4x4, T2_3x4, T3_3x4)
```"""
utils3d.numpy.transforms.transform_points
@overload
def angle_between(v1: numpy_.ndarray, v2: numpy_.ndarray):
"""Calculate the angle between two (batches of) vectors.
Better precision than using the arccos dot product directly.
## Parameters
- `v1`: ndarray, shape (..., D): the first vector.
- `v2`: ndarray, shape (..., D): the second vector.
## Returns
`angle`: ndarray, shape (...): the angle between the two vectors."""
utils3d.numpy.transforms.angle_between
@overload
def kabasch(cov: numpy_.ndarray) -> numpy_.ndarray:
utils3d.numpy.pose.kabasch
@overload
def umeyama(cov_yx: numpy_.ndarray, cov_xx: Optional[numpy_.ndarray] = None, cov_yy: Optional[numpy_.ndarray] = None, mean_x: Optional[numpy_.ndarray] = None, mean_y: Optional[numpy_.ndarray] = None) -> Tuple[numpy_.ndarray, numpy_.ndarray, numpy_.ndarray]:
"""Procrustes analysis to solve for scale `s`, rotation `R` and translation `t` such that `y_i ~= s R x_i + t`.
Parameters
----
- `cov_yx`: (..., 3, 3) covariance matrix between y and x points.
- `cov_xx`: (..., 3, 3) covariance matrix of x points. If None, no scaling is solved.
- `cov_yy`: (..., 3, 3) covariance matrix of y points. If None, no scaling is solved.
- `mean_x`: (..., 3) mean of x points. If None, no translation is solved.
- `mean_y`: (..., 3) mean of y points. If None, no translation is solved.
Specifically, based on provided inputs:
- To solve the rotation `R`, `cov_yx` must be given.
- To solve the scale `s`, at least one of `cov_xx` and `cov_yy` must be given.
- (Recommended) If both `cov_xx` and `cov_yy` are given, the scale will be solved by minimizing a symmetric cost:
`||s R X + t - Y||_F^2 / ||Y||_F^2 + ||s R^T (Y - t) - X||_F^2 / ||X||_F^2`
- If only `cov_xx` is given, the scale will be solved by minimizing forward cost
`||s R X + t - Y||_F^2`
- If only `cov_yy` is given, the scale will be solved by minimizing inverse cost
`||s R^T (Y - t) - X||_F^2`
- To solve the translation `t`, provide `mean_x` and `mean_y`.
Returns
----
- `s`: (...) scale factor. None if both cov_xx and cov_yy are None.
- `R`: (..., 3, 3) rotation matrix.
- `t`: (..., 3) translation vector. None if mean_x or mean_y is None."""
utils3d.numpy.pose.umeyama
@overload
def affine_umeyama(cov_yx: numpy_.ndarray, cov_xx: numpy_.ndarray, cov_yy: numpy_.ndarray, mean_x: numpy_.ndarray, mean_y: numpy_.ndarray, lam: float = 0.01, niter: int = 8) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
"""Extended Procrustes analysis to solve for affine transformation `A` and translation `t` such that `y_i ~= A x_i + t`.
Parameters
----
- `cov_yx`: (..., 3, 3) covariance matrix between y
- `cov_xx`: (..., 3, 3) covariance matrix of x points.
- `cov_yy`: (..., 3, 3) covariance matrix of y
- `mean_x`: (..., 3) mean of x points.
- `mean_y`: (..., 3) mean of y points.
- `lam`: rigidity regularization weight.
- `gamma`: symmetricity regularization annealing factor.
- `niter`: number of iterations for solving.
Returns
----
- `A`: (..., 3, 3) affine transformation matrix.
- `t`: (..., 3) translation vector."""
utils3d.numpy.pose.affine_umeyama
@overload
def solve_pose(p: numpy_.ndarray, q: numpy_.ndarray, w: Optional[numpy_.ndarray] = None, *, mode: Literal['rigid', 'similar', 'affine'] = 'rigid', lam: float = 0.01, niter: int = 5) -> numpy_.ndarray:
"""Solve for the pose (transformation from p to q) given weighted point correspondences.
Parameters
----
- `p`: (..., N, 3) source points
- `q`: (..., N, 3) target points
- `w`: optional (..., N) weights for each point correspondence. If None, uniform weights are used.
- `mode`: mode of transformation to apply. Can be 'rigid', 'similar', or 'affine'.
- For 'rigid', only rotation and translation are allowed.
- For 'similar', uniform scaling, rotation and translation are allowed.
- For 'affine', full affine transformation is allowed. Using least squares.
- `lam`: regularization weight for 'affine' mode.
- `niter`: number of iterations for 'affine' mode.
Returns
----
- `pose`: (..., 4, 4) transformations matrix from p to q."""
utils3d.numpy.pose.solve_pose
@overload
def segment_solve_pose(p: numpy_.ndarray, q: numpy_.ndarray, w: Optional[numpy_.ndarray] = None, *, offsets: numpy_.ndarray, mode: Literal['rigid', 'similar', 'affine'] = 'rigid', lam: float = 0.01, niter: int = 5) -> numpy_.ndarray:
"""Solve for the pose (transformation from p to q) given weighted point correspondences.
Parameters
----
- `p`: (N, 3) source points
- `q`: (N, 3) target points
- `w`: (N,) weights for each point correspondence
- `offsets`: (S + 1,) segment offsets. Points in each segment belong to the same rigid / affine body.
- `mode`: mode of transformation to apply. Can be 'rigid', 'similar', or 'affine'.
- For 'rigid', only rotation and translation are allowed.
- For 'similar', uniform scaling, rotation and translation are allowed.
- For 'affine', full affine transformation is allowed. Using least squares.
- `lam`: regularization weight for 'affine' mode.
- `niter`: number of iterations for 'affine' mode.
Returns
----
- `pose`: (S, 4, 4) transformations matrix from p to q."""
utils3d.numpy.pose.segment_solve_pose
@overload
def solve_poses_sequential(trajectories: numpy_.ndarray, weights: Optional[numpy_.ndarray] = None, *, accum: Optional[Tuple[numpy_.ndarray, ...]] = None, min_valid_size: int = 3, mode: Literal['rigid', 'similar', 'affine'] = 'rigid', lam: float = 0.01, niter: int = 8) -> Tuple[numpy_.ndarray, Tuple[numpy_.ndarray, ...], Tuple[numpy_.ndarray, numpy_.ndarray, numpy_.ndarray, numpy_.ndarray]]:
"""Given trajectories of points over time, sequentially solve for the poses (transformations from canonical to each frame) of each body at each frame.
Parameters
----
- `trajectories`: (T, ..., N, 3) posed points. T is number of frames. `...` is optional batch dimensions. N is number of points per group.
- `weights`: (T, ..., N) quardratic error term weights for each point at each frame
- `accum`: accumulated statistics from previous calls. If None, start fresh.
- `min_valid_size`: minimum number of valid points in each frame to consider the segment / group valid.
- `mode`: mode of transformation to apply. Can be 'rigid', 'similar', or 'affine'.
- For 'rigid', only rotation and translation are allowed.
- For 'similar', uniform scaling, rotation and translation are allowed.
- For 'affine', full affine transformation is allowed. Using least squares.
- `lam`: rigidity regularization weight for 'affine' mode.
- `niter`: number of iterations for 'affine' mode.
Returns
----
- `poses`: (T, ..., 4, 4) transformations from canonical to each frame.
- `valid`: (T, ...) boolean mask indicating valid segments
- `stats`: canonical statistics of each group,
It is a tuple of:
- `mu`: (..., 3) weighted mean of points
- `cov`: (..., 3, 3) weighted covariance of points
- `tot_w`: (...,) total weight of points
- `nnz`: (...,) number of non-zero weight points
- `canonical_points`: (..., N, 3) canonical points.
- `err`: (..., N,) per-point RMS error over all time := sqrt(sum_over_time(per_point_weights * per_point_squared_error) / per_point_nnz)
Use this to filter outliers as needed.
- `accum`: per point accumulated statistics. Just pass it to the next call for incremental solving.
It is a tuple of:
- `accum_sqrtw`: (..., N,) sum of sqrt(weights)
- `accum_sqrtwx`: (..., N, 3) sum of sqrt(weights) * x
- `accum_sqrtwxx`: (...N, 3, 3) sum of sqrt(weights) * outer(x - mean_sqrtwx, x - mean_sqrtwx)
- `accum_w`: (..., N,) sum of weights
- `accum_wx`: (..., N, 3) sum of weights * x
- `accum_wxx`: (..., N, 3, 3) sum of weights * outer(x - mean_wx, x - mean_wx)
- `accum_nnz`: (..., N,) number of non-zero weight accumulations
Example
----
```
accum = None
poses, valid = [], []
for new_trajectories_chunk in data_stream:
# new_trajectories_chunk: (T_chunk, N, 3)
poses_chunk, valid_chunk, stats, canonical_points, err, accum = solve_poses(
new_trajectories_chunk,
accum=accum,
)
poses.append(poses_chunk)
valid.append(valid_chunk)
# `stats`, `canonical_points` and `err` are returned and updated every chunk.
poses = np.concatenate(poses, axis=0) # (T_all, 4, 4), poses over all frames
valid = np.concatenate(valid, axis=0) # (T_all,), poses' validity over all frames"""
utils3d.numpy.pose.solve_poses_sequential
@overload
def segment_solve_poses_sequential(trajectories: numpy_.ndarray, weights: Optional[numpy_.ndarray] = None, offsets: numpy_.ndarray = None, *, accum: Optional[Tuple[numpy_.ndarray, ...]] = None, min_valid_size: int = 3, mode: Literal['rigid', 'similar', 'affine'] = 'rigid', lam: float = 0.01, niter: int = 8) -> Tuple[numpy_.ndarray, Tuple[numpy_.ndarray, ...], Tuple[numpy_.ndarray, numpy_.ndarray, numpy_.ndarray, numpy_.ndarray]]:
"""Segment array mode for `solve_poses_sequential`.
Parameters
----
- `trajectories`: (T, N, 3) posed points.
- `weights`: (T, N) quardratic error term weights for each point at each frame
- `offsets`: (S + 1,) segment offsets. Points in each segment belong to the same rigid / affine body.
- `accum`: accumulated statistics from previous calls. If None, start fresh.
- `min_valid_size`: minimum number of valid points in each frame to consider the segment / group valid.
- `mode`: mode of transformation to apply. Can be 'rigid', 'similar', or 'affine'.
- For 'rigid', only rotation and translation are allowed.
- For 'similar', uniform scaling, rotation and translation are allowed.
- For 'affine', full affine transformation is allowed. Using least squares.
- `lam`: rigidity regularization weight for 'affine' mode.
- `niter`: number of iterations for 'affine' mode.
Returns
----
- `poses`: (T, S, 4, 4) transformations from canonical to each frame.
- `valid`: (T, S) boolean mask indicating valid segments
- `stats`: canonical statistics of each group,
It is a tuple of:
- `mu`: (S, 3) weighted mean of points
- `cov`: (S, 3, 3) weighted covariance of points
- `tot_w`: (S,) total weight of points
- `nnz`: (S,) number of non-zero weight points
- `canonical_points`: (N, 3) canonical points.
- `err`: (N,) per-point RMS error over all time := sqrt(sum_over_time(per_point_weights * per_point_squared_error) / per_point_nnz)
Use this to filter outliers as needed.
- `accum`: per point accumulated statistics. Just pass it to the next call for incremental solving.
It is a tuple of:
- `accum_sqrtw`: (N,) sum of sqrt(weights)
- `accum_sqrtwx`: (N, 3) sum of sqrt(weights) * x
- `accum_sqrtwxx`: (N, 3, 3) sum of sqrt(weights) * outer(x - mean_sqrtwx, x - mean_sqrtwx)
- `accum_w`: (N,) sum of weights
- `accum_wx`: (N, 3) sum of weights * x
- `accum_wxx`: (N, 3, 3) sum of weights * outer(x - mean_wx, x - mean_wx)
- `accum_nnz`: (N,) number of non-zero weight accumulations"""
utils3d.numpy.pose.segment_solve_poses_sequential
@overload
def segment_roll(data: numpy_.ndarray, offsets: numpy_.ndarray, shift: int, axis: int = 0) -> numpy_.ndarray:
"""Roll the data within each segment.
Parameters
------
- `data`: (ndarray).
- `offsets`: (ndarray) shape `(M + 1,)` the offsets of the segmented data. `M` is the number of segments. Starts with 0 and end with `data.shape[axis]`.
- `shift`: (int) the number of places by which elements are shifted. If negative, shift to left.
- `axis`: (int) the segment axis to roll along. Default is 0.
Returns
-------
- `data`: (ndarray) the rolled data, same shape as input."""
utils3d.numpy.segment_ops.segment_roll
@overload
def segment_take(data: numpy_.ndarray, offsets: numpy_.ndarray, taking: numpy_.ndarray, axis: int = 0) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
"""Take some segments from a segmented array
Parameters
------
- `data`: (ndarray) the segmented data.
- `offsets`: (ndarray) shape `(M + 1,)` the offsets of the segmented data. `M` is the number of segments. Starts with 0 and end with `data.shape[axis]`.
- `taking`: (ndarray) the indices of segments to take of shape `(K,)`, or boolean mask of shape `(M,)`
- `axis`: (int) the segment axis to take along. Default is 0. Other axes are treated as batch dimensions.
Returns
-------
- `new_data`: (ndarray) the new segmented data.
- `new_offsets`: (ndarray) shape `(K + 1,)` the offsets of the new segmented data. `K` is the number of taken segments."""
utils3d.numpy.segment_ops.segment_take
@overload
def segment_argmax(data: numpy_.ndarray, offsets: numpy_.ndarray, axis: int = 0) -> numpy_.ndarray:
"""Compute the argmax of each segment in the segmented data.
Parameters
-----
- `data`: (ndarray). shape `(..., N, ...)`. `N` is the segment dimension. If `data` may have multiple dimensionsm, extra dimensions are treated as batch dimensions.
- `offsets`: (ndarray) shape `(M + 1,)` the offsets of the segmented data
- `axis`: (int) the segment axis to compute along. Default is 0.
Returns
-------
- `argmax_indices`: (ndarray) shape `(..., M, ...)` the argmax indices of each segment along the first dimension.
Notes
-----
If there are multiple maximum values in a segment, the index of the first one is returned. If a segment is empty, -1 is returned."""
utils3d.numpy.segment_ops.segment_argmax
@overload
def segment_argmin(data: numpy_.ndarray, offsets: numpy_.ndarray, axis: int = 0) -> numpy_.ndarray:
"""Compute the argmin of each segment in the segmented data.
Parameters
-----
- `data`: (ndarray) shape `(..., N, ...)` the data to compute argmin from. If `data` may have multiple dimensionsm, extra dimensions are treated as batch dimensions.
- `offsets`: (ndarray) shape `(M + 1,)` the offsets of the segmented data
- `axis`: (int) the segment axis to compute along. Default is 0.
Returns
-----
- `argmin_indices`: (ndarray) shape `(..., M, ...)` the argmin indices of each segment along the first dimension.
Notes
-----
If there are multiple minimum values in a segment, the index of the first one is returned. If a segment is empty, -1 is returned."""
utils3d.numpy.segment_ops.segment_argmin
@overload
def segment_concatenate(segments: Sequence[Tuple[numpy_.ndarray, numpy_.ndarray]], axis: int = 0) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
"""Concatenate segmented arrays within each segment. All numbers of segments remain the same.
Parameters
------
- `segments`: (Sequence[Tuple[ndarray, ndarray]]) A sequence of segmented arrays:
- `data`: (ndarray) shape `(..., N_i, ...)`
- `offsets`: (ndarray) shape `(M + 1,)` segment offsets.
- `axis`: (int) the segment axis.
Returns
-------
- `data`: (ndarray) shape `(..., sum(N_i), ...)` the concatenated data
- `offsets`: (ndarray) shape `(M + 1,)` the offsets of the concatenated segmented data."""
utils3d.numpy.segment_ops.segment_concatenate
@overload
def segment_concat(segments: Sequence[Tuple[numpy_.ndarray, numpy_.ndarray]], axis: int = 0) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
"""(Alias for segment_concatenate).
Concatenate segmented arrays within each segment.
Parameters
------
- `segments`: (Sequence[Tuple[ndarray, ndarray]]) A sequence of segmented arrays:
- `data`: (ndarray) shape `(..., N_i, ...)`
- `offsets`: (ndarray) shape `(M + 1,)` segment offsets.
- `axis`: (int) the segment axis.
Returns
-------
- `data`: (ndarray) shape `(N, *data_dims)` the concatenated data
- `offsets`: (ndarray) shape `(M + 1,)` the offsets of the concatenated segmented data."""
utils3d.numpy.segment_ops.segment_concat
@overload
def segment_chain(segments: Sequence[Tuple[numpy_.ndarray, numpy_.ndarray]], axis: int = 0) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
"""Concatenate segmented arrays in sequence. The number of segments are summed.
Parameters
------
- `segments`: (Sequence[Tuple[ndarray, ndarray]]) A sequence of segmente arrays:
- `data`: (ndarray) shape `(..., N_i, ...)`
- `offsets`: (ndarray) shape `(M + 1,)` segment offsets.
- `axis`: (int) the segment axis.
Returns
-------
- `data`: (ndarray) shape `(..., sum(N_i), ...)` the chain-concatenated data
- `offsets`: (ndarray) shape `(sum(M_i) + 1,)` the offsets of the concatenated segmented data."""
utils3d.numpy.segment_ops.segment_chain
@overload
def group_as_segments(labels: numpy_.ndarray, data: Optional[numpy_.ndarray] = None, return_inverse: bool = False, return_group_ids: bool = False) -> Tuple[numpy_.ndarray, numpy_.ndarray, numpy_.ndarray]:
"""Group as segments by labels
Parameters
-----
- `labels` (ndarray): shape `(N, *label_dims)` array of labels for each data point. Labels can be multi-dimensional.
- `data` (ndarray, optional): shape `(N, *data_dims)` array.
If None, return the indices in each group instead.
Returns
-------
Assuming there are `M` difference labels:
- `segment_labels`: `(ndarray)` shape `(M, *label_dims)` labels of of each segment
- `rearranged_data`: `(ndarray)` shape `(N,)` or `(N, *data_dims)` the rearranged data (or indices) where the same labels are grouped as a continous segment.
- `offsets`: `(ndarray)` shape `(M + 1,)`
`rearranged_data[offsets[i]:offsets[i + 1]]` corresponding to the i-th segment whose label is `segment_labels[i]`"""
utils3d.numpy.segment_ops.group_as_segments
@overload
def triangulate_mesh(faces: numpy_.ndarray, vertices: numpy_.ndarray = None, method: Literal['fan', 'strip', 'diagonal'] = 'fan', return_face_indices: bool = False) -> numpy_.ndarray:
"""Triangulate a polygonal mesh.
## Parameters
faces (ndarray): [L, P] polygonal faces
vertices (ndarray, optional): [N, 3] 3-dimensional vertices.
If given, the triangulation is performed according to the distance
between vertices. Defaults to None.
method (str, optional): triangulation method. Defaults to 'fan'.
- 'fan': connect the first vertex to all other vertex pairs
- 'strip': create a triangle strip
- 'diagonal': for quad faces only, split according to the shorter diagonal
return_face_indices (bool, optional): whether to return the original face indices for each triangle. Defaults to False.
## Returns
(ndarray): [L * (P - 2), 3] triangular faces"""
utils3d.numpy.mesh.triangulate_mesh
@overload
def compute_face_corner_angles(vertices: numpy_.ndarray, faces: Optional[numpy_.ndarray] = None) -> numpy_.ndarray:
"""Compute face corner angles of a mesh
## Parameters
- `vertices` (ndarray): `(..., N, 3)` vertices if `faces` is provided, or `(..., F, P, 3)` if `faces` is None
- `faces` (ndarray, optional): `(F, P)` face vertex indices, where P is the number of vertices per face
## Returns
- `angles` (ndarray): `(..., F, P)` face corner angles"""
utils3d.numpy.mesh.compute_face_corner_angles
@overload
def compute_face_corner_normals(vertices: numpy_.ndarray, faces: Optional[numpy_.ndarray] = None, normalize: bool = True) -> numpy_.ndarray:
"""Compute the face corner normals of a mesh
## Parameters
- `vertices` (ndarray): `(..., N, 3)` vertices if `faces` is provided, or `(..., F, P, 3)` if `faces` is None
- `faces` (ndarray, optional): `(F, P)` face vertex indices, where P is the number of vertices per face
- `normalize` (bool): whether to normalize the normals to unit vectors. If not, the normals are the raw cross products.
## Returns
- `normals` (ndarray): (..., F, P, 3) face corner normals"""
utils3d.numpy.mesh.compute_face_corner_normals
@overload
def compute_face_corner_tangents(vertices: numpy_.ndarray, uv: numpy_.ndarray, faces_vertices: Optional[numpy_.ndarray] = None, faces_uv: Optional[numpy_.ndarray] = None, normalize: bool = True) -> numpy_.ndarray:
"""Compute the face corner tangent (and bitangent) vectors of a mesh
## Parameters
- `vertices` (ndarray): `(..., N, 3)` if `faces` is provided, or `(..., F, P, 3)` if `faces_vertices` is None
- `uv` (ndarray): `(..., N, 2)` if `faces` is provided, or `(..., F, P, 2)` if `faces_uv` is None
- `faces_vertices` (ndarray, optional): `(F, P)` face vertex indices
- `faces_uv` (ndarray, optional): `(F, P)` face UV indices
- `normalize` (bool): whether to normalize the tangents to unit vectors. If not, the tangents (dX/du, dX/dv) matches the UV parameterized manifold.
## Returns
- `tangents` (ndarray): `(..., F, P, 3, 2)` face corner tangents (and bitangents),
where the last dimension represents the tangent and bitangent vectors."""
utils3d.numpy.mesh.compute_face_corner_tangents
@overload
def compute_face_normals(vertices: numpy_.ndarray, faces: Optional[numpy_.ndarray] = None) -> numpy_.ndarray:
"""Compute face normals of a mesh
## Parameters
- `vertices` (ndarray): `(..., N, 3)` vertices if `faces` is provided, or `(..., F, P, 3)` if `faces` is None
- `faces` (ndarray, optional): `(F, P)` face vertex indices, where P is the number of vertices per face
## Returns
- `normals` (ndarray): `(..., F, 3)` face normals. Always normalized."""
utils3d.numpy.mesh.compute_face_normals
@overload
def compute_face_tangents(vertices: numpy_.ndarray, uv: numpy_.ndarray, faces_vertices: Optional[numpy_.ndarray] = None, faces_uv: Optional[numpy_.ndarray] = None, normalize: bool = True) -> numpy_.ndarray:
"""Compute the face corner tangent (and bitangent) vectors of a mesh
## Parameters
- `vertices` (ndarray): `(..., N, 3)` if `faces` is provided, or `(..., F, P, 3)` if `faces_vertices` is None
- `uv` (ndarray): `(..., N, 2)` if `faces` is provided, or `(..., F, P, 2)` if `faces_uv` is None
- `faces_vertices` (ndarray, optional): `(F, P)` face vertex indices
- `faces_uv` (ndarray, optional): `(F, P)` face UV indices
## Returns
- `tangents` (ndarray): `(..., F, 3, 2)` face corner tangents (and bitangents),
where the last dimension represents the tangent and bitangent vectors."""
utils3d.numpy.mesh.compute_face_tangents
@overload
def compute_vertex_normals(vertices: numpy_.ndarray, faces: numpy_.ndarray, weighted: Literal['uniform', 'area', 'angle'] = 'uniform') -> numpy_.ndarray:
"""Compute vertex normals of a triangular mesh by averaging neighboring face normals
## Parameters
vertices (ndarray): [..., N, 3] 3-dimensional vertices
faces (ndarray): [T, P] face vertex indices, where P is the number of vertices per face
## Returns
normals (ndarray): [..., N, 3] vertex normals (already normalized to unit vectors)"""
utils3d.numpy.mesh.compute_vertex_normals
@overload
def remove_corrupted_faces(faces: numpy_.ndarray) -> numpy_.ndarray:
"""Remove corrupted faces (faces with duplicated vertices)
## Parameters
faces (ndarray): [T, 3] triangular face indices
## Returns
ndarray: [T_, 3] triangular face indices"""
utils3d.numpy.mesh.remove_corrupted_faces
@overload
def merge_duplicate_vertices(vertices: numpy_.ndarray, faces: numpy_.ndarray, tol: float = 1e-06) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
"""Merge duplicate vertices of a triangular mesh.
Duplicate vertices are merged by selecte one of them, and the face indices are updated accordingly.
## Parameters
vertices (ndarray): [N, 3] 3-dimensional vertices
faces (ndarray): [T, 3] triangular face indices
tol (float, optional): tolerance for merging. Defaults to 1e-6.
## Returns
vertices (ndarray): [N_, 3] 3-dimensional vertices
faces (ndarray): [T, 3] triangular face indices"""
utils3d.numpy.mesh.merge_duplicate_vertices
@overload
def remove_unused_vertices(faces: numpy_.ndarray, *vertice_attrs, return_indices: bool = False) -> Tuple[numpy_.ndarray, ...]:
"""Remove unreferenced vertices of a mesh.
Unreferenced vertices are removed, and the face indices are updated accordingly.
## Parameters
faces (ndarray): [T, P] face indices
*vertice_attrs: vertex attributes
## Returns
faces (ndarray): [T, P] face indices
*vertice_attrs: vertex attributes
indices (ndarray, optional): [N] indices of vertices that are kept. Defaults to None."""
utils3d.numpy.mesh.remove_unused_vertices
@overload
def subdivide_mesh(vertices: numpy_.ndarray, faces: numpy_.ndarray, level: int = 1) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
"""Subdivide a triangular mesh by splitting each triangle into 4 smaller triangles.
NOTE: All original vertices are kept, and new vertices are appended to the end of the vertex list.
## Parameters
vertices (ndarray): [N, 3] 3-dimensional vertices
faces (ndarray): [T, 3] triangular face indices
level (int, optional): level of subdivisions. Defaults to 1.
## Returns
vertices (ndarray): [N_, 3] subdivided 3-dimensional vertices
faces (ndarray): [(4 ** level) * T, 3] subdivided triangular face indices"""
utils3d.numpy.mesh.subdivide_mesh
@overload
def mesh_edges(faces: Union[numpy_.ndarray, Tuple[numpy_.ndarray, numpy_.ndarray], ForwardRef('csr_array')], return_face2edge: bool = False, return_edge2face: bool = False, return_counts: bool = False) -> Tuple[numpy_.ndarray, Union[numpy_.ndarray, ForwardRef('csr_array')], ForwardRef('csr_array'), ForwardRef('ndarray')]:
"""Get undirected edges of a mesh. Optionally return additional mappings.
## Parameters
- `faces` (ndarray): polygon faces, which can be in 3 formats:
- Regular mesh in regular array: `(F, P)`, where each face has `P` vertices.
- Irregular mesh in segmented array: tuple of `(vertex_indices, offsets)`, where vertex_indices[offsets[i]:offsets[i+1]] are the vertex indices of face i.
- Irregular mesh in CSR array: `(F, V)` binary CSR array of indices, each row corresponds to the vertices of a face.
(Note that segmented array is almost equivalent to csr array: `vertex_indices` ~ `faces.indices`, `offsets` ~ `faces.indptr`.)
- `return_face2edge` (bool): whether to return the face to edge mapping
- `return_edge2face` (bool): whether to return the edge to face mapping
- `return_counts` (bool): whether to return the counts of edges
## Returns
- `edges` (ndarray): `(E, 2)` unique edges' vertex indices
If `return_face2edge`, `return_edge2face`, `return_opposite_edge`, or `return_counts` is True, the corresponding outputs will be appended in order:
- `face2edge` (ndarray | csr_array): mapping from faces to the indices of edges
- `(F, P)` if input `faces` is a dense array
- `(F, E)` if input `faces` is segmented array
- `edge2face` (csr_array): `(E, F)` binary sparse CSR matrix of edge to face.
- `counts` (ndarray): `(E,)` counts of each edge"""
utils3d.numpy.mesh.mesh_edges
@overload
def mesh_half_edges(faces: Union[numpy_.ndarray, Tuple[numpy_.ndarray, numpy_.ndarray], ForwardRef('csr_array')], return_face2edge: bool = False, return_edge2face: bool = False, return_twin: bool = False, return_next: bool = False, return_prev: bool = False, return_counts: bool = False) -> Tuple[numpy_.ndarray, Union[numpy_.ndarray, ForwardRef('csr_array')], ForwardRef('csr_array'), numpy_.ndarray, numpy_.ndarray, numpy_.ndarray, numpy_.ndarray]:
"""Get half edges of a mesh. Optionally return additional mappings.
## Parameters
- `faces` (ndarray): polygon faces, which can be in 3 formats:
- `faces` (ndarray): polygon faces, which can be in 3 formats:
- Regular mesh in regular array: `(F, P)`, where each face has `P` vertices.
- Irregular mesh in segmented array: tuple of `(vertex_indices, offsets)`, where vertex_indices[offsets[i]:offsets[i+1]] are the vertex indices of face i.
- Irregular mesh in CSR array: `(F, V)` binary CSR array of indices, each row corresponds to the vertices of a face.
(Note that segmented array is almost equivalent to csr array: `vertex_indices` ~ `faces.indices`, `offsets` ~ `faces.indptr`.)
- `return_face2edge` (bool): whether to return the face to edge mapping
- `return_edge2face` (bool): whether to return the edge to face mapping
- `return_twin` (bool): whether to return the mapping from one edge to its opposite/twin edge
- `return_next` (bool): whether to return the mapping from one edge to its next edge in the face loop
- `return_prev` (bool): whether to return the mapping from one edge to its previous edge in the face loop
- `return_counts` (bool): whether to return the counts of edges
## Returns
- `edges` (ndarray): `(E, 2)` unique edges' vertex indices
If `return_face2edge`, `return_edge2face`, `return_opposite_edge`, or `return_counts` is True, the corresponding outputs will be appended in order:
- `face2edge` (ndarray | csr_array): mapping from faces to the indices of edges
- `(F, P)` if input `faces` is a dense array
- `(F, E)` if input `faces` is a sparse csr array
- `edge2face` (csr_array): `(E, F)` binary sparse CSR matrix of edge to face.
- `twin` (ndarray): `(E,)` mapping from edges to indices of opposite edges. -1 if not found.
- `next` (ndarray): `(E,)` mapping from edges to indices of next edges in the face loop.
- `prev` (ndarray): `(E,)` mapping from edges to indices of previous edges in the face loop.
- `counts` (ndarray): `(E,)` counts of each half edge
NOTE: If the mesh is not manifold, `twin`, `next`, and `prev` can point to arbitrary one of the candidates."""
utils3d.numpy.mesh.mesh_half_edges
@overload
def mesh_connected_components(faces: Union[numpy_.ndarray, Tuple[numpy_.ndarray, numpy_.ndarray], ForwardRef('csr_array'), NoneType] = None, num_vertices: Optional[int] = None) -> Union[numpy_.ndarray, Tuple[numpy_.ndarray, numpy_.ndarray]]:
"""Compute connected faces of a mesh.
## Parameters
- `faces` (ndarray): polygon faces, which can be in 3 formats:
- Regular mesh in regular array: `(F, P)`, where each face has `P` vertices.
- Irregular mesh in segmented array: tuple of `(vertex_indices, offsets)`, where vertex_indices[offsets[i]:offsets[i+1]] are the vertex indices of face i.
- Irregular mesh in CSR array: `(F, V)` binary CSR array of indices, each row corresponds to the vertices of a face.
(Note that segmented array is almost equivalent to csr array: `vertex_indices` ~ `faces.indices`, `offsets` ~ `faces.indptr`.)
- `num_vertices` (int, optional): total number of vertices. If not given, only presented vertices in `faces` are considered.
## Returns
If `num_vertices` is given, return:
- `labels` (ndarray): (N,) component labels of each vertex
If `num_vertices` is None, return:
- `vertices_ids` (ndarray): (N,) vertex indices that are in the edges
- `labels` (ndarray): (N,) int32 component labels corresponding to `vertices_ids`"""
utils3d.numpy.mesh.mesh_connected_components
@overload
def graph_connected_components(edges: numpy_.ndarray, num_vertices: Optional[int] = None) -> Union[numpy_.ndarray, Tuple[numpy_.ndarray, numpy_.ndarray]]:
"""Compute connected components of an undirected graph.
Using scipy.sparse.csgraph.connected_components as backend.
## Parameters
- `edges` (ndarray): (E, 2) edge indices
## Returns
If `num_vertices` is given, return:
- `labels` (ndarray): (N,) component labels of each vertex
If `num_vertices` is None, return:
- `vertices_ids` (ndarray): (N,) vertex indices that are in the edges
- `labels` (ndarray): (N,) int32 component labels corresponding to `vertices_ids`"""
utils3d.numpy.mesh.graph_connected_components
@overload
def mesh_adjacency_graph(adjacency: Literal['vertex2edge', 'vertex2face', 'edge2vertex', 'edge2face', 'face2edge', 'face2vertex', 'vertex2edge2vertex', 'vertex2face2vertex', 'edge2vertex2edge', 'edge2face2edge', 'face2edge2face', 'face2vertex2face'], faces: Union[numpy_.ndarray, Tuple[numpy_.ndarray, numpy_.ndarray], ForwardRef('csr_array'), NoneType] = None, edges: Optional[numpy_.ndarray] = None, num_vertices: Optional[int] = None, self_loop: bool = False) -> 'csr_array':
"""Get adjacency graph of a mesh.
## Parameters
- `adjacency` (str): type of adjacency graph. Options:
- `'vertex2edge'`: vertex to adjacent edges. Returns (V, E) csr
- `'vertex2face'`: vertex to adjacent faces. Returns (V, F) csr
- `'edge2vertex'`: edge to adjacent vertices. Returns (E, V) csr
- `'edge2face'`: edge to its adjacent faces. Returns (E, F) csr
- `'face2edge'`: face to its adjacent edges. Returns (F, E) csr
- `'face2vertex'`: face to its adjacent vertices. Returns (F, V) csr
- `'vertex2edge2vertex'`: vertex to adjacent vertices if they share an edge. Returns (V, V) csr
- `'vertex2face2vertex'`: vertex to adjacent vertices if they share a face. Returns (V, V) csr
- `'edge2vertex2edge'`: edge to adjacent edges if they share a vertex. Returns (E, E) csr
- `'edge2face2edge'`: edge to adjacent edges if they share a face. Returns (E, E) csr
- `'face2edge2face'`: face to adjacent faces if they share an edge. Returns (F, F) csr
- `'face2vertex2face'`: face to adjacent faces if they share a vertex. Returns (F, F) csr
- `faces` (ndarray): polygon faces
- `(F, P)` dense array of indices, where each face has `P` vertices.
- `(F, V)` binary sparse csr array of indices, each row corresponds to the vertices of a face.
- `edges` (ndarray, optional): (E, 2) edge indices. NOTE: assumed to be undirected edges.
- `num_vertices` (int, optional): total number of vertices.
- `self_loop` (bool): whether to include self-loops in the adjacency graph. Defaults to False.
## Returns
- `graph` (csr_array): adjacency graph in csr format"""
utils3d.numpy.mesh.mesh_adjacency_graph
@overload
def flatten_mesh_indices(*args: numpy_.ndarray) -> Tuple[numpy_.ndarray, ...]:
utils3d.numpy.mesh.flatten_mesh_indices
@overload
def create_cube_mesh(tri: bool = False) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
"""Create a cube mesh of size 1 centered at origin.
### Parameters
tri (bool, optional): return triangulated mesh. Defaults to False, which returns quad mesh.
### Returns
vertices (ndarray): shape (8, 3)
faces (ndarray): shape (12, 3)"""
utils3d.numpy.mesh.create_cube_mesh
@overload
def create_icosahedron_mesh():
"""Create an icosahedron mesh of centered at origin."""
utils3d.numpy.mesh.create_icosahedron_mesh
@overload
def create_square_mesh(tri: bool = False) -> Tuple[numpy_.ndarray, numpy_.ndarray]:
"""Create a square mesh of area 1 centered at origin in the xy-plane.
## Returns
vertices (ndarray): shape (4, 3)
faces (ndarray): shape (1, 4)"""
utils3d.numpy.mesh.create_square_mesh
@overload
def create_camera_frustum_mesh(extrinsics: numpy_.ndarray, intrinsics: numpy_.ndarray, depth: float = 1.0) -> Tuple[numpy_.ndarray, numpy_.ndarray, numpy_.ndarray]:
"""Create a triangle mesh of camera frustum."""
utils3d.numpy.mesh.create_camera_frustum_mesh
@overload
def merge_meshes(meshes: List[Tuple[numpy_.ndarray, ...]]) -> Tuple[numpy_.ndarray, ...]:
"""Merge multiple meshes into one mesh. Vertices will be no longer shared.
## Parameters
- `meshes`: a list of tuple (faces, vertices_attr1, vertices_attr2, ....)
## Returns
- `faces`: [sum(T_i), P] merged face indices, contigous from 0 to sum(T_i) * P - 1
- `*vertice_attrs`: [sum(T_i) * P, ...] merged vertex attributes, where every P values correspond to a face"""
utils3d.numpy.mesh.merge_meshes
@overload
def uv_map(*size: Union[int, Tuple[int, int]], top: float = 0.0, left: float = 0.0, bottom: float = 1.0, right: float = 1.0, dtype: numpy_.dtype = numpy_.float32) -> numpy_.ndarray:
"""Get image UV space coordinate map, where (0., 0.) is the top-left corner of the image, and (1., 1.) is the bottom-right corner of the image.
This is commonly used as normalized image coordinates in texture mapping (when image is not flipped vertically).
## Parameters
- `*size`: `Tuple[int, int]` or two integers of map size `(height, width)`
- `top`: `float`, optional top boundary in uv space. Defaults to 0.
- `left`: `float`, optional left boundary in uv space. Defaults to 0.
- `bottom`: `float`, optional bottom boundary in uv space. Defaults to 1.
- `right`: `float`, optional right boundary in uv space. Defaults to 1.
- `dtype`: `np.dtype`, optional data type of the output uv map. Defaults to np.float32.
## Returns
- `uv (ndarray)`: shape `(height, width, 2)`
## Example Usage
>>> uv_map(10, 10):
[[[0.05, 0.05], [0.15, 0.05], ..., [0.95, 0.05]],
[[0.05, 0.15], [0.15, 0.15], ..., [0.95, 0.15]],
... ... ...
[[0.05, 0.95], [0.15, 0.95], ..., [0.95, 0.95]]]"""
utils3d.numpy.maps.uv_map
@overload
def pixel_coord_map(*size: Union[int, Tuple[int, int]], top: int = 0, left: int = 0, convention: Literal['integer-center', 'integer-corner'] = 'integer-center', dtype: numpy_.dtype = numpy_.float32) -> numpy_.ndarray:
"""Get image pixel coordinates map, where (0, 0) is the top-left corner of the top-left pixel, and (width, height) is the bottom-right corner of the bottom-right pixel.
## Parameters
- `*size`: `Tuple[int, int]` or two integers of map size `(height, width)`
- `top`: `int`, optional top boundary of the pixel coord map. Defaults to 0.
- `left`: `int`, optional left boundary of the pixel coord map. Defaults to 0.
- `convention`: `str`, optional `'integer-center'` or `'integer-corner'`, whether integer coordinates correspond to pixel centers or corners. Defaults to 'integer-center'.
- `'integer-center'`: `pixel[i][j]` has integer coordinates `(j, i)` as its center, and occupies square area `[j - 0.5, j + 0.5) × [i - 0.5, i + 0.5)`.
The top-left corner of the top-left pixel is `(-0.5, -0.5)`, and the bottom-right corner of the bottom-right pixel is `(width - 0.5, height - 0.5)`.
- `'integer-corner'`: `pixel[i][j]` has coordinates `(j + 0.5, i + 0.5)` as its center, and occupies square area `[j, j + 1) × [i, i + 1)`.
The top-left corner of the top-left pixel is `(0, 0)`, and the bottom-right corner of the bottom-right pixel is `(width, height)`.
- `dtype`: `np.dtype`, optional data type of the output pixel coord map. Defaults to np.float32.
## Returns
ndarray: shape (height, width, 2)
>>> pixel_coord_map(10, 10, convention='integer-center', dtype=int):
[[[0, 0], [1, 0], ..., [9, 0]],
[[0, 1], [1, 1], ..., [9, 1]],
... ... ...
[[0, 9], [1, 9], ..., [9, 9]]]
>>> pixel_coord_map(10, 10, convention='integer-corner', dtype=np.float32):
[[[0.5, 0.5], [1.5, 0.5], ..., [9.5, 0.5]],
[[0.5, 1.5], [1.5, 1.5], ..., [9.5, 1.5]],
... ... ...
[[0.5, 9.5], [1.5, 9.5], ..., [9.5, 9.5]]]"""
utils3d.numpy.maps.pixel_coord_map
@overload
def screen_coord_map(*size: Union[int, Tuple[int, int]], top: float = 1.0, left: float = 0.0, bottom: float = 0.0, right: float = 1.0, dtype: numpy_.dtype = numpy_.float32) -> numpy_.ndarray:
"""Get screen space coordinate map, where (0., 0.) is the bottom-left corner of the image, and (1., 1.) is the top-right corner of the image.
This is commonly used in graphics APIs like OpenGL.
## Parameters
- `*size`: `Tuple[int, int]` or two integers of map size `(height, width)`
- `top`: `float`, optional top boundary in the screen space. Defaults to 1.
- `left`: `float`, optional left boundary in the screen space. Defaults to 0.
- `bottom`: `float`, optional bottom boundary in the screen space. Defaults to 0.
- `right`: `float`, optional right boundary in the screen space. Defaults to 1.
- `dtype`: `np.dtype`, optional data type of the output map. Defaults to np.float32.
## Returns
(ndarray): shape (height, width, 2)"""
utils3d.numpy.maps.screen_coord_map
@overload
def build_grid_mesh(height: int, width: int, *, shared_vertices: bool = True) -> numpy_.ndarray:
"""Get mesh of `height * width` faces arranged in a 2D grid.
Parameters
----
height (int): height of the grid
width (int): width of the grid
shared_vertices (bool, optional): whether the vertices are shared among faces. Defaults to True.
Returns
----
faces (ndarray): faces in shape (height, width, 4).
- If shared_vertices is `True`, the vertex indices are arranged from 0 to `(H + 1) * (W + 1) - 1` like
```
0 ----------- 1 --- ... -------- W-1 --------------- W
| (0,0) | (0,1) | (0,W-1) |
W+1 ------- W+2 --- ... -------- 2*W --------------- 2*W+1
| (1,0) | (1,1) | ... |
...
| (H-1,0) | (H-1,1) | (H-1,W-1) |
H*(W+1) ----- H*(W+1)+1 --- ... --- (H+1)*(W+1)-2 ----- (H+1)*(W+1)-1
```
- If shared_vertices is `False`, each face has its own 4 vertices.
The vertex indices are arranged from 0 to `H * W * 4 - 1`, like
```
0 ------- 3 4 ------- 7 ... (W-1)*4 ---- (W-1)*4+3
| (0,0) | | (0,1) | | (0,W-1) |
1 ------- 2 5 ------- 6 ... (W-1)*4+1 -- (W-1)*4+2
W*4 ----- W*4+3
| (1,0) | ....
W*4+1 --- W*4+2
...
(H-1)*W*4 ---- (H-1)*W*4+3 ... H*W*4 - 4 ----- H*W*4 - 1
| (H-1,0) | | (H-1,W-1) |
(H-1)*W*4+1 -- (H-1)*W*4+2 ... H*W*4 - 3 ------ H*W*4 - 2
```"""
utils3d.numpy.maps.build_grid_mesh
@overload
def build_mesh_from_map(*maps: numpy_.ndarray, mask: Optional[numpy_.ndarray] = None, domain: Literal['vertex', 'face'] = 'vertex', tri: bool = False) -> Tuple[numpy_.ndarray, ...]:
"""Get a mesh regarding image pixel uv coordinates as vertices and image grid as faces.
## Parameters
*maps (ndarray): attribute maps in shape (height, width, [channels])
mask (ndarray, optional): binary mask of shape (height, width), dtype=bool. Defaults to None.
domain (Literal['vertex', 'face'], optional): whether the pixel attributes correspond to vertices or faces. Defaults to 'vertex'.
tri (bool, optional): whether to triangulate the mesh. Defaults to False.
## Returns
faces (ndarray): faces connecting neighboring pixels. shape (T, 4) if tri is False, else (T, 3)
*attributes (ndarray): vertex or face attributes in corresponding order with input maps"""
utils3d.numpy.maps.build_mesh_from_map
@overload
def build_mesh_from_depth_map(depth: numpy_.ndarray, *maps: numpy_.ndarray, intrinsics: numpy_.ndarray, extrinsics: Optional[numpy_.ndarray] = None, atol: Optional[float] = None, rtol: Optional[float] = None, domain: Literal['vertex', 'face'] = 'vertex', tri: bool = False) -> Tuple[numpy_.ndarray, ...]:
"""Get a mesh by lifting depth map to 3D, while removing depths of large depth difference.
## Parameters
depth (ndarray): [H, W] depth map
extrinsics (ndarray, optional): [4, 4] extrinsics matrix. Defaults to None.
intrinsics (ndarray, optional): [3, 3] intrinsics matrix. Defaults to None.
*maps (ndarray): [H, W, C] vertex attributes. Defaults to None.
atol (float, optional): absolute tolerance of difference. Defaults to None.
rtol (float, optional): relative tolerance of difference. Defaults to None.
triangles with vertices having depth difference larger than atol + rtol * depth will be marked.
domain (Literal['vertex', 'face'], optional): whether the pixel attributes correspond to vertices or faces. Defaults to 'vertex'.
tri (bool, optional): whether to triangulate the mesh. Defaults to False.
## Returns
faces (ndarray): [T, 3] faces
vertices (ndarray): [N, 3] vertices
*attributes (ndarray): [N, C] vertex attributes or [T, C] face attributes"""
utils3d.numpy.maps.build_mesh_from_depth_map
@overload
def depth_map_edge(depth: numpy_.ndarray, atol: Optional[float] = None, rtol: Optional[float] = None, ltol: Optional[float] = None, kernel_size: int = 3, mask: numpy_.ndarray = None) -> numpy_.ndarray:
"""Compute the edge mask from depth map. The edge is defined as the pixels whose neighbors have large difference in depth.
## Parameters
depth (ndarray): shape (..., height, width), linear depth map
atol (float): absolute tolerance
rtol (float): relative tolerance
ltol (float): relative tolerance of inverse depth laplacian
## Returns
edge (ndarray): shape (..., height, width) of dtype torch.bool"""
utils3d.numpy.maps.depth_map_edge
@overload
def depth_map_aliasing(depth: numpy_.ndarray, atol: float = None, rtol: float = None, kernel_size: int = 3, mask: numpy_.ndarray = None) -> numpy_.ndarray:
"""Compute the map that indicates the aliasing of x depth map, identifying pixels which neither close to the maximum nor the minimum of its neighbors.
## Parameters
depth (ndarray): shape (..., height, width), linear depth map
atol (float): absolute tolerance
rtol (float): relative tolerance
## Returns
edge (ndarray): shape (..., height, width) of dtype torch.bool"""
utils3d.numpy.maps.depth_map_aliasing
@overload
def normal_map_edge(normals: numpy_.ndarray, tol: float, kernel_size: int = 3, mask: numpy_.ndarray = None) -> numpy_.ndarray:
"""Compute the edge mask from normal map.
## Parameters
normal (ndarray): shape (..., height, width, 3), normal map
tol (float): tolerance in degrees
## Returns
edge (ndarray): shape (..., height, width) of dtype torch.bool"""
utils3d.numpy.maps.normal_map_edge
@overload
def point_map_to_normal_map(point: numpy_.ndarray, mask: numpy_.ndarray = None, edge_threshold: float = None) -> numpy_.ndarray:
"""Calculate normal map from point map. Value range is [-1, 1].
## Parameters
point (ndarray): shape (height, width, 3), point map
mask (optional, ndarray): shape (height, width), dtype=bool. Mask of valid depth pixels. Defaults to None.
edge_threshold (optional, float): threshold for the angle (in degrees) between the normal and the view direction. Defaults to None.
## Returns
normal (ndarray): shape (height, width, 3), normal map. """
utils3d.numpy.maps.point_map_to_normal_map
@overload
def depth_map_to_point_map(depth: numpy_.ndarray, intrinsics: numpy_.ndarray, extrinsics: numpy_.ndarray = None) -> numpy_.ndarray:
"""Unproject depth map to 3D points.
## Parameters
depth (ndarray): [..., H, W] depth value
intrinsics ( ndarray): [..., 3, 3] intrinsics matrix
extrinsics (optional, ndarray): [..., 4, 4] extrinsics matrix
## Returns
points (ndarray): [..., N, 3] 3d points"""
utils3d.numpy.maps.depth_map_to_point_map
@overload
def depth_map_to_normal_map(depth: numpy_.ndarray, intrinsics: numpy_.ndarray, mask: numpy_.ndarray = None, edge_threshold: float = None) -> numpy_.ndarray:
"""Calculate normal map from depth map. Value range is [-1, 1]. Normal direction in OpenCV identity camera's coordinate system.
## Parameters
depth (ndarray): shape (height, width), linear depth map
intrinsics (ndarray): shape (3, 3), intrinsics matrix
mask (optional, ndarray): shape (height, width), dtype=bool. Mask of valid depth pixels. Defaults to None.
edge_threshold (optional, float): threshold for the angle (in degrees) between the normal and the view direction. Defaults to None.
## Returns
normal (ndarray): shape (height, width, 3), normal map. """
utils3d.numpy.maps.depth_map_to_normal_map
@overload
def chessboard(*size: Union[int, Tuple[int, int]], grid_size: int, color_a: numpy_.ndarray, color_b: numpy_.ndarray) -> numpy_.ndarray:
"""Get a chessboard image
## Parameters
- `*size`: `Tuple[int, int]` or two integers of map size `(height, width)`
- `grid_size (int)`: size of chessboard grid
- `color_a (ndarray)`: color of the grid at the top-left corner
- `color_b (ndarray)`: color in complementary grid cells
## Returns
image (ndarray): shape (height, width, channels), chessboard image"""
utils3d.numpy.maps.chessboard
@overload
def masked_nearest_resize(*image: numpy_.ndarray, mask: numpy_.ndarray, size: Tuple[int, int], return_index: bool = False) -> Tuple[Unpack[Tuple[numpy_.ndarray, ...]], numpy_.ndarray, Tuple[numpy_.ndarray, ...]]:
"""Resize image(s) by nearest sampling with mask awareness. Suitable for sparse maps. 
- Downsampling: Assign the nearest valid pixel within the target pixel's receptive field.
- Upsampling: Assign the valid pixel to only the nearest pixel in the resized map.
### Parameters
- `*image`: Input image(s) of shape `(..., H, W, C)` or `(... , H, W)`
- You can pass multiple images to be resized at the same time for efficiency.
- `mask`: input mask of shape `(..., H, W)`, dtype=bool
- `size`: target size `(H', W')`
- `return_index`: whether to return the nearest neighbor indices in the original map for each pixel in the resized map.
Defaults to False.
### Returns
- `*resized_image`: resized image(s) of shape `(..., H', W', C)`. or `(..., H', W')`
- `resized_mask`: mask of the resized map of shape `(..., H', W')`
- `nearest_indices`: tuple of shape `(..., H', W')`. The nearest neighbor indices of the resized map of each dimension."""
utils3d.numpy.maps.masked_nearest_resize
@overload
def masked_area_resize(*image: numpy_.ndarray, mask: numpy_.ndarray, size: Tuple[int, int]) -> Tuple[Unpack[Tuple[numpy_.ndarray, ...]], numpy_.ndarray]:
"""Resize 2D map by area sampling with mask awareness.
### Parameters
- `*image`: Input image(s) of shape `(..., H, W, C)` or `(..., H, W)`
- You can pass multiple images to be resized at the same time for efficiency.
- `mask`: Input mask of shape `(..., H, W)`
- `size`: target image size `(H', W')`
### Returns
- `*resized_image`: resized image(s) of shape `(..., H', W', C)`. or `(..., H', W')`
- `resized_mask`: mask of the resized map of shape `(..., H', W')`"""
utils3d.numpy.maps.masked_area_resize
@overload
def colorize_depth_map(depth: numpy_.ndarray, mask: numpy_.ndarray = None, near: Optional[float] = None, far: Optional[float] = None, cmap: str = 'Spectral') -> numpy_.ndarray:
"""Colorize depth map for visualization.
## Parameters
- `depth` (ndarray): shape (..., H, W), linear depth map
- `mask` (ndarray, optional): shape (..., H, W), dtype=bool. Mask of valid depth pixels. Defaults to None.
- `near` (float, optional): near plane for depth normalization. If None, use the 0.1% quantile of valid depth values. Defaults to None.
- `far` (float, optional): far plane for depth normalization. If None, use the 99.9% quantile of valid depth values. Defaults to None.
- `cmap` (str, optional): colormap name in matplotlib. Defaults to 'Spectral'.
## Returns
- `colored` (ndarray): shape (..., H, W, 3), dtype=uint8, RGB [0, 255]"""
utils3d.numpy.maps.colorize_depth_map
@overload
def colorize_normal_map(normal: numpy_.ndarray, mask: numpy_.ndarray = None, flip_yz: bool = False, normalize: bool = True) -> numpy_.ndarray:
"""Colorize normal map for visualization. Value range is [-1, 1].
## Parameters
- `normal` (ndarray): shape (H, W, 3), normal
- `mask` (ndarray, optional): shape (H, W), dtype=bool. Mask of valid depth pixels. Defaults to None.
- `flip_yz` (bool, optional): whether to flip the y and z.
- This is useful when converting between OpenCV and OpenGL camera coordinate systems. Defaults to False.
- `normalize` (bool, optional): whether to normalize the normal vectors. Defaults to True.
## Returns
- `colored` (ndarray): shape (H, W, 3), dtype=uint8, RGB in [0, 255]"""
utils3d.numpy.maps.colorize_normal_map
@overload
def colorize_segmentation_map(segmentation: numpy_.ndarray, mask: Optional[numpy_.ndarray] = None, vdim: int = 0) -> numpy_.ndarray:
"""Colorize segmentation map for visualization. The same value will be assigned with the same color.
Parameters
----
- `segmentation` (ndarray): shape (..., H, W, [...]), segmentation map. The last `ndim` dimensions are treated as value channels.
- `mask` (ndarray, optional): shape (..., H, W), binary mask indicating valid regions. Defaults to None (all regions are valid).
- `vdim` (int, optional): number of dimensions to treat as value channels. Defaults to 0 (scalars)
Returns
----
- `colored` (ndarray): shape (..., H, W, 3), dtype=uint8, RGB in [0, 255]"""
utils3d.numpy.maps.colorize_segmentation_map
@overload
def colorize_probability_map(probability: numpy_.ndarray, mask: Optional[numpy_.ndarray] = None, cmap: str = 'viridis', alpha: float = 1.0, beta: float = 1.0):
"""Colorize probability map for visualization.
The remapping is:
`p' = p^alpha / (p^alpha + (1 - p)^beta)`
where larger `alpha` suppresses low-to-mid probabilities and larger `beta` suppresses high probabilities.
Parameters
-------
- `probability` (ndarray): shape (..., H, W), probability map with values in [0, 1].
- `mask` (ndarray, optional): shape (..., H, W), binary mask indicating valid regions. Defaults to None (all regions are valid).
- `cmap` (str, optional): colormap name in matplotlib. Defaults to 'viridis'.
- `alpha` (float, optional): exponent applied to `probability` in contrast remapping. Defaults to 1.0.
- `beta` (float, optional): exponent applied to `(1 - probability)` in contrast remapping. Defaults to 1.0.
Returns
------
- `colored` (ndarray): shape (..., H, W, 3), dtype=uint8, RGB in [0, 255].
Examples for tuning `alpha` and `beta`
------
| Parameters | Curve shape | Effect |
|---|---|---|
| `alpha=2.5, beta=2.5` | Steep S-shape | Separate "possible" and "impossible" around 0.5 |
| `alpha=0.3, beta=1.0` | Fast early rise, then gradual flattening | Emphasize tiny probabilities near zero |
| `alpha=1.0, beta=0.3` | Flat early, then sharp rise near the end | Emphasize subtle differences near certainty (close to 1) |
| `alpha=0.5, beta=0.5` | Hourglass-like (inverse-S) | Increase contrast near both extremes globally |"""
utils3d.numpy.maps.colorize_probability_map
@overload
def flood_fill(*image: numpy_.ndarray, mask: numpy_.ndarray, return_index: bool = False) -> numpy_.ndarray:
"""Flooding fill the holes in the image(s) according to the mask. 
Parameters
----
- `*image` (ndarray): shape (..., height, width, [C]), input image(s)
- `mask` (ndarray): shape (..., height, width), binary mask indicating valid regions
Returns
----
- `*filled_image` (ndarray): shape (..., height, width, [C]), flood filled map
- `filled_indices` (Tuple[ndarray, ...], optional): tuple of shape (..., height, width). The nearest neighbor indices of each pixel in the original map.
It satisfies `filled_image = image[filled_indices]`"""
utils3d.numpy.maps.flood_fill
@overload
def perlin_noise(x: numpy_.ndarray, seed: Optional[int] = None) -> numpy_.ndarray:
"""Generate Perlin noise for the given coordinates.
Parameters
----
- `x` (ndarray): shape (*batch_shape, N_1, ..., N_D, D), coordinates to sample Perlin.
If input ndim is more than D + 1, the leading dimensions are treated as batch dimensions. Instances in the batch have different noise patterns.
- `seed` (int, optional): random seed. The same seed will generate the same noise pattern(s). Defaults to None.
Returns
----
- `y` (ndarray): shape (*batch_shape, N_1, ..., N_D), Perlin noise value at the given coordinates and seed. Value range is approximately [-1, 1]"""
utils3d.numpy.maps.perlin_noise
@overload
def perlin_noise_map(size: Tuple[int, ...], frequency: Union[float, numpy_.ndarray], seed: Optional[int] = None, dtype: Optional[numpy_.dtype] = numpy_.float32) -> numpy_.ndarray:
"""Generate Perlin noise map.
Parameters
----
- `size` (Tuple[int, ...]): size of the noise map (..., H, W)
- `frequency` (float | ndarray): frequency relative to map's larger dimension max(H, W) of the Perlin noise.
Represents how many periods of noise fit in the larger dimension of the map.
- `seed` (int, optional): random seed. The same seed will generate the same noise pattern(s). Defaults to None.
Returns
----
- `noise_map` (ndarray): shape (..., H, W), Perlin noise map. Value range is approximately [-1, 1]"""
utils3d.numpy.maps.perlin_noise_map
@overload
def fractal_perlin_noise_map(size: Tuple[int, ...], base_frequency: Union[float, numpy_.ndarray], octaves: int = 4, lacunarity: float = 2.0, gain: float = 0.5, seed: Optional[int] = None, dtype: Optional[numpy_.dtype] = numpy_.float32) -> numpy_.ndarray:
"""Generate fractal Perlin noise map. 
Parameters
----
- `size` (Tuple[int, ...]): size of the noise map (..., H, W)
- `base_frequency` (float | ndarray): base frequency (relative to map's larger dimension max(H, W)) of the Perlin noise.
Represents how many periods of noise fit in the larger dimension of the map.
- `octaves` (int, optional): number of octaves. Defaults to 4.
- `lacunarity` (float, optional): frequency multiplier between octaves. Defaults to 2.0.
- `gain` (float, optional): amplitude multiplier between octaves. Defaults to 0.5.
- `seed` (int, optional): random seed. The same seed will generate the same noise pattern. Defaults to None.
Returns
----
- `noise_map` (ndarray): shape (..., H, W), fractal Perlin noise map. Value range is approximately [-1, 1]"""
utils3d.numpy.maps.fractal_perlin_noise_map
@overload
def RastContext(*args, **kwargs):
"""Context for numpy-side rasterization. Based on moderngl.
"""
utils3d.numpy.rasterization.RastContext
@overload
def rasterize_triangles(size: Tuple[int, int], *, vertices: numpy_.ndarray, attributes: Optional[numpy_.ndarray] = None, attributes_domain: Optional[Literal['vertex', 'face']] = 'vertex', faces: Optional[numpy_.ndarray] = None, view: numpy_.ndarray = None, projection: numpy_.ndarray = None, extrinsics: numpy_.ndarray = None, intrinsics: numpy_.ndarray = None, near: float = 0.01, far: float = inf, cull_backface: bool = False, return_depth: bool = False, return_interpolation: bool = False, background: Optional[Dict[str, numpy_.ndarray]] = None, ctx: Optional[utils3d.numpy.rasterization.RastContext] = None) -> Dict[str, numpy_.ndarray]:
"""Rasterize triangles.
Parameters
----
- `size` (Tuple[int, int]): (height, width) of the output image
- `vertices` (ndarray): (N, 3) or (T, 3, 3)
- `faces` (Optional[ndarray]): (T, 3) or None. If `None`, the vertices must be an array with shape (T, 3, 3)
- `attributes` (ndarray): (N, C), (T, 3, C) for vertex domain or (T, C) for face domain
- `attributes_domain` (Literal['vertex', 'face']): domain of the attributes
- `view` | `extrinsics` (ndarray): (4, 4) View matrix or extrinsics matrix. Provide either one of them.
- `projection` | `intrinsics` (ndarray): (4, 4) Projection matrix or (3, 3) Intrinsics matrix. Provide either one of them.
- `cull_backface` (bool): whether to cull backface
- `background` (Optional[Dict[str, ndarray]]): background to composite with. Contains the same keys as the return dictionary, each with shape matching the output.
- `ctx` (RastContext): rasterization context. Created by `RastContext()`. Default to the thread-local default context.
Returns
----
A dictionary containing
- `mask` (ndarray): (H, W) bool mask of valid pixels
if attributes is not None
- `image` (ndarray): (H, W, C) float32 rendered image corresponding to the input attributes
if return_depth is True
- `depth` (ndarray): (H, W) float32 camera space linear depth. Empty pixels are filled with inf.
if return_interpolation is True
- `interpolation_id` (ndarray): (H, W) int32 triangle ID map
- `interpolation_uv` (ndarray): (H, W, 2) float32 triangle UV (first two channels of barycentric coordinates)"""
utils3d.numpy.rasterization.rasterize_triangles
@overload
def rasterize_triangles_peeling(size: Tuple[int, int], *, vertices: numpy_.ndarray, attributes: numpy_.ndarray, attributes_domain: Literal['vertex', 'face'] = 'vertex', faces: Optional[numpy_.ndarray] = None, view: numpy_.ndarray = None, projection: numpy_.ndarray = None, extrinsics: numpy_.ndarray = None, intrinsics: numpy_.ndarray = None, near: float = 0.01, far: float = inf, cull_backface: bool = False, return_depth: bool = False, return_interpolation: bool = False, ctx: Optional[utils3d.numpy.rasterization.RastContext] = None) -> Iterator[Iterator[Dict[str, numpy_.ndarray]]]:
"""Rasterize triangles with depth peeling.
Parameters
----
- `size` (Tuple[int, int]): (height, width) of the output image
- `vertices` (ndarray): (N, 3) or (T, 3, 3)
- `faces` (Optional[ndarray]): (T, 3) or None. If `None`, the vertices must be an array with shape (T, 3, 3)
- `attributes` (ndarray): (N, C), (T, 3, C) for vertex domain or (T, C) for face domain
- `attributes_domain` (Literal['vertex', 'face']): domain of the attributes
- `view` | `extrinsics` (ndarray): (4, 4) View matrix or extrinsics matrix. Provide either one of them.
- `projection` | `intrinsics` (ndarray): (4, 4) Projection matrix or (3, 3) Intrinsics matrix. Provide either one of them.
- `near` (float): near clipping plane. Only used for intrinsics. Ignored if projection matrix is provided.
- `far` (float): far clipping plane. Only used for intrinsics. Ignored if projection matrix is provided.
- `cull_backface` (bool): whether to cull backfaces
- `ctx` (RastContext): rasterization context. Created by `RastContext()`. Default to the thread-local default context.
Returns
----
A generator that yields dictionaries for each peeling layer containing:
- `mask` (ndarray): (H, W) bool mask of valid pixels in this layer
if attributes is not None
- `image` (ndarray): (H, W, C) float32 rendered image corresponding to the input attributes
if return_depth is True
- `depth` (ndarray): (H, W) float32 camera space linear depth. Empty pixels are filled with inf.
if return_interpolation is True
- `interpolation_id` (ndarray): (H, W) int32 triangle ID map
- `interpolation_uv` (ndarray): (H, W, 2) float32 triangle UV (first two channels of barycentric coordinates)
The last layer yielded will be empty (no pixels covered), then the generator stops.
Example
----
```
for i, layer_output in enumerate(rasterize_triangles_peeling(
(512, 512),
vertices=vertices,
faces=faces,
attributes=attributes,
view=view,
projection=projection
)):
print(f"Layer {i}:")
for key, value in layer_output.items():
print(f" {key}: {value.shape}")
if i >= 4: # Stop after 5 layers at most
break
```"""
utils3d.numpy.rasterization.rasterize_triangles_peeling
@overload
def rasterize_lines(size: Tuple[int, int], *, vertices: numpy_.ndarray, attributes: Optional[numpy_.ndarray], attributes_domain: Literal['vertex', 'line'] = 'vertex', lines: numpy_.ndarray | None = None, view: Optional[numpy_.ndarray] = None, projection: Optional[numpy_.ndarray] = None, extrinsics: Optional[numpy_.ndarray] = None, intrinsics: Optional[numpy_.ndarray] = None, near: float = 0.01, far: float = inf, line_width: float = 1.0, return_depth: bool = False, return_interpolation: bool = False, background: Optional[Dict[str, numpy_.ndarray]] = None, ctx: Optional[utils3d.numpy.rasterization.RastContext] = None) -> Tuple[numpy_.ndarray, ...]:
"""Rasterize lines.
Parameters
----
- `size` (Tuple[int, int]): (height, width) of the output image
- `vertices` (ndarray): (N, 3) or (L, 2, 3)
- `attributes` (ndarray): (N, C), (T, 3, C) for vertex domain or (T, C) for face domain
- `attributes_domain` (Literal['vertex', 'face']): domain of the attributes
- `lines` (ndarray): (L, 2) int32 array of line vertex indices. If None, vertices shape must be (L, 2, 3) and will be interpreted as line segments directly.
- `view` | `extrinsics` (ndarray): (4, 4) View matrix or extrinsics matrix. Provide either one of them.
- `projection` | `intrinsics` (ndarray): (4, 4) Projection matrix or (3, 3) Intrinsics matrix. Provide either one of them.
- `near` (float): near clipping plane. Only used for intrinsics. Ignored if projection matrix is provided.
- `far` (float): far clipping plane. Only used for intrinsics. Ignored if projection matrix is provided.
- `background` (Optional[Dict[str, ndarray]]): background to composite with. Contains the same keys as the return dictionary, each with shape matching the output.
- `ctx` (RastContext): rasterization context. Created by `RastContext()`. Defaults to the current default context.
Returns
----
A dictionary containing
- `mask` (ndarray): (H, W) bool mask of valid pixels
if attributes is not None
- `image` (ndarray): (H, W, C) float32 rendered image corresponding to the input attributes
if return_depth is True
- `depth` (ndarray): (H, W) float32 camera space linear depth, ranging from 0 to 1.
if return_interpolation is True
- `interpolation_id` (ndarray): (H, W) int32 triangle ID map
- `interpolation_uv` (ndarray): (H, W, 2) float32 triangle UV (first two channels of barycentric coordinates)"""
utils3d.numpy.rasterization.rasterize_lines
@overload
def rasterize_point_cloud(size: Tuple[int, int], *, points: numpy_.ndarray, point_sizes: Union[float, numpy_.ndarray] = 10, point_size_in: Literal['2d', '3d'] = '2d', point_shape: Literal['triangle', 'square', 'pentagon', 'hexagon', 'circle'] = 'square', attributes: Optional[numpy_.ndarray] = None, view: numpy_.ndarray = None, projection: numpy_.ndarray = None, extrinsics: numpy_.ndarray = None, intrinsics: numpy_.ndarray = None, near: float = 0.01, far: float = inf, return_depth: bool = False, return_point_id: bool = False, background: Optional[Dict[str, numpy_.ndarray]] = None, ctx: Optional[utils3d.numpy.rasterization.RastContext] = None) -> Dict[str, numpy_.ndarray]:
"""Rasterize point cloud.
Parameters
----
- `size` (Tuple[int, int]): (height, width) of the output image
- `points` (ndarray): (N, 3)
- `point_sizes` (ndarray): (N,) or float
- `point_size_in`: Literal['2d', '3d'] = '2d'. Whether the point sizes are in 2D (size in pixels) or 3D (size in world units).
- `point_shape`: Literal['triangle', 'square', 'pentagon', 'hexagon', 'circle'] = 'square'. The visual shape of the points.
- `attributes` (ndarray): (N, C)
- `view` | `extrinsics` (ndarray): (4, 4) View matrix or extrinsics matrix. Provide either one of them.
- `projection` | `intrinsics` (ndarray): (4, 4) Projection matrix or (3, 3) Intrinsics matrix. Provide either one of them.
- `near` (float): near clipping plane. Only used for intrinsics. Ignored if projection matrix is provided.
- `far` (float): far clipping plane. Only used for intrinsics. Ignored if projection matrix is provided.
- `return_depth` (bool): whether to return depth map
- `return_point_id` (bool): whether to return point ID map
- `background` (Optional[Dict[str, ndarray]]): background to composite with. Contains the same keys as the return dictionary, each with shape matching the output.
- `ctx` (RastContext): rasterization context. Created by `RastContext()`. Defaults to the current default context.
Returns
----
A dictionary containing
if attributes is not None
- `image` (ndarray): (H, W, C) float32 rendered image corresponding to the input attributes
if return_depth is True
- `depth` (ndarray): (H, W) float32 camera space linear depth, ranging from 0 to 1.
if return_point_id is True
- `point_id` (ndarray): (H, W) int32 point ID map"""
utils3d.numpy.rasterization.rasterize_point_cloud
@overload
def sample_texture(uv_map: numpy_.ndarray, texture_map: numpy_.ndarray, interpolation: Literal['linear', 'nearest'] = 'linear', mipmap_level: Union[int, Tuple[int, int]] = 0, repeat: Union[bool, Tuple[bool, bool]] = False, anisotropic: float = 1.0, ctx: Optional[utils3d.numpy.rasterization.RastContext] = None) -> numpy_.ndarray:
"""Sample from a texture map with a UV map."""
utils3d.numpy.rasterization.sample_texture
@overload
def test_rasterization(ctx: Optional[utils3d.numpy.rasterization.RastContext] = None):
"""Test if rasterization works. It will render a cube with random colors and save it as a CHECKME.png file."""
utils3d.numpy.rasterization.test_rasterization
@overload
def read_extrinsics_from_colmap(file: Union[str, pathlib._local.Path]) -> Union[numpy_.ndarray, List[int], List[str]]:
"""Read extrinsics from colmap `images.txt` file.
## Parameters
file: Path to `images.txt` file.
## Returns
extrinsics: (N, 4, 4) array of extrinsics.
camera_ids: List of int, camera ids. Length is N. Note that camera ids in colmap typically starts from 1.
image_names: List of str, image names. Length is N."""
utils3d.numpy.io.colmap.read_extrinsics_from_colmap
@overload
def read_intrinsics_from_colmap(file: Union[str, pathlib._local.Path], normalize: bool = False) -> Tuple[List[int], numpy_.ndarray, numpy_.ndarray]:
"""Read intrinsics from colmap `cameras.txt` file.
## Parameters
file: Path to `cameras.txt` file.
normalize: Whether to normalize the intrinsics. If True, the intrinsics will be normalized. (mapping coordinates to [0, 1] range)
## Returns
camera_ids: List of int, camera ids. Length is N. Note that camera ids in colmap typically starts from 1.
intrinsics: (N, 3, 3) array of intrinsics.
distortions: (N, 5) array of distortions."""
utils3d.numpy.io.colmap.read_intrinsics_from_colmap
@overload
def write_extrinsics_as_colmap(file: Union[str, pathlib._local.Path], extrinsics: numpy_.ndarray, image_names: Union[str, List[str]] = 'image_{i:04d}.png', camera_ids: List[int] = None):
"""Write extrinsics to colmap `images.txt` file.
## Parameters
file: Path to `images.txt` file.
extrinsics: (N, 4, 4) array of extrinsics.
image_names: str or List of str, image names. Length is N.
If str, it should be a format string with `i` as the index. (i starts from 1, in correspondence with IMAGE_ID in colmap)
camera_ids: List of int, camera ids. Length is N.
If None, it will be set to [1, 2, ..., N]."""
utils3d.numpy.io.colmap.write_extrinsics_as_colmap
@overload
def write_intrinsics_as_colmap(file: Union[str, pathlib._local.Path], intrinsics: numpy_.ndarray, width: int, height: int, normalized: bool = False):
"""Write intrinsics to colmap `cameras.txt` file. Currently only support PINHOLE model (no distortion)
## Parameters
file: Path to `cameras.txt` file.
intrinsics: (N, 3, 3) array of intrinsics.
width: Image width.
height: Image height.
normalized: Whether the intrinsics are normalized. If True, the intrinsics will unnormalized for writing."""
utils3d.numpy.io.colmap.write_intrinsics_as_colmap
@overload
def read_obj(file: Union[str, pathlib._local.Path, _io.TextIOWrapper], encoding: Optional[str] = None, ignore_unknown: bool = False) -> utils3d.numpy.io.obj.WavefrontOBJDict:
"""Read wavefront .obj file.
Parameters
----
- `file` (str, Path, TextIOWrapper): filepath or file object
- `encoding` (str, optional): file encoding
- `ignore_unknown` (bool): whether to ignore unknown keywords in .obj file. Default to False.
Returns
----
A dictionary maybe containing the following fields. Note that some fields may be absent if not present in the .obj file:
Vertices and attributes data:
- `v` (ndarray): (N_v, 3 or 4) vertex coordinates.
- `vt` (ndarray): (N_vt, 2 or 3). vertex texture coordinates.
- `vn` (ndarray): (N_vn, 3). vertex normals.
Primitive definitions (face/line). NOTE: all indices are 0-based, unlike the 1-based indexing in .obj file.
- `f` (ndarray): Vertex indices in each face.
- If all faces have the same number of vertices: (M, K)
- If faces have different numbers of vertices: a tuple of segmented array:
- `data` (ndarray): flattened array of shape (sum(K_i),)
- `offsets` (ndarray): shape (M + 1,), offsets of each face in the flattened array
- `ft` (ndarray): Vertex texture coordinate indices of each face. The same format as `f`.
- `fn` (ndarray): Vertex normal indices of each face. The same format as `f`.
- `l` (ndarray): Vertex indices of each line segment.
- If all lines have the same number of vertices: (L, K_line)
- If lines have different numbers of vertices: a tuple of segmented array:
- `data` (ndarray): flattened array of shape (sum(K_line_i),)
- `offsets` (ndarray): shape (L + 1,), offsets of each line in the flattened array
- `lt` (ndarray): Vertex texture coordinate indices of each line. The same format as `l`.
- `p` (ndarray): Vertex indices of each point. 1D array of shape (N_p,)
- `pt` (ndarray): Vertex texture coordinate indices of each point. The same format as `p`.
Object/Group/Material info:
- `o` (Dict[str, Dict[Literal['f', 'l', 'p'], slice]]). The objects and their corresponding faces/lines/points. E.g. `o['object_A']['f']` gives the slice of faces belonging to object_A.
- `g` (Dict[str, Dict[Literal['f', 'l', 'p'], slice]]). The groups and their corresponding faces/lines/points. E.g. `g['group_A']['f']` gives the slice of faces belonging to group_A.
- `usemtl` (Dict[str, Dict[Literal['f', 'l', 'p'], slice]]). The materials and their corresponding faces/lines/points. E.g. `usemtl['material_A']['f']` gives the slice of faces using material_A.
Here, `names` is a list of names, and `offsets` is an array of shape (num_entities + 1,) indicating the start and end indices of faces belonging to each object/group/material.
For example, the second material has name `material_names[1]`, and its faces are `f[material_offsets[1]:material_offsets[2]]`.
Material library:
- `mtllib` (List[str]): list of material library filenames - `mtllib` lines in .obj file."""
utils3d.numpy.io.obj.read_obj
@overload
def write_obj(file: Union[str, pathlib._local.Path, os.PathLike], obj: utils3d.numpy.io.obj.WavefrontOBJDict, encoding: Optional[str] = None):
utils3d.numpy.io.obj.write_obj
@overload
def read_ply(file: Union[str, os.PathLike, IO]) -> Dict[str, Dict[str, Union[numpy_.ndarray, Tuple[numpy_.ndarray, numpy_.ndarray]]]]:
"""Read a PLY file. Supports arbitrary properties, polygonal meshes. Very fast.
Parameters
----------
- `file` (str | os.PathLike | IO): Path to the PLY file or a file-like object.
Returns
-------
- `data` (Dict): Parsed PLY data. Example
```python
{
"vertex": {
"x": ndarray,
"y": ndarray,
"z": ndarray,
... # other properties, like "nx", "ny", "nz", "red", "green", "blue", etc.
},
"face": {
"vertex_indices": ndarray for regular lists or (ndarray, offsets ndarray) for irregular lists,
...
},
...
}
```
Performance
-------
Tested on a few binary PLY files:
| Content Type | `utils3d` | `Open3D` | `Trimesh` | `plyfile` | `meshio` |
|----------- |------------| -------- |-----------|-----------| ---------|
| Point Cloud (V=921,600) | 26.3 ms | 132.8 ms | 36.8 ms | 23.1 ms | 25.8 ms |
| Triangle Mesh (V=425,949, F=841,148) | 17.4 ms | 144.8 ms | 341.9 ms | 2655.5 ms | 366.8 ms |
| Polygon Mesh (V=437,645, F=871,414) | 289.5 ms | x | x | 1999.5 ms | 3905.3 ms |"""
utils3d.numpy.io.ply.read_ply
@overload
def write_ply(file: Union[str, os.PathLike, IO], data: Dict[str, Dict[str, Union[numpy_.ndarray, Tuple[numpy_.ndarray, numpy_.ndarray]]]], format_: Literal['ascii', 'binary_little_endian', 'binary_big_endian'] = 'binary_little_endian') -> None:
"""Write a PLY file. Supports arbitrary properties, polygonal meshes.
Parameters
----------
- `file` (str | os.PathLike | IO): Path to the PLY file or a file-like object.
- `data` (Dict): PLY data to write. The structure is like
```python
{
"vertex": {
"x": ndarray,
"y": ndarray,
"z": ndarray,
... # other properties, like "nx", "ny", "nz", "red", "green", "blue", etc.
},
"face": {
"vertex_indices": ndarray for regular lists or (ndarray, offsets ndarray) for irregular lists,
...
},
...
}
```
- `format` (str): PLY format. Options are 'ascii', 'binary_little_endian', 'binary_big_endian'.
Performance
-------
| Content Type | `utils3d` | `Open3D` | `Trimesh` | `plyfile` | `meshio` |
|----------- |------------| -------- |-----------|-----------|---------|
| Point Cloud (V=921,600)| 45.1 ms | 175.1 ms | 47.7 ms | 9.2 ms | 43.9 ms |
| Triangle Mesh (V=425,949, F=841,148) | 38.3 ms | 137.9 ms | 41.3 ms | 2063.1 ms | 46.9 ms |
| Polygon Mesh (V=437,645, F=871,414) | 234.0 ms | x | x | 1653.2 ms | 12360.8 ms |"""
utils3d.numpy.io.ply.write_ply
@overload
def sliding_window(x: torch_.Tensor, window_size: Union[int, Tuple[int, ...]], stride: Union[int, Tuple[int, ...], NoneType] = None, dilation: Union[int, Tuple[int, ...], NoneType] = None, pad_size: Union[int, Tuple[int, int], Tuple[Tuple[int, int]], NoneType] = None, pad_mode: str = 'constant', pad_value: numbers.Number = 0, dim: Tuple[int, ...] = None) -> torch_.Tensor:
"""Get a sliding window of the input array.
This function is a wrapper of `torch.nn.functional.unfold` with additional support for padding and stride.
## Parameters
- `x` (Tensor): Input tensor.
- `window_size` (int or Tuple[int,...]): Size of the sliding window. If int
is provided, the same size is used for all specified axes.
- `stride` (Optional[Tuple[int,...]]): Stride between the sliding windows. If None,
no stride is applied. If int is provided, the same stride is used for all specified axes.
- `dilation` (Optional[Tuple[int,...]]): Dilation in each sliding window. If None,
no dilation is applied. If int is provided, the same dilation is used for all specified axes.
- `pad_size` (Optional[Union[int, Tuple[int, int], Tuple[Tuple[int, int]]]]): Size of padding to apply before sliding window.
Corresponding to `axis`.
- General format is `((before_1, after_1), (before_2, after_2), ...)`.
- Shortcut formats:
- `int` -> same padding before and after for all axes;
- `(int, int)` -> same padding before and after for each axis;
- `((int,), (int,) ...)` -> specify padding for each axis, same before and after.
- `pad_mode` (str): Padding mode to use. Refer to `numpy.pad` for more details.
- `pad_value` (Union[int, float]): Value to use for constant padding. Only used
when `pad_mode` is 'constant'.
- `axis` (Optional[Tuple[int,...]]): Axes to apply the sliding window. If None, all axes are used.
## Returns
- (Tensor): Sliding window of the input array.
- If no padding, the output is a view of the input array with zero copy.
- Otherwise, the output is no longer a view but a copy of the padded array."""
utils3d.torch.utils.sliding_window
@overload
def masked_min(input: torch_.Tensor, mask: torch_.BoolTensor, dim: int = None, keepdim: bool = False) -> Union[torch_.Tensor, Tuple[torch_.Tensor, torch_.Tensor]]:
"""Similar to torch.min, but with mask
"""
utils3d.torch.utils.masked_min
@overload
def masked_max(input: torch_.Tensor, mask: torch_.BoolTensor, dim: int = None, keepdim: bool = False) -> Union[torch_.Tensor, Tuple[torch_.Tensor, torch_.Tensor]]:
"""Similar to torch.max, but with mask
"""
utils3d.torch.utils.masked_max
@overload
def lookup(key: torch_.Tensor, query: torch_.Tensor) -> torch_.LongTensor:
"""Look up `query` in `key` like a dictionary. Useful for COO indexing.
Parameters
----
- `key` (Tensor): shape `(K, *key_shape)`, the array to search in
- `query` (Tensor): shape `(..., *key_shape)`, the array to search for. `...` represents any number of batch dimensions.
Returns
----
- `indices` (Tensor): shape `(...,)` shape `(...,)` indices in `key` for each `query`. If a query is not found in key, the corresponding index will be -1.
Notes
----
- If using pytorch implementation (based on `torch.unique`), the complexity is `O((Q + K) * log(Q + K))` where `Q` is the number of queries and `K` is the number of keys.
- If using triton implementation (based on hashmap), the average complexity `O(Q + K)`. Much faster for large `Q` and `K`."""
utils3d.torch.utils.lookup
@overload
def lookup_get(key: torch_.Tensor, value: torch_.Tensor, get_key: torch_.Tensor, default_value: Union[numbers.Number, torch_.Tensor] = 0) -> torch_.Tensor:
"""Dictionary-like get for arrays
## Parameters
- `key` (Tensor): shape `(N, *key_shape)`, the key array of the dictionary to get from
- `value` (Tensor): shape `(N, *value_shape)`, the value array of the dictionary to get from
- `get_key` (Tensor): shape `(M, *key_shape)`, the key array to get for
- `default_value` (Union[Number, Tensor]): value to return if a key in `get_key` is not found in `key`. A scalar or tensor broadcastable to shape `(..., *value_shape)`
## Returns
`get_value` (Tensor): shape `(M, *value_shape)`, result values corresponding to `get_key`"""
utils3d.torch.utils.lookup_get
@overload
def lookup_set(key: torch_.Tensor, value: torch_.Tensor, set_key: torch_.Tensor, set_value: torch_.Tensor, append: bool = False, inplace: bool = False) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Dictionary-like set for arrays.
## Parameters
- `key` (Tensor): shape `(N, *key_shape)`, the key array of the dictionary to set
- `value` (Tensor): shape `(N, *value_shape)`, the value array of the dictionary to set
- `set_key` (Tensor): shape `(M, *key_shape)`, the key array to set for
- `set_value` (Tensor): shape `(M, *value_shape)`, the value array to set as
- `append` (bool): If True, append the (key, value) pairs in (set_key, set_value) that are not in (key, value) to the result.
- `inplace` (bool): If True, modify the input `value` array
## Returns
- `result_key` (Tensor): shape `(N_new, *value_shape)`. N_new = N + number of new keys added if append is True, else N.
- `result_value (Tensor): shape `(N_new, *value_shape)` """
utils3d.torch.utils.lookup_set
@overload
def csr_matrix_from_dense_indices(indices: torch_.Tensor, n_cols: int) -> torch_.Tensor:
"""Convert a regular indices array to a sparse CSR adjacency matrix format
## Parameters
- `indices` (Tensor): shape (N, M) dense tensor. Each one in `N` has `M` connections.
- `values` (Tensor): shape (N, M) values of the connections
- `n_cols` (int): total number of columns in the adjacency matrix
## Returns
Tensor: shape `(N, n_cols)` sparse CSR adjacency matrix"""
utils3d.torch.utils.csr_matrix_from_dense_indices
@overload
def csr_eliminate_zeros(input: torch_.Tensor):
"""Remove zero elements from a sparse CSR tensor.
"""
utils3d.torch.utils.csr_eliminate_zeros
@overload
def group(labels: torch_.Tensor, data: Optional[torch_.Tensor] = None) -> List[Tuple[torch_.Tensor, torch_.Tensor]]:
"""Split the data into groups based on the provided labels.
## Parameters
- `labels` (Tensor): shape `(N, *label_dims)` array of labels for each data point. Labels can be multi-dimensional.
- `data` (Tensor, optional): shape `(N, *data_dims)` dense tensor. Each one in `N` has `D` features.
If None, return the indices in each group instead.
## Returns
- `groups` (List[Tuple[Tensor, Tensor]]): List of each group, a tuple of `(label, data_in_group)`.
- `label` (Tensor): shape (*label_dims,) the label of the group.
- `data_in_group` (Tensor): shape (M, *data_dims) the data points in the group.
If `data` is None, `data_in_group` will be the indices of the data points in the original array."""
utils3d.torch.utils.group
@overload
def lexsort(keys: Union[Sequence[torch_.Tensor], torch_.Tensor], dim: int = -1) -> torch_.Tensor:
"""Perform lexicographical sort on multiple keys. Like `numpy.lexsort`.
Given multiple sorting keys, lexsort returns an array of integer indices that describes the sort order by multiple keys.
The last key in the sequence is used for the primary sort order, ties are broken by the second-to-last key, and so on.
Parameters
----
- `keys`: (Sequence[Tensor]) sequence of Tensors to sort by, or a single Tensor with shape `(num_keys, ...)`.
- `dim`: (int) the dimension to sort along. Note that if `keys` is a single Tensor, `dim=0` refers to the second dimension of `keys`.
Returns
----
- `indices`: (Tensor) the indices that would sort the keys lexicographically along the specified dimension.
Notes
-----
Sorting is always stable."""
utils3d.torch.utils.lexsort
@overload
def index_reduce(input: torch_.Tensor, indices: Union[Tuple[torch_.Tensor], List[torch_.Tensor]], values: torch_.Tensor, reduce: Literal['amin', 'amax', 'sum', 'prod', 'mean'], include_self: bool = True) -> torch_.Tensor:
"""Put values into the input tensor at the specified indices (like `index_put`), with reduction support.
Behaves like `numpy.ufunc.at`.
Parameters
----
- `input`: (Tensor) the input tensor to modify.
- `indices`: (Tensor) the indices at which to put the values.
- `values`: (Tensor) the values to put into the input tensor.
- `reduce`: (str) the reduction method to use when multiple values are put at the same index. Options are 'amin', 'amax', 'sum', 'prod', and 'mean'.
Returns
----
- (Tensor) the modified tensor after putting the values."""
utils3d.torch.utils.index_reduce
@overload
def index_reduce_(input: torch_.Tensor, indices: Union[Tuple[torch_.Tensor], List[torch_.Tensor]], values: torch_.Tensor, reduce: Literal['amin', 'amax', 'sum', 'prod', 'mean'], include_self: bool = True) -> torch_.Tensor:
"""In-place put values into the input tensor at the specified indices (like `index_put_`), with reduction support.
Behaves like `numpy.ufunc.at`.
Parameters
----
- `input`: (Tensor) the input tensor to modify.
- `indices`: (Tensor) the indices at which to put the values.
- `values`: (Tensor) the values to put into the input tensor.
- `reduce`: (str) the reduction method to use when multiple values are put at the same index. Options are 'amin', 'amax', 'sum', 'prod', and 'mean'.
Returns
----
- (Tensor) the modified tensor after putting the values."""
utils3d.torch.utils.index_reduce_
@overload
def scatter_argmax(input: torch_.Tensor, dim: int, index: torch_.Tensor, src: torch_.Tensor, include_self: bool = True) -> torch_.Tensor:
"""Scatter src into input at index along dim with min reduction. Return the indices of the winners in src.
Parameters
----
- `input`: (Tensor) the input tensor to scatter into.
- `dim`: (int) the dimension along which to index.
- `index`: (LongTensor) the indices at which to scatter.
- `src`: (Tensor) the source tensor to scatter from.
- `include_self`: (bool) whether to include the original values in `input` when computing the min.
Returns
----
- `argmin`: (LongTensor) shape same as `input`, the indices of the min values in `src`.
Notes
----
- If multiple values in `src` are equal to the min value at a position, the one with the smallest index in `src` will be chosen.
- If none of src was scattered to a position (i.e., not presented, or the min value is from the original input), the index will be -1."""
utils3d.torch.utils.scatter_argmax
@overload
def scatter_argmin(input: torch_.Tensor, dim: int, index: torch_.Tensor, src: torch_.Tensor, include_self: bool = True) -> torch_.Tensor:
"""Scatter src into input at index along dim with min reduction. Return the indices of the winners in src.
Parameters
----
- `input`: (Tensor) the input tensor to scatter into.
- `dim`: (int) the dimension along which to index.
- `index`: (LongTensor) the indices at which to scatter.
- `src`: (Tensor) the source tensor to scatter from.
- `include_self`: (bool) whether to include the original values in `input` when computing the min.
Returns
----
- `argmin`: (LongTensor) shape same as `input`, the indices of the min values in `src`.
Notes
----
- If multiple values in `src` are equal to the min value at a position, the one with the smallest index in `src` will be chosen.
- If none of src was scattered to a position (i.e., not presented, or the min value is from the original input), the index will be -1."""
utils3d.torch.utils.scatter_argmin
@overload
def reverse_permutation(perm: torch_.Tensor, dim: int = 0) -> torch_.Tensor:
"""Reverse a permutation tensor along a specified dimension.
Parameters
----
- `perm`: (LongTensor) the permutation tensor to reverse.
- `dim`: (int) the dimension of permutation indices. Other dimensions are treated as batch dimensions.
Returns
----
- (LongTensor) the reversed permutation tensor, such that `reversed_perm[perm] == torch.arange(perm.shape[dim])`
Notes
-----
Equivalent to `torch.argsort(perm, dim=dim)`, but more efficient."""
utils3d.torch.utils.reverse_permutation
@overload
def large_multinomial(weights: torch_.Tensor, num_samples: int, replacement: bool = False) -> torch_.Tensor:
utils3d.torch.utils.large_multinomial
@overload
def matrix_trace(input: torch_.Tensor, dim1: int = -2, dim2: int = -1) -> torch_.Tensor:
"""Compute the trace of a batch of matrices"""
utils3d.torch.utils.matrix_trace
@overload
def vector_outer(x: torch_.Tensor, y: Optional[torch_.Tensor] = None) -> torch_.Tensor:
"""Compute the outer product of two arrays.
Parameters
----
- `x` (Tensor): shape `(..., M)` first array.
- `y` (Tensor, optional): shape `(..., N)` second array. If None, compute the outer product of `x` with itself.
Returns
----
- `outer` (Tensor): shape `(..., M, N)` outer product of `x` and `y`."""
utils3d.torch.utils.vector_outer
@overload
def perspective_from_fov(*, fov_x: Union[float, torch_.Tensor, NoneType] = None, fov_y: Union[float, torch_.Tensor, NoneType] = None, fov_min: Union[float, torch_.Tensor, NoneType] = None, fov_max: Union[float, torch_.Tensor, NoneType] = None, aspect_ratio: Union[float, torch_.Tensor, NoneType] = None, near: Union[float, torch_.Tensor, NoneType], far: Union[float, torch_.Tensor, NoneType]) -> torch_.Tensor:
"""Get OpenGL perspective matrix from field of view
## Returns
(Tensor): [..., 4, 4] perspective matrix"""
utils3d.torch.transforms.perspective_from_fov
@overload
def perspective_from_window(left: Union[float, torch_.Tensor], right: Union[float, torch_.Tensor], bottom: Union[float, torch_.Tensor], top: Union[float, torch_.Tensor], near: Union[float, torch_.Tensor], far: Union[float, torch_.Tensor]) -> torch_.Tensor:
"""Get OpenGL perspective matrix from the window of z=-1 projection plane
## Returns
(Tensor): [..., 4, 4] perspective matrix"""
utils3d.torch.transforms.perspective_from_window
@overload
def intrinsics_from_fov(*, fov_x: Union[float, torch_.Tensor, NoneType] = None, fov_y: Union[float, torch_.Tensor, NoneType] = None, fov_max: Union[float, torch_.Tensor, NoneType] = None, fov_min: Union[float, torch_.Tensor, NoneType] = None, cx: Union[float, torch_.Tensor] = 0.5, cy: Union[float, torch_.Tensor] = 0.5, aspect_ratio: Union[float, torch_.Tensor, NoneType] = None) -> torch_.Tensor:
"""Get normalized OpenCV intrinsics matrix from given field of view.
You can provide either fov_x, fov_y, fov_max or fov_min and aspect_ratio
Parameters
----
fov_x (float | Tensor): field of view in x axis
fov_y (float | Tensor): field of view in y axis
fov_max (float | Tensor): field of view in largest dimension
fov_min (float | Tensor): field of view in smallest dimension
cx (float | Tensor): principal point x coordinate
cy (float | Tensor): principal point y coordinate
aspect_ratio (float | Tensor): aspect ratio of the image
Returns
----
(Tensor): [..., 3, 3] OpenCV intrinsics matrix"""
utils3d.torch.transforms.intrinsics_from_fov
@overload
def intrinsics_from_focal_center(fx: Union[float, torch_.Tensor], fy: Union[float, torch_.Tensor], cx: Union[float, torch_.Tensor], cy: Union[float, torch_.Tensor]) -> torch_.Tensor:
"""Get OpenCV intrinsics matrix
## Parameters
focal_x (float | Tensor): focal length in x axis
focal_y (float | Tensor): focal length in y axis
cx (float | Tensor): principal point in x axis
cy (float | Tensor): principal point in y axis
## Returns
(Tensor): [..., 3, 3] OpenCV intrinsics matrix"""
utils3d.torch.transforms.intrinsics_from_focal_center
@overload
def focal_to_fov(focal: torch_.Tensor):
utils3d.torch.transforms.focal_to_fov
@overload
def fov_to_focal(fov: torch_.Tensor):
utils3d.torch.transforms.fov_to_focal
@overload
def intrinsics_to_fov(intrinsics: torch_.Tensor) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""NOTE: approximate FOV by assuming centered principal point"""
utils3d.torch.transforms.intrinsics_to_fov
@overload
def view_look_at(eye: torch_.Tensor, look_at: torch_.Tensor, up: torch_.Tensor) -> torch_.Tensor:
"""Get OpenGL view matrix looking at something
## Parameters
eye (Tensor): [..., 3] the eye position
look_at (Tensor): [..., 3] the position to look at
up (Tensor): [..., 3] head up direction (y axis in screen space). Not necessarily othogonal to view direction
## Returns
(Tensor): [..., 4, 4], view matrix"""
utils3d.torch.transforms.view_look_at
@overload
def extrinsics_look_at(eye: torch_.Tensor, look_at: torch_.Tensor, up: torch_.Tensor) -> torch_.Tensor:
"""Get OpenCV extrinsics matrix looking at something
## Parameters
eye (Tensor): [..., 3] the eye position
look_at (Tensor): [..., 3] the position to look at
up (Tensor): [..., 3] head up direction (-y axis in screen space). Not necessarily othogonal to view direction
## Returns
(Tensor): [..., 4, 4], extrinsics matrix"""
utils3d.torch.transforms.extrinsics_look_at
@overload
def perspective_to_intrinsics(perspective: torch_.Tensor) -> torch_.Tensor:
"""OpenGL perspective matrix to OpenCV intrinsics
## Parameters
perspective (Tensor): [..., 4, 4] OpenGL perspective matrix
## Returns
(Tensor): shape [..., 3, 3] OpenCV intrinsics"""
utils3d.torch.transforms.perspective_to_intrinsics
@overload
def intrinsics_to_perspective(intrinsics: torch_.Tensor, near: Union[float, torch_.Tensor], far: Union[float, torch_.Tensor]) -> torch_.Tensor:
"""OpenCV intrinsics to OpenGL perspective matrix
NOTE: not work for tile-shifting intrinsics currently
## Parameters
intrinsics (Tensor): [..., 3, 3] OpenCV intrinsics matrix
near (float | Tensor): [...] near plane to clip
far (float | Tensor): [...] far plane to clip
## Returns
(Tensor): [..., 4, 4] OpenGL perspective matrix"""
utils3d.torch.transforms.intrinsics_to_perspective
@overload
def extrinsics_to_view(extrinsics: torch_.Tensor) -> torch_.Tensor:
"""OpenCV camera extrinsics to OpenGL view matrix
## Parameters
extrinsics (Tensor): [..., 4, 4] OpenCV camera extrinsics matrix
## Returns
(Tensor): [..., 4, 4] OpenGL view matrix"""
utils3d.torch.transforms.extrinsics_to_view
@overload
def view_to_extrinsics(view: torch_.Tensor) -> torch_.Tensor:
"""OpenGL view matrix to OpenCV camera extrinsics
## Parameters
view (Tensor): [..., 4, 4] OpenGL view matrix
## Returns
(Tensor): [..., 4, 4] OpenCV camera extrinsics matrix"""
utils3d.torch.transforms.view_to_extrinsics
@overload
def normalize_intrinsics(intrinsics: torch_.Tensor, size: Union[Tuple[numbers.Number, numbers.Number], torch_.Tensor], pixel_convention: Literal['integer-corner', 'integer-center'] = 'integer-center') -> torch_.Tensor:
"""Normalize camera intrinsics to uv space
## Parameters
- `intrinsics` (Tensor): `(..., 3, 3)` camera intrinsics to normalize
- `size` (tuple | Tensor): A tuple `(height, width)` of the image size,
or an array of shape `(..., 2)` corresponding to the multiple image size(s)
- `pixel_convention`: `str`, optional `'integer-center'` or `'integer-corner'`, whether integer coordinates correspond to pixel centers or corners. Defaults to 'integer-center'.
- For more definitions, please refer to `pixel_coord_map()`
## Returns
(Tensor): [..., 3, 3] normalized camera intrinsics"""
utils3d.torch.transforms.normalize_intrinsics
@overload
def denormalize_intrinsics(intrinsics: torch_.Tensor, size: Union[Tuple[numbers.Number, numbers.Number], torch_.Tensor], pixel_convention: Literal['integer-center', 'integer-corner'] = 'integer-center') -> torch_.Tensor:
"""Denormalize camera intrinsics(s) from uv space to pixel space
## Parameters
- `intrinsics` (Tensor): `(..., 3, 3)` camera intrinsics
- `size` (tuple | Tensor): A tuple `(height, width)` of the image size,
or an array of shape `(..., 2)` corresponding to the multiple image size(s)
- `pixel_convention`: `str`, optional `'integer-center'` or `'integer-corner'`, whether integer coordinates correspond to pixel centers or corners. Defaults to 'integer-center'.
- For more definitions, please refer to `pixel_coord_map()`
## Returns
(Tensor): [..., 3, 3] denormalized camera intrinsics in pixel space"""
utils3d.torch.transforms.denormalize_intrinsics
@overload
def crop_intrinsics(intrinsics: torch_.Tensor, size: Union[Tuple[numbers.Number, numbers.Number], torch_.Tensor], cropped_top: Union[numbers.Number, torch_.Tensor], cropped_left: Union[numbers.Number, torch_.Tensor], cropped_height: Union[numbers.Number, torch_.Tensor], cropped_width: Union[numbers.Number, torch_.Tensor]) -> torch_.Tensor:
"""Evaluate the new intrinsics after cropping the image
## Parameters
intrinsics (Tensor): (..., 3, 3) camera intrinsics(s) to crop
height (int | Tensor): (...) image height(s)
width (int | Tensor): (...) image width(s)
cropped_top (int | Tensor): (...) top pixel index of the cropped image(s)
cropped_left (int | Tensor): (...) left pixel index of the cropped image(s)
cropped_height (int | Tensor): (...) height of the cropped image(s)
cropped_width (int | Tensor): (...) width of the cropped image(s)
## Returns
(Tensor): (..., 3, 3) cropped camera intrinsics"""
utils3d.torch.transforms.crop_intrinsics
@overload
def pixel_to_uv(pixel: torch_.Tensor, size: Union[Tuple[numbers.Number, numbers.Number], torch_.Tensor], pixel_convention: Literal['integer-corner', 'integer-center'] = 'integer-center') -> torch_.Tensor:
"""## Parameters
- `pixel` (Tensor): `(..., 2)` pixel coordinrates
- `size` (tuple | Tensor): A tuple `(height, width)` of the image size,
or an array of shape `(..., 2)` corresponding to the multiple image size(s)
- `pixel_convention`: `str`, optional `'integer-center'` or `'integer-corner'`, whether integer coordinates correspond to pixel centers or corners. Defaults to 'integer-center'.
- For more definitions, please refer to `pixel_coord_map()`
## Returns
(Tensor): `(..., 2)` uv coordinrates"""
utils3d.torch.transforms.pixel_to_uv
@overload
def pixel_to_ndc(pixel: torch_.Tensor, size: Union[Tuple[numbers.Number, numbers.Number], torch_.Tensor], pixel_convention: Literal['integer-corner', 'integer-center'] = 'integer-center') -> torch_.Tensor:
"""Convert pixel coordinates to NDC (Normalized Device Coordinates).
## Parameters
- `pixel` (Tensor): `(..., 2)` pixel coordinrates.
- `size` (tuple | Tensor): A tuple `(height, width)` of the image size,
or an array of shape `(..., 2)` corresponding to the multiple image size(s)
- `pixel_convention`: `str`, optional `'integer-center'` or `'integer-corner'`, whether integer coordinates correspond to pixel centers or corners. Defaults to 'integer-center'.
- For more definitions, please refer to `pixel_coord_map()`
## Returns
(Tensor): `(..., 2)` ndc coordinrates, the range is (-1, 1)"""
utils3d.torch.transforms.pixel_to_ndc
@overload
def uv_to_pixel(uv: torch_.Tensor, size: Union[Tuple[numbers.Number, numbers.Number], torch_.Tensor], pixel_convention: Literal['integer-corner', 'integer-center'] = 'integer-center') -> torch_.Tensor:
"""Convert UV space coordinates to pixel space coordinates.
## Parameters
- `uv` (Tensor): `(..., 2)` uv coordinrates.
- `size` (tuple | Tensor): A tuple `(height, width)` of the image size,
or an array of shape `(..., 2)` corresponding to the multiple image size(s)
- `pixel_convention`: `str`, optional `'integer-center'` or `'integer-corner'`, whether integer coordinates correspond to pixel centers or corners. Defaults to 'integer-center'.
- For more definitions, please refer to `pixel_coord_map()`
## Returns
(Tensor): `(..., 2)` pixel coordinrates"""
utils3d.torch.transforms.uv_to_pixel
@overload
def depth_linear_to_buffer(depth: torch_.Tensor, near: Union[float, torch_.Tensor], far: Union[float, torch_.Tensor]) -> torch_.Tensor:
"""Project linear depth to depth value in screen space
## Parameters
depth (Tensor): [...] depth value
near (float | Tensor): [...] near plane to clip
far (float | Tensor): [...] far plane to clip
## Returns
(Tensor): [..., 1] depth value in screen space, value ranging in [0, 1]"""
utils3d.torch.transforms.depth_linear_to_buffer
@overload
def depth_buffer_to_linear(depth: torch_.Tensor, near: Union[float, torch_.Tensor], far: Union[float, torch_.Tensor]) -> torch_.Tensor:
"""Linearize depth value to linear depth
## Parameters
depth (Tensor): [...] screen depth value, ranging in [0, 1]
near (float | Tensor): [...] near plane to clip
far (float | Tensor): [...] far plane to clip
## Returns
(Tensor): [...] linear depth"""
utils3d.torch.transforms.depth_buffer_to_linear
@overload
def project_gl(points: torch_.Tensor, projection: torch_.Tensor, view: torch_.Tensor = None) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Project 3D points to 2D following the OpenGL convention (except for row major matrices)
## Parameters
points (Tensor): [..., N, 3] or [..., N, 4] 3D points to project, if the last
dimension is 4, the points are assumed to be in homogeneous coordinates
view (Tensor): [..., 4, 4] view matrix
projection (Tensor): [..., 4, 4] projection matrix
## Returns
scr_coord (Tensor): [..., N, 3] screen space coordinates, value ranging in [0, 1].
The origin (0., 0., 0.) is corresponding to the left & bottom & nearest
linear_depth (Tensor): [..., N] linear depth"""
utils3d.torch.transforms.project_gl
@overload
def project_cv(points: torch_.Tensor, intrinsics: torch_.Tensor, extrinsics: Optional[torch_.Tensor] = None) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Project 3D points to 2D following the OpenCV convention
## Parameters
points (Tensor): [..., N, 3] 3D points
intrinsics (Tensor): [..., 3, 3] intrinsics matrix
extrinsics (Tensor): [..., 4, 4] extrinsics matrix
## Returns
uv_coord (Tensor): [..., N, 2] uv coordinates, value ranging in [0, 1].
The origin (0., 0.) is corresponding to the left & top
linear_depth (Tensor): [..., N] linear depth"""
utils3d.torch.transforms.project_cv
@overload
def unproject_gl(uv: torch_.Tensor, depth: torch_.Tensor, projection: torch_.Tensor, view: Optional[torch_.Tensor] = None) -> torch_.Tensor:
"""Unproject screen space coordinates to 3D view space following the OpenGL convention (except for row major matrices)
## Parameters
uv (Tensor): (..., N, 2) screen space XY coordinates, value ranging in [0, 1].
The origin (0., 0.) is corresponding to the left & bottom
depth (Tensor): (..., N) linear depth values
projection (Tensor): (..., 4, 4) projection matrix
view (Tensor): (..., 4, 4) view matrix
## Returns
points (Tensor): (..., N, 3) 3d points"""
utils3d.torch.transforms.unproject_gl
@overload
def unproject_cv(uv: torch_.Tensor, depth: torch_.Tensor, intrinsics: torch_.Tensor, extrinsics: torch_.Tensor = None) -> torch_.Tensor:
"""Unproject uv coordinates to 3D view space following the OpenCV convention
## Parameters
uv (Tensor): [..., N, 2] uv coordinates, value ranging in [0, 1].
The origin (0., 0.) is corresponding to the left & top
depth (Tensor): [..., N] depth value
extrinsics (Tensor): [..., 4, 4] extrinsics matrix
intrinsics (Tensor): [..., 3, 3] intrinsics matrix
## Returns
points (Tensor): [..., N, 3] 3d points"""
utils3d.torch.transforms.unproject_cv
@overload
def project(points: torch_.Tensor, *, intrinsics: Optional[torch_.Tensor] = None, extrinsics: Optional[torch_.Tensor] = None, view: Optional[torch_.Tensor] = None, projection: Optional[torch_.Tensor] = None) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Calculate projection.
- For OpenCV convention, use `intrinsics` and `extrinsics` matrices.
- For OpenGL convention, use `view` and `projection` matrices.
## Parameters
- `points`: (..., N, 3) 3D world-space points
- `intrinsics`: (..., 3, 3) intrinsics matrix
- `extrinsics`: (..., 4, 4) extrinsics matrix
- `view`: (..., 4, 4) view matrix
- `projection`: (..., 4, 4) projection matrix
## Returns
- `uv`: (..., N, 2) 2D coordinates.
- For OpenCV convention, it is the normalized image coordinate where (0, 0) is the top left corner.
- For OpenGL convention, it is the screen space XY coordinate where (0, 0) is the bottom left corner.
- `depth`: (..., N) linear depth values, where `depth > 0` is visible.
- For OpenCV convention, it is the Z coordinate in camera space.
- For OpenGL convention, it is the -Z coordinate in camera space."""
utils3d.torch.transforms.project
@overload
def unproject(uv: torch_.Tensor, depth: Optional[torch_.Tensor], *, intrinsics: Optional[torch_.Tensor] = None, extrinsics: Optional[torch_.Tensor] = None, projection: Optional[torch_.Tensor] = None, view: Optional[torch_.Tensor] = None) -> torch_.Tensor:
"""Calculate inverse projection.
- For OpenCV convention, use `intrinsics` and `extrinsics` matrices.
- For OpenGL convention, use `view` and `projection` matrices.
## Parameters
- `uv`: (..., N, 2) 2D coordinates.
- For OpenCV convention, it is the normalized image coordinate where (0, 0) is the top left corner.
- For OpenGL convention, it is the screen space XY coordinate where (0, 0) is the bottom left corner.
- `depth`: (..., N) linear depth values, where `depth > 0` is visible.
- For OpenCV convention, it is the Z coordinate in camera space.
- For OpenGL convention, it is the -Z coordinate in camera space.
- `intrinsics`: (..., 3, 3) intrinsics matrix
- `extrinsics`: (..., 4, 4) extrinsics matrix
- `view`: (..., 4, 4) view matrix
- `projection`: (..., 4, 4) projection matrix
## Returns
- `points`: (..., N, 3) 3D world-space points"""
utils3d.torch.transforms.unproject
@overload
def skew_symmetric(v: torch_.Tensor):
"""Skew symmetric matrix from a 3D vector"""
utils3d.torch.transforms.skew_symmetric
@overload
def rotation_matrix_from_vectors(v1: torch_.Tensor, v2: torch_.Tensor):
"""Rotation matrix that rotates v1 to v2"""
utils3d.torch.transforms.rotation_matrix_from_vectors
@overload
def euler_axis_angle_rotation(axis: str, angle: torch_.Tensor) -> torch_.Tensor:
"""Return the rotation matrices for one of the rotations about an axis
of which Euler angles describe, for each value of the angle given.
## Parameters
axis: Axis label "X" or "Y or "Z".
angle: any shape tensor of Euler angles in radians
## Returns
Rotation matrices as tensor of shape (..., 3, 3)."""
utils3d.torch.transforms.euler_axis_angle_rotation
@overload
def euler_angles_to_matrix(euler_angles: torch_.Tensor, convention: str = 'XYZ') -> torch_.Tensor:
"""Convert rotations given as Euler angles in radians to rotation matrices.
## Parameters
euler_angles: Euler angles in radians as tensor of shape (..., 3), XYZ
convention: permutation of "X", "Y" or "Z", representing the order of Euler rotations to apply.
## Returns
Rotation matrices as tensor of shape (..., 3, 3)."""
utils3d.torch.transforms.euler_angles_to_matrix
@overload
def matrix_to_euler_angles(matrix: torch_.Tensor, convention: str) -> torch_.Tensor:
"""Convert rotations given as rotation matrices to Euler angles in radians.
NOTE: The composition order eg. `XYZ` means `Rz * Ry * Rx` (like blender), instead of `Rx * Ry * Rz` (like pytorch3d)
## Parameters
matrix: Rotation matrices as tensor of shape (..., 3, 3).
convention: Convention string of three uppercase letters.
## Returns
Euler angles in radians as tensor of shape (..., 3), in the order of XYZ (like blender), instead of convention (like pytorch3d)"""
utils3d.torch.transforms.matrix_to_euler_angles
@overload
def matrix_to_quaternion(rot_mat: torch_.Tensor, eps: float = 1e-12) -> torch_.Tensor:
"""Convert 3x3 rotation matrix to quaternion (w, x, y, z)
## Parameters
rot_mat (Tensor): shape (..., 3, 3), the rotation matrices to convert
## Returns
Tensor: shape (..., 4), the quaternions corresponding to the given rotation matrices"""
utils3d.torch.transforms.matrix_to_quaternion
@overload
def quaternion_to_matrix(quaternion: torch_.Tensor, eps: float = 1e-12) -> torch_.Tensor:
"""Converts a batch of quaternions (w, x, y, z) to rotation matrices
## Parameters
quaternion (Tensor): shape (..., 4), the quaternions to convert
## Returns
Tensor: shape (..., 3, 3), the rotation matrices corresponding to the given quaternions"""
utils3d.torch.transforms.quaternion_to_matrix
@overload
def quaternion_multiply(q1: torch_.Tensor, q2: torch_.Tensor) -> torch_.Tensor:
"""Multiplies two quaternions (w, x, y, z)
Parameters
----
q1 (Tensor): shape (..., 4), the first quaternion
q2 (Tensor): shape (..., 4), the second quaternion
Returns
----
Tensor: shape (..., 4), the product of the two quaternions"""
utils3d.torch.transforms.quaternion_multiply
@overload
def quaternion_inverse(quaternion: torch_.Tensor) -> torch_.Tensor:
"""Calculate the inverse of a batch of quaternions (w, x, y, z)
Parameters
----
quaternion (Tensor): shape (..., 4), the quaternions to invert
Returns
----
Tensor: shape (..., 4), no normalization applied. It depends on the input quaternion."""
utils3d.torch.transforms.quaternion_inverse
@overload
def quaternion_normalize(quaternion: torch_.Tensor, eps: float = 1e-12) -> torch_.Tensor:
"""Normalize quaternions (w, x, y, z) to unit length and positive w component
Parameters
----
quaternion (Tensor): shape (..., 4), the quaternions to normalize
Returns
----
Tensor: shape (..., 4), the normalized quaternions with unit length and positive w component"""
utils3d.torch.transforms.quaternion_normalize
@overload
def matrix_to_axis_angle(rot_mat: torch_.Tensor, eps: float = 1e-12) -> torch_.Tensor:
"""Convert a batch of 3x3 rotation matrices to axis-angle representation (rotation vector)
## Parameters
rot_mat (Tensor): shape (..., 3, 3), the rotation matrices to convert
## Returns
Tensor: shape (..., 3), the axis-angle vectors corresponding to the given rotation matrices"""
utils3d.torch.transforms.matrix_to_axis_angle
@overload
def axis_angle_to_matrix(axis_angle: torch_.Tensor, eps: float = 1e-12) -> torch_.Tensor:
"""Convert axis-angle representation (rotation vector) to rotation matrix, whose direction is the axis of rotation and length is the angle of rotation
## Parameters
axis_angle (Tensor): shape (..., 3), axis-angle vcetors
## Returns
Tensor: shape (..., 3, 3) The rotation matrices for the given axis-angle parameters"""
utils3d.torch.transforms.axis_angle_to_matrix
@overload
def axis_angle_to_quaternion(axis_angle: torch_.Tensor, eps: float = 1e-12) -> torch_.Tensor:
"""Convert axis-angle representation (rotation vector) to quaternion (w, x, y, z)
## Parameters
axis_angle (Tensor): shape (..., 3), axis-angle vcetors
## Returns
Tensor: shape (..., 4) The quaternions for the given axis-angle parameters"""
utils3d.torch.transforms.axis_angle_to_quaternion
@overload
def quaternion_to_axis_angle(quaternion: torch_.Tensor, eps: float = 1e-12) -> torch_.Tensor:
"""Convert a batch of quaternions (w, x, y, z) to axis-angle representation (rotation vector)
## Parameters
quaternion (Tensor): shape (..., 4), the quaternions to convert
## Returns
Tensor: shape (..., 3), the axis-angle vectors corresponding to the given quaternions"""
utils3d.torch.transforms.quaternion_to_axis_angle
@overload
def make_affine_matrix(M: torch_.Tensor, t: torch_.Tensor):
"""Make an affine transformation matrix from a linear matrix and a translation vector.
## Parameters
M (Tensor): [..., D, D] linear matrix (rotation, scaling or general deformation)
t (Tensor): [..., D] translation vector
## Returns
Tensor: [..., D + 1, D + 1] affine transformation matrix"""
utils3d.torch.transforms.make_affine_matrix
@overload
def random_rotation_matrix(*size: int, dtype=torch_.float32, device: torch_.device = None) -> torch_.Tensor:
"""Generate random 3D rotation matrix.
## Parameters
dtype: The data type of the output rotation matrix.
## Returns
Tensor: `(*size, 3, 3)` random rotation matrix."""
utils3d.torch.transforms.random_rotation_matrix
@overload
def lerp(v1: torch_.Tensor, v2: torch_.Tensor, t: torch_.Tensor) -> torch_.Tensor:
"""Linear interpolation between two vectors.
## Parameters
- `v1` (Tensor): `(..., D)` vector 1
- `v2` (Tensor): `(..., D)` vector 2
- `t` (Tensor): `(..., N)` interpolation parameter in [0, 1]
## Returns
Tensor: `(..., N, D)` interpolated vector"""
utils3d.torch.transforms.lerp
@overload
def slerp(v1: torch_.Tensor, v2: torch_.Tensor, t: torch_.Tensor, eps: float = 1e-12) -> torch_.Tensor:
"""Spherical linear interpolation between two (unit) vectors.
## Parameters
`v1` (Tensor): `(..., D)` (unit) vector 1
`v2` (Tensor): `(..., D)` (unit) vector 2
`t` (Tensor): `(..., N)` interpolation parameter in [0, 1]
## Returns
Tensor: `(..., N, D)` interpolated unit vector"""
utils3d.torch.transforms.slerp
@overload
def slerp_rotation_matrix(R1: torch_.Tensor, R2: torch_.Tensor, t: Union[numbers.Number, torch_.Tensor]) -> torch_.Tensor:
"""Spherical linear interpolation between two 3D rotation matrices
## Parameters
R1 (Tensor): shape (..., 3, 3), the first rotation matrix
R2 (Tensor): shape (..., 3, 3), the second rotation matrix
t (Tensor): scalar or shape (..., N), the interpolation factor
## Returns
Tensor: shape (..., N, 3, 3), the interpolated rotation matrix"""
utils3d.torch.transforms.slerp_rotation_matrix
@overload
def interpolate_se3_matrix(T1: torch_.Tensor, T2: torch_.Tensor, t: torch_.Tensor):
"""Interpolate between two SE(3) transformation matrices.
- Spherical linear interpolation (SLERP) is used for the rotational part.
- Linear interpolation is used for the translational part.
## Parameters
- `T1` (Tensor): (..., 4, 4) SE(3) matrix 1
- `T2` (Tensor): (..., 4, 4) SE(3) matrix 2
- `t` (Tensor): (..., N) interpolation parameter in [0, 1]
## Returns
Tensor: (..., N, 4, 4) interpolated SE(3) matrix"""
utils3d.torch.transforms.interpolate_se3_matrix
@overload
def extrinsics_to_essential(extrinsics: torch_.Tensor):
"""extrinsics matrix `[[R, t] [0, 0, 0, 1]]` such that `x' = R (x - t)` to essential matrix such that `x' E x = 0`
## Parameters
extrinsics (Tensor): [..., 4, 4] extrinsics matrix
## Returns
(Tensor): [..., 3, 3] essential matrix"""
utils3d.torch.transforms.extrinsics_to_essential
@overload
def rotation_matrix_2d(theta: Union[float, torch_.Tensor]):
"""2x2 matrix for 2D rotation
## Parameters
theta (float | Tensor): rotation angle in radians, arbitrary shape (...,)
## Returns
(Tensor): (..., 2, 2) rotation matrix"""
utils3d.torch.transforms.rotation_matrix_2d
@overload
def rotate_2d(theta: Union[float, torch_.Tensor], center: torch_.Tensor = None):
"""3x3 matrix for 2D rotation around a center
```
[[Rxx, Rxy, tx],
[Ryx, Ryy, ty],
[0, 0, 1]]
```
## Parameters
theta (float | Tensor): rotation angle in radians, arbitrary shape (...,)
center (Tensor): rotation center, arbitrary shape (..., 2). Default to (0, 0)
## Returns
(Tensor): (..., 3, 3) transformation matrix"""
utils3d.torch.transforms.rotate_2d
@overload
def translate_2d(translation: torch_.Tensor):
"""Translation matrix for 2D translation
```
[[1, 0, tx],
[0, 1, ty],
[0, 0, 1]]
```
## Parameters
translation (Tensor): translation vector, arbitrary shape (..., 2)
## Returns
(Tensor): (..., 3, 3) transformation matrix"""
utils3d.torch.transforms.translate_2d
@overload
def scale_2d(scale: Union[float, torch_.Tensor], center: torch_.Tensor = None):
"""Scale matrix for 2D scaling
```
[[s, 0, tx],
[0, s, ty],
[0, 0, 1]]
```
## Parameters
scale (float | Tensor): scale factor, arbitrary shape (...,)
center (Tensor): scale center, arbitrary shape (..., 2). Default to (0, 0)
## Returns
(Tensor): (..., 3, 3) transformation matrix"""
utils3d.torch.transforms.scale_2d
@overload
def transform_points(x: torch_.Tensor, *Ts: torch_.Tensor) -> torch_.Tensor:
"""Apply transformation(s) to a point or a set of points.
It is like `(Tn @ ... @ T2 @ T1 @ x[:, None]).squeeze(0)`, but:
1. Automatically handle the homogeneous coordinate;
- x will be padded with homogeneous coordinate 1.
- Each T will be padded by identity matrix to match the dimension.
2. Using efficient contraction path when array sizes are large, based on `einsum`.
## Parameters
- `x`: Tensor, shape `(..., D)`: the points to be transformed.
- `Ts`: Tensor, shape `(..., D + 1, D + 1)`: the affine transformation matrix (matrices)
If more than one transformation is given, they will be applied in corresponding order.
## Returns
- `y`: Tensor, shape `(..., D)`: the transformed point or a set of points.
## Example Usage
- Just linear transformation
```
y = transform(x_3, mat_3x3)
```
- Affine transformation
```
y = transform(x_3, mat_3x4)
```
- Chain multiple transformations
```
y = transform(x_3, T1_4x4, T2_3x4, T3_3x4)
```"""
utils3d.torch.transforms.transform_points
@overload
def angle_between(v1: torch_.Tensor, v2: torch_.Tensor, eps: float = 1e-08) -> torch_.Tensor:
"""Calculate the angle between two (batches of) vectors.
Better precision than using the arccos dot product directly.
## Parameters
- `v1`: Tensor, shape (..., D): the first vector.
- `v2`: Tensor, shape (..., D): the second vector.
- `eps`: float, optional: prevents zero angle difference (indifferentiable).
## Returns
`angle`: Tensor, shape (...): the angle between the two vectors."""
utils3d.torch.transforms.angle_between
@overload
def kabasch(cov: torch_.Tensor, eps: float = 1e-12):
"""Backward gradients friendly Kabasch method (compute rotation from input covarience matrix).
"""
utils3d.torch.pose.kabasch
@overload
def umeyama(cov_yx: torch_.Tensor, cov_xx: Optional[torch_.Tensor] = None, cov_yy: Optional[torch_.Tensor] = None, mean_x: Optional[torch_.Tensor] = None, mean_y: Optional[torch_.Tensor] = None, eps: float = 1e-12) -> Tuple[torch_.Tensor, torch_.Tensor, torch_.Tensor]:
"""Umeyama method to solve for scale `s`, rotation `R` and translation `t` such that `y_i ~= s R x_i + t`.
Parameters
----
- `cov_yx`: (..., 3, 3) covariance matrix between y and x points.
- `cov_xx`: (..., 3, 3) covariance matrix of x points. If None, no scaling is solved.
- `cov_yy`: (..., 3, 3) covariance matrix of y points. If None, no scaling is solved.
- `mean_x`: (..., 3) mean of x points. If None, no translation is solved.
- `mean_y`: (..., 3) mean of y points. If None, no translation is solved.
Specifically, based on provided inputs:
- To solve the rotation `R`, `cov_yx` must be given.
- To solve the scale `s`, at least one of `cov_xx` and `cov_yy` must be given.
- (Recommended) If both `cov_xx` and `cov_yy` are given, the scale will be solved by minimizing a symmetric cost:
`||s R X + t - Y||_F^2 / ||Y||_F^2 + ||s R^T (Y - t) - X||_F^2 / ||X||_F^2`
- If only `cov_xx` is given, the scale will be solved by minimizing forward cost
`||s R X + t - Y||_F^2`
- If only `cov_yy` is given, the scale will be solved by minimizing inverse cost
`||s R^T (Y - t) - X||_F^2`
- To solve the translation `t`, provide `mean_x` and `mean_y`.
Returns
----
- `s`: (...) scale factor. None if both cov_xx and cov_yy are None.
- `R`: (..., 3, 3) rotation matrix.
- `t`: (..., 3) translation vector. None if mean_x or mean_y is None."""
utils3d.torch.pose.umeyama
@overload
def affine_umeyama(cov_yx: torch_.Tensor, cov_xx: torch_.Tensor, cov_yy: torch_.Tensor, mean_x: torch_.Tensor, mean_y: torch_.Tensor, lam: float = 0.01, niter: int = 8, eps: float = 1e-12) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Extended Procrustes analysis to solve for affine transformation `A` and translation `t` such that `y_i ~= A x_i + t`.
NOTE: This function is indifferentiable due to the iterative solving process.
Parameters
----
- `cov_yx`: (..., 3, 3) covariance matrix between y and x points.
- `cov_xx`: (..., 3, 3) covariance matrix of x points.
- `cov_yy`: (..., 3, 3) covariance matrix of y points.
- `mean_x`: (..., 3) mean of x points.
- `mean_y`: (..., 3) mean of y points.
- `lam`: rigidity regularization weight.
- `gamma`: symmetricity regularization annealing factor.
- `niter`: number of iterations for solving.
Returns
----
- `A`: (..., 3, 3) affine transformation matrix.
- `t`: (..., 3) translation vector."""
utils3d.torch.pose.affine_umeyama
@overload
def solve_pose(p: torch_.Tensor, q: torch_.Tensor, w: Optional[torch_.Tensor] = None, *, mode: Literal['rigid', 'similar', 'affine'] = 'rigid', lam: float = 0.01, niter: int = 5, eps: float = 1e-12) -> torch_.Tensor:
"""Solve for the pose (transformation from p to q) given weighted point correspondences.
Parameters
----
- `p`: (..., N, 3) source points
- `q`: (..., N, 3) target points
- `w`: optional (..., N) weights for each point correspondence. If None, uniform weights are used.
- `mode`: mode of transformation to apply. Can be 'rigid', 'similar', or 'affine'.
- For 'rigid', only rotation and translation are allowed.
- For 'similar', uniform scaling, rotation and translation are allowed.
- For 'affine', full affine transformation is allowed. Using least squares.
- `lam`: regularization weight for 'affine' mode.
- `niter`: number of iterations for 'affine' mode.
- `eps`: small value to prevent division by zero.
Returns
----
- `pose`: (..., 4, 4) transformations matrix from p to q."""
utils3d.torch.pose.solve_pose
@overload
def segment_solve_pose(p: torch_.Tensor, q: torch_.Tensor, w: Optional[torch_.Tensor] = None, *, offsets: torch_.Tensor, mode: Literal['rigid', 'similar', 'affine'] = 'rigid', lam: float = 0.01, niter: int = 5, eps: float = 1e-12) -> torch_.Tensor:
"""Solve for the pose (transformation from p to q: q ≈ pose @ p) given weighted point correspondences.
NOTE: Affine mode is solved by iterative method and may be indifferentiable. Use with `torch.no_grad()` if you don't need gradients.
Parameters
----
- `p`: (N, 3) source points
- `q`: (N, 3) target points
- `w`: (N,) weights for each point correspondence
- `offsets`: (S + 1,) segment offsets. Points in each segment belong to the same rigid / affine body.
- `mode`: mode of transformation to apply. Can be 'rigid', 'similar', or 'affine'.
- For 'rigid', only rotation and translation are allowed.
- For 'similar', uniform scaling, rotation and translation are allowed.
- For 'affine', full affine transformation is allowed. Using least squares.
- `lam`: regularization weight for 'affine' mode.
- `niter`: number of iterations for 'affine' mode.
- `eps`: small value to prevent division by zero.
Returns
----
- `pose`: (S, 4, 4) transformations matrix from p to q."""
utils3d.torch.pose.segment_solve_pose
@overload
def pose_graph_optimization(num_nodes: int, edges: torch_.Tensor, poses: torch_.Tensor, w: torch_.Tensor | None = None, niter: int = 10) -> tuple[torch_.Tensor, torch_.Tensor, torch_.Tensor]:
"""Pose graph optimization to solve for global poses given relative poses (must be rigid transformations).
Parameters
----
- `num_nodes`: number of nodes `N` in the pose graph.
- `edges`: (E, 2) edge list of the pose graph. Each edge is represented by a pair of node indices `i -> j`.
- `poses`: (E, 4, 4) relative poses of transformation from node `i` to node `j` for each edge. Must be rigid transformations.
- `w`: (E,) optional weights for each edge.
- `niter`: number of Procrustes iterations to refine global poses. If 0, only the initial solution by Laplacian SVD is returned.
Returns
----
- `poses_global`: (N, 4, 4) global poses (world-to-camera, canonical-to-observation, global-to-node, etc.) for each node.
`poses_relative[i->j] ≈ poses_global[j] @ poses_global[i].inv()`"""
utils3d.torch.pose.pose_graph_optimization
@overload
def segment_roll(data: torch_.Tensor, offsets: torch_.Tensor, shift: int, dim: int = 0) -> torch_.Tensor:
"""Roll the data within each segment.
Parameters
------
- `data`: (Tensor).
- `offsets`: (Tensor) shape `(M + 1,)` the offsets of the segmented data. `M` is the number of segments. Starts with 0 and end with `data.shape[dim]`.
- `shift`: (int) the number of places by which elements are shifted. If negative, shift to left.
- `dim`: (int) the segment dimension to roll along. Default is 0.
Returns
-------
- `data`: (Tensor) the rolled data, same shape as input."""
utils3d.torch.segment_ops.segment_roll
@overload
def segment_take(data: torch_.Tensor, offsets: torch_.Tensor, taking: torch_.Tensor, dim: int = 0) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Take some segments from a segmented array
Parameters
------
- `data`: (Tensor) the segmented data.
- `offsets`: (Tensor) 1-D tensor of shape `(M + 1,)` the offsets of the segmented data. `M` is the number of segments. Starts with 0 and end with `data.shape[dim]`.
- `taking`: (Tensor) 1-D tensor of the indices of segments to take of shape `(K,)`, or boolean mask of shape `(M,)`
- `dim`: (int) the segment dimension to take along. Default is 0. Other dimensions are treated as batch dimensions.
Returns
-------
- `new_data`: (Tensor) the new segmented data.
- `new_offsets`: (Tensor) shape `(K + 1,)` the offsets of the new segmented data. `K` is the number of taken segments."""
utils3d.torch.segment_ops.segment_take
@overload
def segment_concatenate(segments: Sequence[Tuple[torch_.Tensor, torch_.Tensor]], dim: int = 0) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Concatenate segmented arrays within each segment. All numbers of segments remain the same.
Parameters
------
- `segments`: (Sequence[Tuple[Tensor, Tensor]]) A sequence of segmented arrays:
- `data`: (Tensor) shape `(..., N_i, ...)`
- `offsets`: (Tensor) shape `(M + 1,)` segment offsets.
- `axis`: (int) the segment axis.
Returns
-------
- `data`: (Tensor) shape `(..., sum(N_i), ...)` the concatenated data
- `offsets`: (Tensor) shape `(M + 1,)` the offsets of the concatenated segmented data."""
utils3d.torch.segment_ops.segment_concatenate
@overload
def segment_concat(segments: Sequence[Tuple[torch_.Tensor, torch_.Tensor]], axis: int = 0) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""(Alias for segment_concatenate).
Concatenate segmented arrays within each segment.
Parameters
------
- `segments`: (Sequence[Tuple[Tensor, Tensor]]) A sequence of segmented arrays:
- `data`: (Tensor) shape `(..., N_i, ...)`
- `offsets`: (Tensor) shape `(M + 1,)` segment offsets.
- `axis`: (int) the segment axis.
Returns
-------
- `data`: (Tensor) shape `(N, *data_dims)` the concatenated data
- `offsets`: (Tensor) shape `(M + 1,)` the offsets of the concatenated segmented data."""
utils3d.torch.segment_ops.segment_concat
@overload
def segment_chain(segments: Sequence[Tuple[torch_.Tensor, torch_.Tensor]], axis: int = 0) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Concatenate segmented arrays in sequence. The number of segments are summed.
Parameters
------
- `segments`: (Sequence[Tuple[Tensor, Tensor]]) A sequence of segmente arrays:
- `data`: (Tensor) shape `(..., N_i, ...)`
- `offsets`: (Tensor) shape `(M + 1,)` segment offsets.
- `axis`: (int) the segment axis.
Returns
-------
- `data`: (Tensor) shape `(..., sum(N_i), ...)` the chain-concatenated data
- `offsets`: (Tensor) shape `(sum(M_i) + 1,)` the offsets of the concatenated segmented data."""
utils3d.torch.segment_ops.segment_chain
@overload
def segment_argmax(data: torch_.Tensor, offsets: torch_.Tensor, dim: int = 0) -> torch_.Tensor:
"""Compute the argmax of each segment in the segmented data.
Parameters
----------
- `data`: (Tensor) shape `(..., N, ...)` the data to compute argmax from. If `data` may have multiple dimensions, extra dimensions are treated as batch dimensions.
- `offsets`: (Tensor) shape `(M + 1,)` the offsets of the segmented data
- `dim`: (int) the segment axis to compute along. Default is 0.
Returns
-------
- `argmax_indices`: (Tensor) shape `(..., M, ...)` the argmax indices of each segment along the first dimension.
NOTE: If there are multiple maximum values in a segment, the index of the first one is returned. If a segment is empty, -1 is returned."""
utils3d.torch.segment_ops.segment_argmax
@overload
def segment_argmin(data: torch_.Tensor, offsets: torch_.Tensor, dim: int = 0) -> torch_.Tensor:
"""Compute the argmin of each segment in the segmented data.
Parameters
----------
- `data`: (Tensor) shape `(..., N, ...)` the data to compute argmin from. If `data` may have multiple dimensionsm, extra dimensions are treated as batch dimensions.
- `offsets`: (Tensor) shape `(M + 1,)` the offsets of the segmented data
- `dim`: (int) the segment axis to compute along. Default is 0.
Returns
-------
- `argmin_indices`: (Tensor) shape `(..., M, ...)` the argmin indices of each segment along the first dimension.
NOTE: If there are multiple minimum values in a segment, the index of the first one is returned. If a segment is empty, -1 is returned."""
utils3d.torch.segment_ops.segment_argmin
@overload
def segment_median(input: torch_.Tensor, offsets: torch_.Tensor, dim: int = 0) -> torch_.return_types.median:
"""Compute the median of each segment.
Parameters
----
- `input`: (Tensor) shape `(..., N, ...)` the data to compute median from. The first dimension is treated as the segment dimension. Extra dimensions are treated as batch dimensions.
- `offsets`: (Tensor) shape `(M + 1,)` the offsets of each segment.
- `dim`: (int) the segment axis to compute along. Default is 0.
Returns
----
- `medians`: (Tensor) shape `(..., M, ...)` the median of each segment.
- `indices`: (Tensor) shape `(..., M, ...)` the indices of the median values in the original input.
Notes
-----
- If a segment has even length, the lower median is returned.
- If a segment is empty or has negative length, the median value is undefined."""
utils3d.torch.segment_ops.segment_median
@overload
def segment_sum(input: torch_.Tensor, offsets: torch_.Tensor, dim: int = 0) -> torch_.Tensor:
"""Compute the sum of each segment in the segmented data. Workaround supports for dtypes other than float32.
NOTE: Silently assumes that the input does not contain negative lengths.
Parameters
----
- `input`: (Tensor) shape `(..., N, ...)` the data to compute sum from. If `input` may have multiple dimensionsm, extra dimensions are treated as batch dimensions.
- `offsets`: (Tensor) shape `(M + 1,)` the offsets of the segmented data
- `dim`: (int) the segment axis to compute sum along. Default is 0.
Returns
----
- `segment_sums`: (Tensor) shape `(..., M, ...)` the sum of each segment along the specified dimension."""
utils3d.torch.segment_ops.segment_sum
@overload
def segment_cumsum(input: torch_.Tensor, offsets: torch_.Tensor, dim: int) -> torch_.Tensor:
"""Compute the sum of each segment in the segmented data. Workaround supports for dtypes other than float32.
NOTE: Silently assumes that the input does not contain negative lengths.
Parameters
----
- `input`: (Tensor) shape `(..., N, ...)` the data to compute sum from. If `input` may have multiple dimensionsm, extra dimensions are treated as batch dimensions.
- `offsets`: (Tensor) shape `(M + 1,)` the offsets of the segmented data
Returns
----
- `segment_sums`: (Tensor) shape `(..., N, ...)` the cumulative sum of each segment along the specified dimension."""
utils3d.torch.segment_ops.segment_cumsum
@overload
def group_as_segments(labels: torch_.Tensor, data: Optional[torch_.Tensor] = None, return_inverse: bool = False, return_group_ids: bool = False) -> Tuple[torch_.Tensor, ...]:
"""Group as segments by labels
Parameters
----
- `labels` (Tensor): shape `(N, *label_dims)` array of labels for each data point. Labels can be multi-dimensional.
- `data` (Tensor, optional): shape `(N, *data_dims)` array.
If None, return the indices in each group instead.
Returns
-------
Assuming there are `M` difference labels:
- `grouped_labels`: `(Tensor)` shape `(M, *label_dims)` labels of of each segment
- `grouped_data`: `(Tensor)` shape `(N,)` or `(N, *data_dims)` the rearranged data (or indices) where the same labels are grouped as a continous segment.
- `offsets`: `(Tensor)` shape `(M + 1,)`. `grouped_data[offsets[i]:offsets[i + 1]]` corresponding to the i-th segment whose label is `grouped_labels[i]`
- `inverse_indices` (Tensor, optional): shape `(N,)`. `data[inverse_indices]` recovers the original data order,
i.e., `inverse_indices[i]` gives the position that `data[i]` goes to in the `grouped_data`.
- `group_ids` (Tensor, optional): shape `(N,)`. The group id for each data point in the original order,
i.e., `group_ids[i]` gives the group index that `data[i]` belongs to. """
utils3d.torch.segment_ops.group_as_segments
@overload
def segment_sort(input: torch_.Tensor, offsets: torch_.Tensor = None, descending: bool = False, dim: int = -1) -> torch_.return_types.sort:
"""Sort the data within each segment.
Parameters
----
- `input`: (Tensor) shape `(..., N, ...)` the data to sort.
- `lengths`: (Tensor) shape `(M,)` the lengths of each segment, alternatively to `offsets`.
- `offsets`: (Tensor) shape `(M + 1,)` the offsets
- `descending`: (bool) whether to sort in descending order.
- `dim`: (int) the segment axis to sort along. Default is -1.
Returns
----
- `sorted`: (Tensor) shape `(..., N, ...)` the sorted data.
- `indices`: (Tensor) shape `(..., N, ...)` the indices that would sort the data within each segment."""
utils3d.torch.segment_ops.segment_sort
@overload
def segment_argsort(input: torch_.Tensor, offsets: torch_.Tensor, descending: bool = False, dim: int = -1) -> torch_.Tensor:
"""Compute the argsort indices within each segment.
Parameters
----
- `input`: (Tensor) shape `(..., N, ...)` the data to sort. The first dimension is treated as the segment dimension. Extra dimensions are treated as batch dimensions.
- `offsets`: (Tensor) shape `(M + 1,)` the offsets of each segment.
- `descending`: (bool) whether to sort in descending order.
- `dim`: (int) the segment axis to sort along. Default is -1.
Returns
----
- `sorted_indices`: (Tensor) shape `(..., N, ...)` the indices that would sort the data within each segment."""
utils3d.torch.segment_ops.segment_argsort
@overload
def segment_topk(input: torch_.Tensor, offsets: torch_.Tensor, k: Union[int, torch_.Tensor], largest: bool = True, dim: int = -1) -> Tuple[torch_.return_types.topk, torch_.Tensor]:
"""Select the top-k values and indices within each segment.
Parameters
----
- `input`: (Tensor) shape `(..., N, ...)` the data to compute top
- `k`: (int or Tensor) the number of top elements to retrieve from each segment. If a Tensor, it should have shape `(M,)` where `M` is the number of segments.
- `offsets`: (Tensor) shape `(M + 1,)` the offsets of each segment.
- `largest`: (bool) whether to return the largest or smallest elements. Otherwise, return the smallest elements.
- `dim`: (int) the segment axis to compute along. Default is -1.
Returns
----
- `topk`: (namedtuple) with fields `values` and `indices`.
- `values`: (Tensor) shape `(sum_k, ...)` the top-k values where `sum_k` is the sum of all k's across segments.
- `indices`: (Tensor) shape `(sum_k, ...)` the indices of the top-k values in the original input.
- `offsets`: (Tensor) shape `(M + 1,)` the offsets of the top-k values for each segment.
Notes
-----
- If the length of a segment is less than k, the returns will contain all elements in that segment but fewer than k elements."""
utils3d.torch.segment_ops.segment_topk
@overload
def stack_segments(input: torch_.Tensor, offsets: torch_.Tensor, max_length: int = None, padding_value: numbers.Number = 0, dim: int = 0) -> Tuple[torch_.Tensor, torch_.Tensor, torch_.Tensor]:
"""Stack segments into a padded tensor.
Parameters
----
- `input`: (Tensor) shape `(..., N, ...)` the data to stack.
- `offsets`: (Tensor) shape `(M + 1,)` the offsets of each segment.
- `max_length`: (int, optional) the maximum length to pad/truncate each segment to. If None, use the maximum segment length.
- `padding_value`: (Number) the value to use for padding.
- `dim`: (int) the segment axis to stack along. Default is 0.
Returns
----
- `stacked`: (Tensor) shape `(..., M, max_length, ...)` the stacked segments, where `max_length` is the maximum segment length.
- `mask`: (Tensor) shape `(..., M, max_length)` boolean mask indicating valid entries in `stacked`.
- `indices`: (Tensor) shape `(..., M, max_length)` the indices of the stacked entries in the original input."""
utils3d.torch.segment_ops.stack_segments
@overload
def segment_multinomial(weights: torch_.Tensor, offsets: torch_.Tensor, num_samples: torch_.Tensor, eps: float = 1e-12, replacement: bool = False) -> torch_.LongTensor:
"""Perform multinomial sampling within each segment.
Parameters
----
- `weights`: (Tensor) 1-D tensor of shape `(N,)` the weights for sampling.
- `offsets`: (Tensor) 1-D tensor of shape `(M + 1,)` the offsets of each segment.
- `n`: (int) the number of samples to draw from each segment.
- `eps`: (float) a small value to avoid division by zero.
- `replacement`: (bool) whether to sample with replacement.
Returns
----
- `sampled_indices`: (LongTensor) shape `(tot_samples,)` the sampled indices from each segment.
- `offsets`: (LongTensor) shape `(M + 1,)` the offsets of the sampled indices for each segment."""
utils3d.torch.segment_ops.segment_multinomial
@overload
def segment_combinations(input: torch_.Tensor, offsets: torch_.Tensor, r: int = 2, with_replacement: bool = False) -> torch_.Tensor:
"""Generate all combinations of elements within each segment. Vectorized implementation.
Parameters
----
- `input`: (Tensor) shape `(N,)` the data to generate combinations from. The first dimension is treated as the segment dimension. Extra dimensions are treated as batch dimensions.
- `offsets`: (Tensor) shape `(M + 1,)` the offsets of each segment.
- `r`: (int) the number of elements in each combination.
- `with_replacement`: (bool) whether to allow repeated elements in a combination.
Returns
----
- `combinations`: (Tensor) shape `(K, r,)` the combinations from all segments, where `K` is the total number of combinations across all segments.
- `combination_offsets`: (Tensor) shape `(M + 1,)` the offsets of combinations for each segment.
Notes
----
- The result may contain zero-length segments if a segment has less than `r` elements."""
utils3d.torch.segment_ops.segment_combinations
@overload
def segment_searchsorted(sorted_sequence: torch_.Tensor, offsets: torch_.Tensor, input: torch_.Tensor, segment_ids: torch_.Tensor, side: Literal['left', 'right'] = 'left') -> torch_.Tensor:
"""Per-segment searchsorted operation implemented with triton.
Parameters
----------
- `sorted_sequence: Tensor` of shape (..., N), the concatenated sorted sequences of all segments.
- `offsets: Tensor` of shape (M + 1,), segment offsets applied to the last dimension of `sorted_sequence`.
- `input: Tensor` of shape (..., Q), the values to search for.
- `segment_ids: Tensor` of shape (..., Q), the segment ids to search within for each value in `input`.
Returns
- `indices: Tensor` of shape (..., Q), the insertion indices for each value in `input` within its corresponding segment in `sorted_sequence`."""
utils3d.torch.segment_ops.segment_searchsorted
@overload
def triangulate_mesh(faces: torch_.Tensor, vertices: torch_.Tensor = None, method: Literal['fan', 'strip', 'diagonal'] = 'fan') -> torch_.Tensor:
"""Triangulate a polygonal mesh.
## Parameters
- `faces` (Tensor): [L, P] polygonal faces
- `vertices` (Tensor, optional): [N, 3] 3-dimensional vertices.
If given, the triangulation is performed according to the distance
between vertices. Defaults to None.
- `method`
## Returns
(Tensor): [L * (P - 2), 3] triangular faces"""
utils3d.torch.mesh.triangulate_mesh
@overload
def compute_face_corner_angles(vertices: torch_.Tensor, faces: Optional[torch_.Tensor] = None) -> torch_.Tensor:
"""Compute face corner angles of a mesh
## Parameters
- `vertices` (Tensor): `(..., N, 3)` vertices if `faces` is provided, or `(..., F, P, 3)` if `faces` is None
- `faces` (Tensor, optional): `(F, P)` face vertex indices, where P is the number of vertices per face
## Returns
- `angles` (Tensor): `(..., F, P)` face corner angles"""
utils3d.torch.mesh.compute_face_corner_angles
@overload
def compute_face_corner_normals(vertices: torch_.Tensor, faces: Optional[torch_.Tensor] = None, normalize: bool = True) -> torch_.Tensor:
"""Compute the face corner normals of a mesh
## Parameters
- `vertices` (Tensor): `(..., N, 3)` vertices if `faces` is provided, or `(..., F, P, 3)` if `faces` is None
- `faces` (Tensor, optional): `(F, P)` face vertex indices, where P is the number of vertices per face
- `normalize` (bool): whether to normalize the normals to unit vectors. If not, the normals are the raw cross products.
## Returns
- `normals` (Tensor): (..., F, P, 3) face corner normals"""
utils3d.torch.mesh.compute_face_corner_normals
@overload
def compute_face_corner_tangents(vertices: torch_.Tensor, uv: torch_.Tensor, faces_vertices: Optional[torch_.Tensor] = None, faces_uv: Optional[torch_.Tensor] = None, normalize: bool = True) -> torch_.Tensor:
""" Compute the face corner tangent (and bitangent) vectors of a mesh
## Parameters
- `vertices` (Tensor): `(..., N, 3)` if `faces` is provided, or `(..., F, P, 3)` if `faces_vertices` is None
- `uv` (Tensor): `(..., N, 2)` if `faces` is provided, or `(..., F, P, 2)` if `faces_uv` is None
- `faces_vertices` (Tensor, optional): `(F, P)` face vertex indices
- `faces_uv` (Tensor, optional): `(F, P)` face UV indices
- `normalize` (bool): whether to normalize the tangents to unit vectors. If not, the tangents (dX/du, dX/dv) matches the UV parameterized manifold.
s
## Returns
- `tangents` (Tensor): `(..., F, P, 3, 2)` face corner tangents (and bitangents),
where the last dimension represents the tangent and bitangent vectors.
"""
utils3d.torch.mesh.compute_face_corner_tangents
@overload
def compute_face_normals(vertices: torch_.Tensor, faces: Optional[torch_.Tensor] = None) -> torch_.Tensor:
"""Compute face normals of a mesh
## Parameters
- `vertices` (Tensor): `(..., N, 3)` vertices if `faces` is provided, or `(..., F, P, 3)` if `faces` is None
- `faces` (Tensor, optional): `(F, P)` face vertex indices, where P is the number of vertices per face
## Returns
- `normals` (Tensor): `(..., F, 3)` face normals. Always normalized."""
utils3d.torch.mesh.compute_face_normals
@overload
def compute_face_tangents(vertices: torch_.Tensor, uv: torch_.Tensor, faces_vertices: Optional[torch_.Tensor] = None, faces_uv: Optional[torch_.Tensor] = None, normalize: bool = True) -> torch_.Tensor:
"""Compute the face corner tangent (and bitangent) vectors of a mesh
## Parameters
- `vertices` (Tensor): `(..., N, 3)` if `faces` is provided, or `(..., F, P, 3)` if `faces_vertices` is None
- `uv` (Tensor): `(..., N, 2)` if `faces` is provided, or `(..., F, P, 2)` if `faces_uv` is None
- `faces_vertices` (Tensor, optional): `(F, P)` face vertex indices
- `faces_uv` (Tensor, optional): `(F, P)` face UV indices
## Returns
- `tangents` (Tensor): `(..., F, 3, 2)` face corner tangents (and bitangents),
where the last dimension represents the tangent and bitangent vectors."""
utils3d.torch.mesh.compute_face_tangents
@overload
def mesh_edges(faces: torch_.Tensor, return_face2edge: bool = False, return_edge2face: bool = False, return_counts: bool = False) -> Tuple[torch_.Tensor, torch_.Tensor, torch_.Tensor, torch_.Tensor]:
"""Get undirected edges of a mesh. Optionally return additional mappings.
## Parameters
- `faces` (Tensor): polygon faces
- `(F, P)` dense array of indices, where each face has `P` vertices.
- `(F, V)` binary sparse csr array of indices, each row corresponds to the vertices of a face.
- `return_face2edge` (bool): whether to return the face to edge mapping
- `return_edge2face` (bool): whether to return the edge to face mapping
- `return_counts` (bool): whether to return the counts of edges
## Returns
- `edges` (Tensor): `(E, 2)` unique edges' vertex indices
If `return_face2edge`, `return_edge2face`, `return_opposite_edge`, or `return_counts` is True, the corresponding outputs will be appended in order:
- `face2edge` (Tensor): mapping from faces to the indices of edges
- `(F, P)` if input `faces` is a dense array
- `(F, E)` if input `faces` is a sparse csr array
- `edge2face` (Tensor): `(E, F)` binary sparse CSR matrix of edge to face.
- `counts` (Tensor): `(E,)` counts of each edge"""
utils3d.torch.mesh.mesh_edges
@overload
def mesh_half_edges(faces: torch_.Tensor, return_face2edge: bool = False, return_edge2face: bool = False, return_twin: bool = False, return_next: bool = False, return_prev: bool = False, return_counts: bool = False) -> Tuple[torch_.Tensor, torch_.Tensor, torch_.Tensor, torch_.Tensor, torch_.Tensor, torch_.Tensor, torch_.Tensor]:
"""Get half edges of a mesh. Optionally return additional mappings.
## Parameters
- `faces` (Tensor): polygon faces
- `(F, P)` dense array of indices, where each face has `P` vertices.
- `(F, V)` binary sparse csr array of indices, each row corresponds to the vertices of a face.
- `return_face2edge` (bool): whether to return the face to edge mapping
- `return_edge2face` (bool): whether to return the edge to face mapping
- `return_twin` (bool): whether to return the mapping from one edge to its opposite/twin edge
- `return_next` (bool): whether to return the mapping from one edge to its next edge in the face loop
- `return_prev` (bool): whether to return the mapping from one edge to its previous edge in the face loop
- `return_counts` (bool): whether to return the counts of edges
## Returns
- `edges` (Tensor): `(E, 2)` unique edges' vertex indices
If `return_face2edge`, `return_edge2face`, `return_opposite_edge`, or `return_counts` is True, the corresponding outputs will be appended in order:
- `face2edge` (Tensor | Tensor): mapping from faces to the indices of edges
- `(F, P)` if input `faces` is a dense array
- `(F, E)` if input `faces` is a sparse csr array
- `edge2face` (Tensor): `(E, F)` binary sparse CSR matrix of edge to face.
- `twin` (Tensor): `(E,)` mapping from edges to indices of opposite edges. -1 if not found.
- `next` (Tensor): `(E,)` mapping from edges to indices of next edges in the face loop.
- `prev` (Tensor): `(E,)` mapping from edges to indices of previous edges in the face loop.
- `counts` (Tensor): `(E,)` counts of each half edge
NOTE: If the mesh is not manifold, `twin`, `next`, and `prev` can point to arbitrary one of the candidates."""
utils3d.torch.mesh.mesh_half_edges
@overload
def mesh_dual_graph(faces: torch_.Tensor) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Get dual graph of a mesh. (Mesh face as dual graph's vertex, adjacency by edge sharing)
## Parameters
- `faces`: `Tensor` faces indices
- `(F, P)` dense tensor
## Returns
- `dual_graph` (Tensor): `(F, F)` binary sparse CSR matrix. Adjacency matrix of the dual graph."""
utils3d.torch.mesh.mesh_dual_graph
@overload
def mesh_connected_components(faces: torch_.Tensor, num_vertices: Optional[int] = None) -> List[torch_.Tensor]:
"""Compute connected components of a mesh.
## Parameters
- `faces` (Tensor): polygon faces
- `(F, P)` dense tensor of indices, where each face has `P` vertices.
- `(F, V)` binary sparse csr tensor of indices, each row corresponds to the vertices of a face.
- `num_vertices` (int, optional): total number of vertices. If given, the returned components will include all vertices. Defaults to None.
## Returns
If `num_vertices` is given, return:
- `labels` (Tensor): (N,) component labels of each vertex
If `num_vertices` is None, return:
- `vertices_ids` (Tensor): (N,) vertex indices that are in the edges
- `labels` (Tensor): (N,) component labels corresponding to `vertices_ids`"""
utils3d.torch.mesh.mesh_connected_components
@overload
def graph_connected_components(edges: torch_.Tensor, num_vertices: Optional[int] = None) -> Union[torch_.Tensor, Tuple[torch_.Tensor, torch_.Tensor]]:
"""Compute connected components of an undirected graph.
## Parameters
- `edges` (Tensor): (E, 2) edge indices
## Returns
If `num_vertices` is given, return:
- `labels` (Tensor): (N,) component labels of each vertex
If `num_vertices` is None, return:
- `vertices_ids` (Tensor): (N,) vertex indices that are in the edges
- `labels` (Tensor): (N,) component labels corresponding to `vertices_ids`"""
utils3d.torch.mesh.graph_connected_components
@overload
def compute_boundaries(faces: torch_.Tensor, edges: torch_.Tensor = None, face2edge: torch_.Tensor = None, edge_degrees: torch_.Tensor = None) -> Tuple[List[torch_.Tensor], List[torch_.Tensor]]:
"""Compute boundary edges of a mesh.
## Parameters
faces (Tensor): [T, 3] triangular face indices
edges (Tensor): [E, 2] edge indices.
face2edge (Tensor): [T, 3] mapping from face to edge.
edge_degrees (Tensor): [E] degree of each edge.
## Returns
boundary_edge_indices (List[Tensor]): list of boundary edge indices
boundary_face_indices (List[Tensor]): list of boundary face indices"""
utils3d.torch.mesh.compute_boundaries
@overload
def remove_unused_vertices(faces: torch_.Tensor, *vertice_attrs, return_indices: bool = False) -> Tuple[torch_.Tensor, ...]:
"""Remove unreferenced vertices of a mesh.
Unreferenced vertices are removed, and the face indices are updated accordingly.
## Parameters
faces (Tensor): [T, P] face indices
*vertice_attrs: vertex attributes
## Returns
faces (Tensor): [T, P] face indices
*vertice_attrs: vertex attributes
indices (Tensor, optional): [N] indices of vertices that are kept. Defaults to None."""
utils3d.torch.mesh.remove_unused_vertices
@overload
def remove_corrupted_faces(faces: torch_.Tensor) -> torch_.Tensor:
"""Remove corrupted faces (faces with duplicated vertices)
## Parameters
faces (Tensor): [F, 3] face indices
## Returns
Tensor: [F_reduced, 3] face indices"""
utils3d.torch.mesh.remove_corrupted_faces
@overload
def remove_isolated_pieces(vertices: torch_.Tensor, faces: torch_.Tensor, connected_components: List[torch_.Tensor] = None, thresh_num_faces: int = None, thresh_radius: float = None, thresh_boundary_ratio: float = None, remove_unreferenced: bool = True) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Remove isolated pieces of a mesh.
Isolated pieces are removed, and the face indices are updated accordingly.
If no face is left, will return the largest connected component.
## Parameters
vertices (Tensor): [N, 3] 3-dimensional vertices
faces (Tensor): [T, 3] triangular face indices
connected_components (List[Tensor], optional): connected components of the mesh. If None, it will be computed. Defaults to None.
thresh_num_faces (int, optional): threshold of number of faces for isolated pieces. Defaults to None.
thresh_radius (float, optional): threshold of radius for isolated pieces. Defaults to None.
remove_unreferenced (bool, optional): remove unreferenced vertices after removing isolated pieces. Defaults to True.
## Returns
vertices (Tensor): [N_, 3] 3-dimensional vertices
faces (Tensor): [T, 3] triangular face indices"""
utils3d.torch.mesh.remove_isolated_pieces
@overload
def merge_duplicate_vertices(vertices: torch_.Tensor, faces: torch_.Tensor, tol: float = 1e-06) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Merge duplicate vertices of a triangular mesh.
Duplicate vertices are merged by selecte one of them, and the face indices are updated accordingly.
## Parameters
vertices (Tensor): [N, 3] 3-dimensional vertices
faces (Tensor): [T, 3] triangular face indices
tol (float, optional): tolerance for merging. Defaults to 1e-6.
## Returns
vertices (Tensor): [N_, 3] 3-dimensional vertices
faces (Tensor): [T, 3] triangular face indices"""
utils3d.torch.mesh.merge_duplicate_vertices
@overload
def subdivide_mesh(vertices: torch_.Tensor, faces: torch_.Tensor, n: int = 1) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Subdivide a triangular mesh by splitting each triangle into 4 smaller triangles.
NOTE: All original vertices are kept, and new vertices are appended to the end of the vertex list.
## Parameters
vertices (Tensor): [N, 3] 3-dimensional vertices
faces (Tensor): [T, 3] triangular face indices
n (int, optional): number of subdivisions. Defaults to 1.
## Returns
vertices (Tensor): [N_, 3] subdivided 3-dimensional vertices
faces (Tensor): [4 * T, 3] subdivided triangular face indices"""
utils3d.torch.mesh.subdivide_mesh
@overload
def compute_mesh_laplacian(vertices: torch_.Tensor, faces: torch_.Tensor, weight: str = 'uniform') -> torch_.Tensor:
"""Laplacian smooth with cotangent weights
## Parameters
vertices (Tensor): shape (..., N, 3)
faces (Tensor): shape (T, 3)
weight (str): 'uniform' or 'cotangent'"""
utils3d.torch.mesh.compute_mesh_laplacian
@overload
def laplacian_smooth_mesh(vertices: torch_.Tensor, faces: torch_.Tensor, weight: str = 'uniform', times: int = 5) -> torch_.Tensor:
"""Laplacian smooth with cotangent weights
## Parameters
vertices (Tensor): shape (..., N, 3)
faces (Tensor): shape (T, 3)
weight (str): 'uniform' or 'cotangent'"""
utils3d.torch.mesh.laplacian_smooth_mesh
@overload
def taubin_smooth_mesh(vertices: torch_.Tensor, faces: torch_.Tensor, lambda_: float = 0.5, mu_: float = -0.51) -> torch_.Tensor:
"""Taubin smooth mesh
## Parameters
vertices (Tensor): _description_
faces (Tensor): _description_
lambda_ (float, optional): _description_. Defaults to 0.5.
mu_ (float, optional): _description_. Defaults to -0.51.
## Returns
Tensor: _description_"""
utils3d.torch.mesh.taubin_smooth_mesh
@overload
def laplacian_hc_smooth_mesh(vertices: torch_.Tensor, faces: torch_.Tensor, times: int = 5, alpha: float = 0.5, beta: float = 0.5, weight: str = 'uniform'):
"""HC algorithm from Improved Laplacian Smoothing of Noisy Surface Meshes by J.Vollmer et al.
"""
utils3d.torch.mesh.laplacian_hc_smooth_mesh
@overload
def create_cube_mesh(tri: bool = False, device: Optional[torch_.device] = None) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Create a cube mesh of size 1 centered at origin.
### Parameters
tri (bool, optional): return triangulated mesh. Defaults to False, which returns quad mesh.
### Returns
vertices (Tensor): shape (8, 3) float32
faces (Tensor): shape (12, 3) int32"""
utils3d.torch.mesh.create_cube_mesh
@overload
def create_camera_frustum_mesh(extrinsics: torch_.Tensor, intrinsics: torch_.Tensor, depth: float = 1.0) -> Tuple[torch_.Tensor, torch_.Tensor, torch_.Tensor]:
"""Create a triangle mesh of camera frustum."""
utils3d.torch.mesh.create_camera_frustum_mesh
@overload
def create_icosahedron_mesh(device: Optional[torch_.device] = None) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Create an icosahedron mesh of centered at origin."""
utils3d.torch.mesh.create_icosahedron_mesh
@overload
def uv_map(*size: Union[int, Tuple[int, int]], top: float = 0.0, left: float = 0.0, bottom: float = 1.0, right: float = 1.0, dtype: torch_.dtype = torch_.float32, device: torch_.device = None) -> torch_.Tensor:
"""Get image UV coordinate map. By default, (0., 0.) is the top-left corner of the image, and (1., 1.) is the bottom-right corner of the image.
## Parameters
- `*size`: `Tuple[int, int]` or two integers of map size `(height, width)`
- `top`: `float` defaults to 0.
- `left`: `float` defaults to 0.
- `bottom`: `float` defaults to 1.
- `right`: `float` defaults to 1.
- `dtype`: `torch.dtype` data type of the output uv map. Defaults to torch.float32.
- `device`: `torch.device`, device of the output uv map. Defaults to None.
## Returns
- `uv (Tensor)`: shape `(height, width, 2)`
## Example Usage
>>> uv_map(10, 10):
[[[0.05, 0.05], [0.15, 0.05], ..., [0.95, 0.05]],
[[0.05, 0.15], [0.15, 0.15], ..., [0.95, 0.15]],
... ... ...
[[0.05, 0.95], [0.15, 0.95], ..., [0.95, 0.95]]]"""
utils3d.torch.maps.uv_map
@overload
def pixel_coord_map(*size: Union[int, Tuple[int, int]], top: int = 0, left: int = 0, convention: Literal['integer-center', 'integer-corner'] = 'integer-center', dtype: torch_.dtype = torch_.float32, device: torch_.device = None) -> torch_.Tensor:
"""Get image pixel coordinates map. Support two conventions: `'integer-center'` and `'integer-corner'`.
## Parameters
- `*size`: `Tuple[int, int]` or two integers of map size `(height, width)`
- `top`: `int`, optional top boundary of the pixel coord map. Defaults to 0.
- `left`: `int`, optional left boundary of the pixel coord map. Defaults to 0.
- `convention`: `str`, optional `'integer-center'` or `'integer-corner'`, whether integer coordinates correspond to pixel centers or corners. Defaults to 'integer-center'.
- `'integer-center'`: `pixel[i][j]` has integer coordinates `(j, i)` as its center, and occupies square area `[j - 0.5, j + 0.5) × [i - 0.5, i + 0.5)`.
The top-left corner of the top-left pixel is `(-0.5, -0.5)`, and the bottom-right corner of the bottom-right pixel is `(width - 0.5, height - 0.5)`.
- `'integer-corner'`: `pixel[i][j]` has coordinates `(j + 0.5, i + 0.5)` as its center, and occupies square area `[j, j + 1) × [i, i + 1)`.
The top-left corner of the top-left pixel is `(0, 0)`, and the bottom-right corner of the bottom-right pixel is `(width, height)`.
- `dtype`: `torch.dtype`, optional data type of the output pixel coord map. Defaults to torch.float32.
## Returns
Tensor: shape (height, width, 2)
>>> pixel_coord_map(10, 10, convention='integer-center', dtype=torch.long):
[[[0, 0], [1, 0], ..., [9, 0]],
[[0, 1], [1, 1], ..., [9, 1]],
... ... ...
[[0, 9], [1, 9], ..., [9, 9]]]
>>> pixel_coord_map(10, 10, convention='integer-corner', dtype=torch.float32):
[[[0.5, 0.5], [1.5, 0.5], ..., [9.5, 0.5]],
[[0.5, 1.5], [1.5, 1.5], ..., [9.5, 1.5]],
... ... ...
[[0.5, 9.5], [1.5, 9.5], ..., [9.5, 9.5]]]"""
utils3d.torch.maps.pixel_coord_map
@overload
def screen_coord_map(*size: Union[int, Tuple[int, int]], top: float = 1.0, left: float = 0.0, bottom: float = 0.0, right: float = 1.0, dtype: torch_.dtype = torch_.float32, device: torch_.device = None) -> torch_.Tensor:
"""Get screen space coordinate map, where (0., 0.) is the bottom-left corner of the image, and (1., 1.) is the top-right corner of the image.
This is commonly used in graphics APIs like OpenGL.
## Parameters
- `*size`: `Tuple[int, int]` or two integers of map size `(height, width)`
- `top`: `float`, optional top boundary in the screen space. Defaults to 1.
- `left`: `float`, optional left boundary in the screen space. Defaults to 0.
- `bottom`: `float`, optional bottom boundary in the screen space. Defaults to 0.
- `right`: `float`, optional right boundary in the screen space. Defaults to 1.
- `dtype`: `torch.dtype`, optional data type of the output map. Defaults to torch.float32.
## Returns
(Tensor): shape (height, width, 2)"""
utils3d.torch.maps.screen_coord_map
@overload
def build_mesh_from_map(*maps: torch_.Tensor, mask: Optional[torch_.Tensor] = None, tri: bool = False) -> Tuple[torch_.Tensor, ...]:
"""Get a mesh regarding image pixel uv coordinates as vertices and image grid as faces.
## Parameters
*maps (Tensor): attribute maps in shape (height, width, [channels])
mask (Tensor, optional): binary mask of shape (height, width), dtype=bool. Defaults to None.
## Returns
faces (Tensor): faces connecting neighboring pixels. shape (T, 4) if tri is False, else (T, 3)
*attributes (Tensor): vertex attributes in corresponding order with itorchut maps
indices (Tensor, optional): indices of vertices in the original mesh"""
utils3d.torch.maps.build_mesh_from_map
@overload
def build_mesh_from_depth_map(depth: torch_.Tensor, *other_maps: torch_.Tensor, intrinsics: torch_.Tensor, extrinsics: Optional[torch_.Tensor] = None, atol: Optional[float] = None, rtol: Optional[float] = 0.05, tri: bool = False) -> Tuple[torch_.Tensor, ...]:
"""Get a mesh by lifting depth map to 3D, while removing depths of large depth difference.
## Parameters
depth (Tensor): [H, W] depth map
extrinsics (Tensor, optional): [4, 4] extrinsics matrix. Defaults to None.
intrinsics (Tensor, optional): [3, 3] intrinsics matrix. Defaults to None.
*other_maps (Tensor): [H, W, C] vertex attributes. Defaults to None.
atol (float, optional): absolute tolerance. Defaults to None.
rtol (float, optional): relative tolerance. Defaults to None.
triangles with vertices having depth difference larger than atol + rtol * depth will be marked.
remove_by_depth (bool, optional): whether to remove triangles with large depth difference. Defaults to True.
return_uv (bool, optional): whether to return uv coordinates. Defaults to False.
return_indices (bool, optional): whether to return indices of vertices in the original mesh. Defaults to False.
## Returns
faces (Tensor): [T, 3] faces
vertices (Tensor): [N, 3] vertices
*other_attrs (Tensor): [N, C] vertex attributes"""
utils3d.torch.maps.build_mesh_from_depth_map
@overload
def depth_map_edge(depth: torch_.Tensor, atol: float = None, rtol: float = None, kernel_size: int = 3, mask: torch_.Tensor = None) -> torch_.BoolTensor:
"""Compute the edge mask of a depth map. The edge is defined as the pixels whose neighbors have a large difference in depth.
## Parameters
depth (Tensor): shape (..., height, width), linear depth map
atol (float): absolute tolerance
rtol (float): relative tolerance
## Returns
edge (Tensor): shape (..., height, width) of dtype torch.bool"""
utils3d.torch.maps.depth_map_edge
@overload
def depth_map_aliasing(depth: torch_.Tensor, atol: float = None, rtol: float = None, kernel_size: int = 3, mask: torch_.Tensor = None) -> torch_.BoolTensor:
"""Compute the map that indicates the aliasing of a depth map. The aliasing is defined as the pixels which neither close to the maximum nor the minimum of its neighbors.
## Parameters
depth (Tensor): shape (..., height, width), linear depth map
atol (float): absolute tolerance
rtol (float): relative tolerance
## Returns
edge (Tensor): shape (..., height, width) of dtype torch.bool"""
utils3d.torch.maps.depth_map_aliasing
@overload
def point_map_to_normal_map(point: torch_.Tensor, mask: torch_.Tensor = None) -> torch_.Tensor:
"""Calculate normal map from point map. Value range is [-1, 1].
## Parameters
point (Tensor): shape (..., height, width, 3), point map
mask (Tensor): shape (..., height, width), binary mask. Defaults to None.
## Returns
normal (Tensor): shape (..., height, width, 3), normal map. """
utils3d.torch.maps.point_map_to_normal_map
@overload
def depth_map_to_point_map(depth: torch_.Tensor, intrinsics: torch_.Tensor, extrinsics: torch_.Tensor = None):
utils3d.torch.maps.depth_map_to_point_map
@overload
def depth_map_to_normal_map(depth: torch_.Tensor, intrinsics: torch_.Tensor, mask: torch_.Tensor = None) -> torch_.Tensor:
"""Calculate normal map from depth map. Value range is [-1, 1]. Normal direction in OpenCV identity camera's coordinate system.
## Parameters
depth (Tensor): shape (..., height, width), linear depth map
intrinsics (Tensor): shape (..., 3, 3), intrinsics matrix
## Returns
normal (Tensor): shape (..., height, width, 3), normal map. """
utils3d.torch.maps.depth_map_to_normal_map
@overload
def chessboard(*size: Union[int, Tuple[int, int]], grid_size: int, color_a: torch_.Tensor, color_b: torch_.Tensor) -> torch_.Tensor:
"""Get a chessboard image
## Parameters
- `*size`: `Tuple[int, int]` or two integers of map size `(height, width)`
- `grid_size`: `int`, size of chessboard grid
- `color_a`: `Tensor`, shape (channels,), color of the grid at the top-left corner
- `color_b`: `Tensor`, shape (channels,), color in complementary grids
## Returns
- `image` (Tensor): shape (height, width, channels), chessboard image"""
utils3d.torch.maps.chessboard
@overload
def bounding_rect_from_mask(mask: torch_.BoolTensor):
"""Get bounding rectangle of a mask
## Parameters
mask (Tensor): shape (..., height, width), mask
## Returns
rect (Tensor): shape (..., 4), bounding rectangle (left, top, right, bottom)"""
utils3d.torch.maps.bounding_rect_from_mask
@overload
def masked_nearest_resize(*image: torch_.Tensor, mask: torch_.Tensor, size: Tuple[int, int], return_index: bool = False) -> Tuple[Unpack[Tuple[torch_.Tensor, ...]], torch_.Tensor, Tuple[torch_.Tensor, ...]]:
"""Resize image(s) by nearest sampling with mask awareness. Suitable for sparse maps. 
- Downsampling: Assign the nearest valid pixel within the target pixel's receptive field.
- Upsampling: Assign the valid pixel to only the nearest pixel in the resized map.
### Parameters
- `*image`: Itorchut image(s) of shape `(..., H, W, C)` or `(... , H, W)`
- You can pass multiple images to be resized at the same time for efficiency.
- `mask`: itorchut mask of shape `(..., H, W)`, dtype=bool
- `size`: target size `(H', W')`
- `return_index`: whether to return the nearest neighbor indices in the original map for each pixel in the resized map.
Defaults to False.
### Returns
- `*resized_image`: resized image(s) of shape `(..., H', W', C)`. or `(..., H', W')`
- `resized_mask`: mask of the resized map of shape `(..., H', W')`
- `nearest_indices`: tuple of shape `(..., H', W')`. The nearest neighbor indices of the resized map of each dimension."""
utils3d.torch.maps.masked_nearest_resize
@overload
def masked_area_resize(*image: torch_.Tensor, mask: torch_.Tensor, size: Tuple[int, int]) -> Tuple[Unpack[Tuple[torch_.Tensor, ...]], torch_.Tensor]:
"""Resize 2D map by area sampling with mask awareness.
### Parameters
- `*image`: Itorchut image(s) of shape `(..., H, W, C)` or `(..., H, W)`
- You can pass multiple images to be resized at the same time for efficiency.
- `mask`: Itorchut mask of shape `(..., H, W)`
- `size`: target image size `(H', W')`
### Returns
- `*resized_image`: resized image(s) of shape `(..., H', W', C)`. or `(..., H', W')`
- `resized_mask`: mask of the resized map of shape `(..., H', W')`"""
utils3d.torch.maps.masked_area_resize
@overload
def flood_fill(*image: torch_.Tensor, mask: torch_.Tensor, return_index: bool = False) -> torch_.Tensor:
"""Flooding fill the holes in the image(s) according to the mask. 
Parameters
----
- `*image` (Tensor): shape (..., height, width, [C]), itorchut image(s)
- `mask` (Tensor): shape (..., height, width), binary mask indicating valid regions
Returns
----
- `*filled_image` (Tensor): shape (..., height, width, [C]), flood filled map
- `filled_indices` (Tuple[Tensor, ...], optional): tuple of shape (..., height, width). The nearest neighbor indices of each pixel in the original map.
It satisfies `filled_image = image[filled_indices]`"""
utils3d.torch.maps.flood_fill
@overload
def perlin_noise(x: torch_.Tensor, seed: Optional[int] = None) -> torch_.Tensor:
"""Generate Perlin noise for the given coordinates.
Parameters
----
- `x` (Tensor): shape (*batch_shape, N_1, ..., N_D, D), coordinates to sample Perlin.
If itorchut ndim is more than D + 1, the leading dimensions are treated as batch dimensions. Instances in the batch have different noise patterns.
- `seed` (int, optional): random seed. The same seed will generate the same noise pattern(s). Defaults to None.
Returns
----
- `y` (Tensor): shape (*batch_shape, N_1, ..., N_D), Perlin noise value at the given coordinates and seed. Value range is approximately [-1, 1]"""
utils3d.torch.maps.perlin_noise
@overload
def perlin_noise_map(size: Tuple[int, ...], frequency: Union[float, torch_.Tensor], seed: Optional[int] = None, dtype: Optional[torch_.dtype] = None, device: Optional[torch_.device] = None) -> torch_.Tensor:
"""Generate Perlin noise map.
Parameters
----
- `size` (Tuple[int, ...]): size of the noise map (..., H, W)
- `frequency` (float | Tensor): frequency relative to map's larger dimension max(H, W) of the Perlin noise.
Represents how many periods of noise fit in the larger dimension of the map.
- `seed` (int, optional): random seed. The same seed will generate the same noise pattern(s). Defaults to None.
Returns
----
- `noise_map` (Tensor): shape (..., H, W), Perlin noise map. Value range is approximately [-1, 1]"""
utils3d.torch.maps.perlin_noise_map
@overload
def fractal_perlin_noise_map(size: Tuple[int, ...], base_frequency: Union[float, torch_.Tensor], octaves: int = 4, lacunarity: float = 2.0, gain: float = 0.5, seed: Optional[int] = None, dtype: Optional[torch_.dtype] = None, device: Optional[torch_.device] = None) -> torch_.Tensor:
"""Generate fractal Perlin noise map. 
Parameters
----
- `size` (Tuple[int, ...]): size of the noise map (..., H, W)
- `base_frequency` (float | Tensor): base frequency (relative to map's larger dimension max(H, W)) of the Perlin noise.
Represents how many periods of noise fit in the larger dimension of the map.
- `octaves` (int, optional): number of octaves. Defaults to 4.
- `lacunarity` (float, optional): frequency multiplier between octaves. Defaults to 2.0.
- `gain` (float, optional): amplitude multiplier between octaves. Defaults to 0.5.
- `seed` (int, optional): random seed. The same seed will generate the same noise pattern. Defaults to None.
Returns
----
- `noise_map` (Tensor): shape (..., H, W), fractal Perlin noise map. Value range is approximately [-1, 1]"""
utils3d.torch.maps.fractal_perlin_noise_map
@overload
def RastContext(nvd_ctx: Union[nvdiffrast.torch.ops.RasterizeCudaContext, nvdiffrast.torch.ops.RasterizeGLContext] = None, *, backend: Literal['cuda', 'gl'] = 'cuda', device: Union[str, torch_.device] = None):
"""Create a rasterization context. Nothing but a wrapper of nvdiffrast.torch.RasterizeCudaContext or nvdiffrast.torch.RasterizeGLContext."""
utils3d.torch.rasterization.RastContext
@overload
def rasterize_triangles(size: Tuple[int, int], *, vertices: torch_.Tensor, attributes: Optional[torch_.Tensor] = None, faces: torch_.Tensor, view: torch_.Tensor = None, projection: torch_.Tensor = None, extrinsics: torch_.Tensor = None, intrinsics: torch_.Tensor = None, near: float = 0.01, far: float = inf, return_image_derivatives: bool = False, return_depth: bool = False, return_interpolation: bool = False, antialiasing: bool = False, ctx: Optional[utils3d.torch.rasterization.RastContext] = None) -> Tuple[torch_.Tensor, torch_.Tensor, Optional[torch_.Tensor]]:
"""Rasterize triangles.
Parameters
----
size (Tuple[int, int]): (height, width) of the output image
vertices (np.ndarray): (B, N, 2 or 3 or 4)
faces (Tensor): (T, 3)
attributes (Tensor, optional): (B, N, C) vertex attributes. Defaults to None.
texture (Tensor, optional): (B, C, H, W) texture. Defaults to None.
view | extrinsics (Tensor, optional): ([B,] 4, 4) view matrix or extrinsics matrix. Provide either one of them. Defaults to identity.
projection | intrinsics (Tensor, optional): ([B,] 4, 4) projection matrix or ([B,] 3, 3) intrinsics matrix. Provide either one of them. Defaults to identity.
near (float, optional): near plane. Defaults to 0.01. Only used for intrinsics. Ignored if projection matrix is provided.
far (float, optional): far plane. Defaults to inf. Only used for intrinsics. Ignored if projection matrix is provided.
return_image_derivatives (bool, optional): whether to return screen space derivatives of the attributes. Defaults to False.
return_depth (bool, optional): whether to return depth map. Defaults to False.
return_interpolation (bool, optional): whether to return triangle interpolation maps. Defaults to False.
antialiasing (Union[bool, List[int]], optional): whether to perform antialiasing. Defaults to True. If a list of indices is provided, only those channels will be antialiased.
ctx (RastContext): rasterization context. Defaults to the thread-local default context. If custom context is needed, provide one with utils3d.pt.RastContext().
Returns
----
A dictionary containing:
- image: (Tensor): (B, H, W, C)
- image_dr: (Tensor): (B, H, W, C * 2) screen space derivatives of the attributes
- depth: (Tensor): (B, H, W) Linear depth. Empty pixels have depth inf.
- mask: (torch.BoolTensor): (B, H, W) mask of valid pixels
- interpolation_id: (Tensor): (B, H, W) triangle ID map. For empty pixels, the value is -1.
- interpolation_uv: (Tensor): (B, H, W, 2) triangle UV (first two channels of barycentric coordinates)"""
utils3d.torch.rasterization.rasterize_triangles
@overload
def rasterize_triangles_peeling(size: Tuple[int, int], *, vertices: torch_.Tensor, attributes: Optional[torch_.Tensor] = None, faces: torch_.Tensor, view: torch_.Tensor = None, projection: torch_.Tensor = None, extrinsics: torch_.Tensor = None, intrinsics: torch_.Tensor = None, near: float = 0.01, far: float = inf, return_image_derivatives: bool = False, return_depth: bool = False, return_interpolation: bool = False, antialiasing: bool = False, ctx: Optional[utils3d.torch.rasterization.RastContext] = None) -> Iterator[Iterator[Dict[str, torch_.Tensor]]]:
"""Rasterize a mesh with vertex attributes using depth peeling.
Parameters
----
size (Tuple[int, int]): (height, width) of the output image
vertices (np.ndarray): (B, N, 2 or 3 or 4)
faces (Tensor): (T, 3)
attributes (Tensor, optional): (B, N, C) vertex attributes. Defaults to None.
texture (Tensor, optional): (B, C, H, W) texture. Defaults to None.
view | extrinsics (Tensor, optional): ([B,] 4, 4) view matrix or extrinsics matrix. Provide either one of them. Defaults to identity.
projection | intrinsics (Tensor, optional): ([B,] 4, 4) projection matrix or ([B,] 3, 3) intrinsics matrix. Provide either one of them. Defaults to identity.
near (float, optional): near plane. Defaults to 0.01. Only used for intrinsics. Ignored if projection matrix is provided.
far (float, optional): far plane. Defaults to inf. Only used for intrinsics. Ignored if projection matrix is provided.
return_image_derivatives (bool, optional): whether to return screen space derivatives of the attributes. Defaults to False.
return_depth (bool, optional): whether to return depth map. Defaults to False.
return_interpolation (bool, optional): whether to return triangle interpolation maps. Defaults to False.
antialiasing (Union[bool, List[int]], optional): whether to perform antialiasing. Defaults to True. If a list of indices is provided, only those channels will be antialiased.
ctx (RastContext): rasterization context. Defaults to the thread-local default context. If custom context is needed, provide one with utils3d.pt.RastContext().
Returns
----
A generator of dictionaries for each layer containing:
- mask: (List[torch.BoolTensor]): (B, H, W) mask of valid pixels in this layer
- image: (List[Tensor]): (B, C, H, W) rendered images
- image_dr: (List[Tensor]): (B, *, H, W) screen space derivatives of the attributes
- depth: (List[Tensor]): (B, H, W) linear depth. Empty pixels have depth inf.
- interpolation_id: (List[Tensor]): (B, H, W) triangle ID map. For empty pixels, the value is -1.
- interpolation_uv: (List[Tensor]): (B, H, W, 2) triangle UV (first two channels of barycentric coordinates)
The last layer yielded will be empty, then the generator will stop.
Example
----
```
for i, layer_output in enumerate(rasterize_triangles_peeling(
(512, 512),
vertices=vertices,
faces=faces,
attributes=attributes,
view=view,
projection=projection
)):
print(f"Layer {i}:")
for key, value in layer_output.items():
print(f" {key}: {value.shape}")
if i >= 4: # Stop after 5 layers at most
break
```"""
utils3d.torch.rasterization.rasterize_triangles_peeling
@overload
def sample_texture(texture: torch_.Tensor, uv: torch_.Tensor, uv_dr: torch_.Tensor) -> torch_.Tensor:
"""Interpolate texture using uv coordinates.
## Parameters
texture (Tensor): (B, H, W, C) texture
uv (Tensor): (B, H, W, 2) uv coordinates
uv_dr (Tensor): (B, H, W, 4) uv derivatives
## Returns
Tensor: (B, H, W, C) interpolated texture"""
utils3d.torch.rasterization.sample_texture
@overload
def texture_composite(texture: torch_.Tensor, uv: List[torch_.Tensor], uv_da: List[torch_.Tensor], background: torch_.Tensor = None) -> Tuple[torch_.Tensor, torch_.Tensor]:
"""Composite textures with depth peeling output.
## Parameters
texture (Tensor): (B, C+1, H, W) texture
NOTE: the last channel is alpha channel
uv (List[Tensor]): list of (B, H, W, 2) uv coordinates
uv_da (List[Tensor]): list of (B, H, W, 4) uv derivatives
background (Optional[Tensor], optional): (B, C, H, W) background image. Defaults to None (black).
## Returns
image: (Tensor): (B, C, H, W) rendered image
alpha: (Tensor): (B, H, W) alpha channel"""
utils3d.torch.rasterization.texture_composite
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