envs/kitoverlay/skimage/measure/_polygon.py

import numpy as np
from scipy import signal


def approximate_polygon(coords, tolerance):
    """Approximate a polygonal chain with the specified tolerance.

    It is based on the Douglas-Peucker algorithm.

    Note that the approximated polygon is always within the convex hull of the
    original polygon.

    Parameters
    ----------
    coords : (K, 2) array
        Coordinate array.
    tolerance : float
        Maximum distance from original points of polygon to approximated
        polygonal chain. If tolerance is 0, the original coordinate array
        is returned.

    Returns
    -------
    coords : (L, 2) array
        Approximated polygonal chain where L <= K.

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/Ramer-Douglas-Peucker_algorithm
    """
    if tolerance <= 0:
        return coords

    chain = np.zeros(coords.shape[0], 'bool')
    # pre-allocate distance array for all points
    dists = np.zeros(coords.shape[0])
    chain[0] = True
    chain[-1] = True
    pos_stack = [(0, chain.shape[0] - 1)]
    end_of_chain = False

    while not end_of_chain:
        start, end = pos_stack.pop()
        # determine properties of current line segment
        r0, c0 = coords[start, :]
        r1, c1 = coords[end, :]
        dr = r1 - r0
        dc = c1 - c0
        segment_angle = -np.arctan2(dr, dc)
        segment_dist = c0 * np.sin(segment_angle) + r0 * np.cos(segment_angle)

        # select points in-between line segment
        segment_coords = coords[start + 1 : end, :]
        segment_dists = dists[start + 1 : end]

        # check whether to take perpendicular or euclidean distance with
        # inner product of vectors

        # vectors from points -> start and end
        dr0 = segment_coords[:, 0] - r0
        dc0 = segment_coords[:, 1] - c0
        dr1 = segment_coords[:, 0] - r1
        dc1 = segment_coords[:, 1] - c1
        # vectors points -> start and end projected on start -> end vector
        projected_lengths0 = dr0 * dr + dc0 * dc
        projected_lengths1 = -dr1 * dr - dc1 * dc
        perp = np.logical_and(projected_lengths0 > 0, projected_lengths1 > 0)
        eucl = np.logical_not(perp)
        segment_dists[perp] = np.abs(
            segment_coords[perp, 0] * np.cos(segment_angle)
            + segment_coords[perp, 1] * np.sin(segment_angle)
            - segment_dist
        )
        segment_dists[eucl] = np.minimum(
            # distance to start point
            np.sqrt(dc0[eucl] ** 2 + dr0[eucl] ** 2),
            # distance to end point
            np.sqrt(dc1[eucl] ** 2 + dr1[eucl] ** 2),
        )

        if np.any(segment_dists > tolerance):
            # select point with maximum distance to line
            new_end = start + np.argmax(segment_dists) + 1
            pos_stack.append((new_end, end))
            pos_stack.append((start, new_end))
            chain[new_end] = True

        if len(pos_stack) == 0:
            end_of_chain = True

    return coords[chain, :]


# B-Spline subdivision
_SUBDIVISION_MASKS = {
    # degree: (mask_even, mask_odd)
    #         extracted from (degree + 2)th row of Pascal's triangle
    1: ([1, 1], [1, 1]),
    2: ([3, 1], [1, 3]),
    3: ([1, 6, 1], [0, 4, 4]),
    4: ([5, 10, 1], [1, 10, 5]),
    5: ([1, 15, 15, 1], [0, 6, 20, 6]),
    6: ([7, 35, 21, 1], [1, 21, 35, 7]),
    7: ([1, 28, 70, 28, 1], [0, 8, 56, 56, 8]),
}


def subdivide_polygon(coords, degree=2, preserve_ends=False):
    """Subdivision of polygonal curves using B-Splines.

    Note that the resulting curve is always within the convex hull of the
    original polygon. Circular polygons stay closed after subdivision.

    Parameters
    ----------
    coords : (K, 2) array
        Coordinate array.
    degree : {1, 2, 3, 4, 5, 6, 7}, optional
        Degree of B-Spline. Default is 2.
    preserve_ends : bool, optional
        Preserve first and last coordinate of non-circular polygon. Default is
        False.

    Returns
    -------
    coords : (L, 2) array
        Subdivided coordinate array.

    References
    ----------
    .. [1] http://mrl.nyu.edu/publications/subdiv-course2000/coursenotes00.pdf
    """
    if degree not in _SUBDIVISION_MASKS:
        raise ValueError("Invalid B-Spline degree. Only degree 1 - 7 is " "supported.")

    circular = np.all(coords[0, :] == coords[-1, :])

    method = 'valid'
    if circular:
        # remove last coordinate because of wrapping
        coords = coords[:-1, :]
        # circular convolution by wrapping boundaries
        method = 'same'

    mask_even, mask_odd = _SUBDIVISION_MASKS[degree]
    # divide by total weight
    mask_even = np.array(mask_even, float) / (2**degree)
    mask_odd = np.array(mask_odd, float) / (2**degree)

    even = signal.convolve2d(
        coords.T, np.atleast_2d(mask_even), mode=method, boundary='wrap'
    )
    odd = signal.convolve2d(
        coords.T, np.atleast_2d(mask_odd), mode=method, boundary='wrap'
    )

    out = np.zeros((even.shape[1] + odd.shape[1], 2))
    out[1::2] = even.T
    out[::2] = odd.T

    if circular:
        # close polygon
        out = np.vstack([out, out[0, :]])

    if preserve_ends and not circular:
        out = np.vstack([coords[0, :], out, coords[-1, :]])

    return out