Datasets:

zhicao
/

openpi

"""
DROID projection: per-camera ZED left intrinsics @ 1280x720 + h5 camera extrinsics.
Data: ``trajectory.h5`` + ``recordings/MP4``. Intrinsics: cache / SN.conf / SVO / model default.
"""

from __future__ import annotations

import numpy as np
from scipy.spatial.transform import Rotation

# DROID MP4 / SVO left view @ HD
DROID_LEFT_K_1280x720 = np.array(
    [
        [522.42260742, 0.0, 653.9631958],
        [0.0, 522.42260742, 358.79196167],
        [0.0, 0.0, 1.0],
    ],
    dtype=np.float64,
)
DROID_NATIVE_HW = (720, 1280)  # (H, W)

# Polymetis / DROID raw h5 use extrinsic euler in this convention (see droid convert scripts).
DROID_EULER_CONVENTION = "xyz"

GRIPPER_OFFSETS = np.array(
    [
        [0.0, 0.0, 0.0],
        [0.0, 0.045, 0.161],
        [0.0, -0.045, 0.161],
        [0.0, 0.045, 0.13],
        [0.0, -0.045, 0.13],
        [0.0, 0.0, 0.13],
        [0.0, 0.0, 0.065],
    ],
    dtype=np.float64,
)

WRIST_GRIPPER_TEMPLATE_FRAC = np.array(
    [
        [0.48, 0.75],  # palm / wrist bridge

        [0.44, 0.62],  # left finger base
        [0.82, 0.60],  # right finger base

        [0.33, 0.84],  # left finger outer
        [0.86, 0.83],  # right finger outer

        [0.42, 0.93],  # left fingertip  <-- adjusted
        [0.81, 0.96],  # right fingertip
    ],
    dtype=np.float64,
)
def pose6_to_matrix(pose6: np.ndarray, *, euler: str = DROID_EULER_CONVENTION) -> np.ndarray:
    x = np.asarray(pose6, dtype=np.float64).reshape(-1)
    rot = Rotation.from_euler(euler, x[3:6]).as_matrix()
    T = np.eye(4, dtype=np.float64)
    T[:3, :3] = rot
    T[:3, 3] = x[:3]
    return T


def world_to_cam_matrix(extrinsic_6d: np.ndarray) -> np.ndarray:
    """h5 ``camera_extrinsics`` stores cam-to-world; return world-to-cam 4x4."""
    return np.linalg.inv(pose6_to_matrix(extrinsic_6d))


def scale_K_to_image_hw(K: np.ndarray, native_hw: tuple[int, int], image_hw: tuple[int, int]) -> np.ndarray:
    """Scale pinhole K from ``native_hw`` to ``image_hw`` (H, W)."""
    href, wref = native_hw
    hnew, wnew = image_hw
    K = np.asarray(K, dtype=np.float64).reshape(3, 3).copy()
    K[0, 0] *= wnew / float(wref)
    K[0, 2] *= wnew / float(wref)
    K[1, 1] *= hnew / float(href)
    K[1, 2] *= hnew / float(href)
    return K


def droid_left_K_for_image_hw(image_hw: tuple[int, int], *, native_hw: tuple[int, int] = DROID_NATIVE_HW) -> np.ndarray:
    return scale_K_to_image_hw(DROID_LEFT_K_1280x720, native_hw, image_hw)


def wrist_gripper_template_pixels(image_hw: tuple[int, int]) -> np.ndarray:
    """7-point U-shaped gripper seed layout in pixel coords (not a line)."""
    h, w = image_hw
    return (WRIST_GRIPPER_TEMPLATE_FRAC * np.array([float(w), float(h)], dtype=np.float64)).astype(
        np.float64
    )


def gripper_queries_in_image(
    pixels: np.ndarray,
    vis: np.ndarray,
    image_hw: tuple[int, int],
) -> np.ndarray:
    """Boolean mask: visible, finite, and inside ``image_hw`` (H, W)."""
    h, w = image_hw
    pts = np.asarray(pixels, dtype=np.float64)
    mask = np.asarray(vis, dtype=bool).reshape(-1)
    mask &= np.isfinite(pts).all(axis=1)
    mask &= (pts[:, 0] >= 0.0) & (pts[:, 0] < float(w))
    mask &= (pts[:, 1] >= 0.0) & (pts[:, 1] < float(h))
    return mask


def align_gripper_queries_to_template(
    queries: np.ndarray,
    valid: np.ndarray,
    image_hw: tuple[int, int],
) -> np.ndarray:
    """Keep valid projections; place invalid indices from a scaled gripper template."""
    out = wrist_gripper_template_pixels(image_hw).astype(np.float32, copy=True)
    valid = np.asarray(valid, dtype=bool).reshape(-1)
    q = np.asarray(queries, dtype=np.float32)
    if valid.any():
        vpts = q[valid]
        vmin, vmax = vpts.min(axis=0), vpts.max(axis=0)
        tmpl = out.copy()
        tmin, tmax = tmpl.min(axis=0), tmpl.max(axis=0)
        scale = (vmax - vmin) / np.maximum(tmax - tmin, 1e-3)
        out = (tmpl - tmin) * scale + vmin
        out[valid] = q[valid]
    return out


# Wrist mesh indices that usually project onto visible finger geometry (not the EEF center line).
WRIST_FINGER_MESH_INDICES = (1, 2, 3, 4)


def _clamp_queries_to_image(queries: np.ndarray, image_hw: tuple[int, int]) -> np.ndarray:
    h, w = image_hw
    out = np.asarray(queries, dtype=np.float32).copy()
    out[..., 0] = np.clip(out[..., 0], 0.0, float(w - 1))
    out[..., 1] = np.clip(out[..., 1], 0.0, float(h - 1))
    return out


def complete_wrist_mesh_queries(
    pix: np.ndarray,
    vis: np.ndarray,
    image_hw: tuple[int, int],
) -> np.ndarray:
    """
    Build 7 CoTracker seeds from wrist projection.
    Center mesh points (0/5/6) often miss the image on wrist cam; finger points (1-4) are
    reliable. Interpolate missing indices in 2D from finger projections instead of warping
    a fixed template (which caused straight-line / off-gripper seeds).
    """
    h, w = image_hw
    out = np.asarray(pix, dtype=np.float32).copy()
    valid = gripper_queries_in_image(out, vis, image_hw)
    finger_ok = [i for i in WRIST_FINGER_MESH_INDICES if valid[i]]

    if len(finger_ok) >= 2:
        if not valid[0]:
            out[0] = out[finger_ok].mean(axis=0)
        if not valid[2] and valid[1]:
            out[2] = 2.0 * out[0] - out[1]
        if not valid[1] and valid[2]:
            out[1] = 2.0 * out[0] - out[2]
        if not valid[4] and valid[3]:
            out[4] = 2.0 * out[0] - out[3]
        if not valid[3] and valid[4]:
            out[3] = 2.0 * out[0] - out[4]
        if not valid[5]:
            if valid[3] and valid[4]:
                mid = 0.5 * (out[3] + out[4])
            elif valid[1] and valid[2]:
                mid = 0.5 * (out[1] + out[2])
            else:
                mid = out[finger_ok].mean(axis=0)
            out[5] = 0.6 * out[0] + 0.4 * mid
        if not valid[6]:
            tip_dir = out[5] - out[0]
            if float(np.linalg.norm(tip_dir)) > 2.0:
                out[6] = out[5] + 0.5 * tip_dir
            else:
                out[6] = out[5] + np.array([0.0, 0.1 * h], dtype=np.float32)
        return _clamp_queries_to_image(out, image_hw)

    if int(valid.sum()) >= 3:
        return _clamp_queries_to_image(out, image_hw)

    return wrist_gripper_template_pixels(image_hw).astype(np.float32)


def scale_pixels_between_hw(
    pixels: np.ndarray,
    src_hw: tuple[int, int],
    dst_hw: tuple[int, int],
) -> np.ndarray:
    """Affine scale pixel coords when resizing images src_hw -> dst_hw."""
    href, wref = src_hw
    hnew, wnew = dst_hw
    out = np.asarray(pixels, dtype=np.float64).copy()
    sx = wnew / float(wref)
    sy = hnew / float(href)
    out[..., 0] *= sx
    out[..., 1] *= sy
    return out


def project_gripper_mesh_wrist(
    cartesian6: np.ndarray,
    extrinsic_6d: np.ndarray,
    gripper_offset_6d: np.ndarray,
    *,
    K: np.ndarray,
    dist: np.ndarray | None = None,
    native_hw: tuple[int, int] = DROID_NATIVE_HW,
    gripper_open: float | None = None,
) -> tuple[np.ndarray, np.ndarray]:
    """
    Wrist-view gripper mesh: same chain as :func:`project_gripper_mesh`.
    h5 ``{serial}_left_gripper_offset`` is the camera mount (``T_c2w ≈ T_eef @ T_offset``)
    and is already reflected in ``extrinsic_6d``; mesh points live in the EEF frame and
    must not be premultiplied by ``T_gripper_offset``. ``gripper_offset_6d`` is kept for
    API compatibility only.
    """
    del gripper_offset_6d
    return project_gripper_mesh(
        cartesian6,
        extrinsic_6d,
        K=K,
        dist=dist,
        native_hw=native_hw,
        gripper_open=gripper_open,
    )


def project_gripper_mesh(
    cartesian6: np.ndarray,
    extrinsic_6d: np.ndarray,
    *,
    K: np.ndarray,
    dist: np.ndarray | None = None,
    native_hw: tuple[int, int] = DROID_NATIVE_HW,
    gripper_open: float | None = None,
) -> tuple[np.ndarray, np.ndarray]:
    """7 gripper points -> (7,2) pixels and visibility at ``native_hw`` resolution."""
    c = np.asarray(cartesian6, dtype=np.float64).reshape(-1)
    R_wg = Rotation.from_euler(DROID_EULER_CONVENTION, c[3:6]).as_matrix()
    offsets = (
        gripper_offsets_for_opening(gripper_open)
        if gripper_open is not None
        else GRIPPER_OFFSETS
    )
    world = (R_wg @ offsets.T).T + c[:3].reshape(1, 3)

    K = np.asarray(K, dtype=np.float64).reshape(3, 3)
    w2c = world_to_cam_matrix(extrinsic_6d)
    R = w2c[:3, :3]
    t = w2c[:3, 3].reshape(3, 1)

    pixels = np.zeros((7, 2), dtype=np.float64)
    vis = np.zeros((7,), dtype=bool)

    dist_use = None
    if dist is not None:
        dist_use = np.asarray(dist, dtype=np.float64).reshape(-1)
        if dist_use.size >= 5 and np.allclose(dist_use[:5], 0.0):
            dist_use = None

    href, wref = native_hw
    cam_z = np.zeros((7,), dtype=np.float64)

    if dist_use is not None:
        import cv2

        rvec, _ = cv2.Rodrigues(R)
        pts, _ = cv2.projectPoints(
            world.reshape(-1, 1, 3).astype(np.float64),
            rvec,
            t,
            K,
            dist_use[:5],
        )
        pixels = pts.reshape(-1, 2)
        cam_z = (R @ world.T + t).T[:, 2]
    else:
        for i, p in enumerate(world):
            cam3d = (w2c @ np.concatenate([p, [1.0]]))[:3]
            cam_z[i] = cam3d[2]
            if cam_z[i] <= 1e-5:
                pixels[i] = np.nan
                vis[i] = False
                continue
            proj = K @ cam3d
            if abs(proj[2]) < 1e-8:
                pixels[i] = np.nan
                vis[i] = False
            else:
                pixels[i] = (proj / proj[2])[:2]

    for i in range(7):
        if cam_z[i] <= 0.02:
            vis[i] = False
            pixels[i] = np.nan
            continue
        if not (
            np.isfinite(pixels[i, 0])
            and np.isfinite(pixels[i, 1])
            and 0.0 <= pixels[i, 0] < float(wref)
            and 0.0 <= pixels[i, 1] < float(href)
        ):
            vis[i] = False
            pixels[i] = np.nan
        else:
            vis[i] = True
    return pixels.astype(np.float64), vis.astype(np.float64)


def gripper_offsets_for_opening(gripper_open: float) -> np.ndarray:
    """Scale finger keypoint offsets by gripper opening (0=closed, 1=open)."""
    g = float(np.clip(gripper_open, 0.0, 1.0))
    offsets = GRIPPER_OFFSETS.copy()
    # Finger tips (indices 1-4): spread with opening; center / palm points stay fixed.
    for i in (1, 2, 3, 4):
        offsets[i, 1] *= 0.35 + 0.65 * g
        offsets[i, 2] *= 0.55 + 0.45 * g
    return offsets


def _score_wrist_seed_queries(queries: np.ndarray, image_hw: tuple[int, int]) -> float:
    h, w = image_hw
    q = np.asarray(queries, dtype=np.float64).reshape(7, 2)
    cy = float(q[:, 1].mean() / max(h, 1))
    cx_spread = float(q[:, 0].std())
    y_spread = float(q[:, 1].std())
    if cy < 0.28 or cy > 0.92:
        return -1.0
    if cx_spread < 12.0 or y_spread < 8.0:
        return -1.0
    finger = q[list(WRIST_FINGER_MESH_INDICES)]
    finger_spread = float(finger.std(axis=0).mean())
    return finger_spread + cx_spread * 0.08 + (0.68 - abs(cy - 0.58)) * 3.0


def make_wrist_gripper_mesh_queries(
    cartesian: np.ndarray,
    wrist_extrinsics: np.ndarray,
    wrist_gripper_offset: np.ndarray,
    gripper_open: np.ndarray,
    *,
    K: np.ndarray,
    dist: np.ndarray | None,
    out_hw: tuple[int, int],
    K_candidates: list[tuple[np.ndarray, np.ndarray | None]] | None = None,
) -> np.ndarray:
    """
    CoTracker seeds for 7 wrist gripper points.
    Uses the same chain as exterior: ``inv(cam2world) @ T_eef @ mesh`` (see
    :func:`project_gripper_mesh`). Tries KarlP vs ZED intrinsics and several timesteps.
    """
    t_len = int(cartesian.shape[0])
    if t_len < 1:
        return wrist_gripper_template_pixels(out_hw).astype(np.float32)

    seed_times = sorted({0, t_len // 4, t_len // 2, max(0, t_len - 1)})
    k_list: list[tuple[np.ndarray, np.ndarray | None]] = (
        list(K_candidates) if K_candidates else [(K, dist)]
    )
    best_queries: np.ndarray | None = None
    best_score = -1.0
    del wrist_gripper_offset  # mount calib is in wrist_extrinsics, not applied to mesh

    for t_seed in seed_times:
        ext6 = wrist_extrinsics[t_seed]
        for K_use, dist_use in k_list:
            # Wrist seeds: nominal finger mesh only (gripper_open scaling pushes points OOB).
            pix, vis = project_gripper_mesh(
                cartesian[t_seed],
                ext6,
                K=K_use,
                dist=None,
                native_hw=DROID_NATIVE_HW,
                gripper_open=None,
            )
            pix_out = scale_pixels_between_hw(pix, DROID_NATIVE_HW, out_hw)
            cand = complete_wrist_mesh_queries(pix_out, vis, out_hw)
            score = _score_wrist_seed_queries(cand, out_hw)
            if score > best_score:
                best_score = score
                best_queries = cand
            if best_score >= 25.0:
                return best_queries.astype(np.float32)

    if best_queries is not None and best_score >= 5.0:
        return best_queries.astype(np.float32)
    return wrist_gripper_template_pixels(out_hw).astype(np.float32)


def make_image_grid(img_h: int, img_w: int, grid_size: int = 5) -> np.ndarray:
    xs = np.linspace(0.0, float(img_w - 1), grid_size, dtype=np.float64)
    ys = np.linspace(0.0, float(img_h - 1), grid_size, dtype=np.float64)
    return np.stack(np.meshgrid(xs, ys, indexing="xy"), axis=-1).reshape(-1, 2)

	"""
	DROID projection: per-camera ZED left intrinsics @ 1280x720 + h5 camera extrinsics.

	Data: ``trajectory.h5`` + ``recordings/MP4``. Intrinsics: cache / SN.conf / SVO / model default.
	"""

	from __future__ import annotations

	import numpy as np
	from scipy.spatial.transform import Rotation

	# DROID MP4 / SVO left view @ HD
	DROID_LEFT_K_1280x720 = np.array(
	[
	[522.42260742, 0.0, 653.9631958],
	[0.0, 522.42260742, 358.79196167],
	[0.0, 0.0, 1.0],
	],
	dtype=np.float64,
	)
	DROID_NATIVE_HW = (720, 1280) # (H, W)

	# Polymetis / DROID raw h5 use extrinsic euler in this convention (see droid convert scripts).
	DROID_EULER_CONVENTION = "xyz"

	GRIPPER_OFFSETS = np.array(
	[
	[0.0, 0.0, 0.0],
	[0.0, 0.045, 0.161],
	[0.0, -0.045, 0.161],
	[0.0, 0.045, 0.13],
	[0.0, -0.045, 0.13],
	[0.0, 0.0, 0.13],
	[0.0, 0.0, 0.065],
	],
	dtype=np.float64,
	)

	WRIST_GRIPPER_TEMPLATE_FRAC = np.array(
	[
	[0.48, 0.75], # palm / wrist bridge

	[0.44, 0.62], # left finger base
	[0.82, 0.60], # right finger base

	[0.33, 0.84], # left finger outer
	[0.86, 0.83], # right finger outer

	[0.42, 0.93], # left fingertip <-- adjusted
	[0.81, 0.96], # right fingertip
	],
	dtype=np.float64,
	)
	def pose6_to_matrix(pose6: np.ndarray, *, euler: str = DROID_EULER_CONVENTION) -> np.ndarray:
	x = np.asarray(pose6, dtype=np.float64).reshape(-1)
	rot = Rotation.from_euler(euler, x[3:6]).as_matrix()
	T = np.eye(4, dtype=np.float64)
	T[:3, :3] = rot
	T[:3, 3] = x[:3]
	return T


	def world_to_cam_matrix(extrinsic_6d: np.ndarray) -> np.ndarray:
	"""h5 ``camera_extrinsics`` stores cam-to-world; return world-to-cam 4x4."""
	return np.linalg.inv(pose6_to_matrix(extrinsic_6d))


	def scale_K_to_image_hw(K: np.ndarray, native_hw: tuple[int, int], image_hw: tuple[int, int]) -> np.ndarray:
	"""Scale pinhole K from ``native_hw`` to ``image_hw`` (H, W)."""
	href, wref = native_hw
	hnew, wnew = image_hw
	K = np.asarray(K, dtype=np.float64).reshape(3, 3).copy()
	K[0, 0] *= wnew / float(wref)
	K[0, 2] *= wnew / float(wref)
	K[1, 1] *= hnew / float(href)
	K[1, 2] *= hnew / float(href)
	return K


	def droid_left_K_for_image_hw(image_hw: tuple[int, int], *, native_hw: tuple[int, int] = DROID_NATIVE_HW) -> np.ndarray:
	return scale_K_to_image_hw(DROID_LEFT_K_1280x720, native_hw, image_hw)


	def wrist_gripper_template_pixels(image_hw: tuple[int, int]) -> np.ndarray:
	"""7-point U-shaped gripper seed layout in pixel coords (not a line)."""
	h, w = image_hw
	return (WRIST_GRIPPER_TEMPLATE_FRAC * np.array([float(w), float(h)], dtype=np.float64)).astype(
	np.float64
	)


	def gripper_queries_in_image(
	pixels: np.ndarray,
	vis: np.ndarray,
	image_hw: tuple[int, int],
	) -> np.ndarray:
	"""Boolean mask: visible, finite, and inside ``image_hw`` (H, W)."""
	h, w = image_hw
	pts = np.asarray(pixels, dtype=np.float64)
	mask = np.asarray(vis, dtype=bool).reshape(-1)
	mask &= np.isfinite(pts).all(axis=1)
	mask &= (pts[:, 0] >= 0.0) & (pts[:, 0] < float(w))
	mask &= (pts[:, 1] >= 0.0) & (pts[:, 1] < float(h))
	return mask


	def align_gripper_queries_to_template(
	queries: np.ndarray,
	valid: np.ndarray,
	image_hw: tuple[int, int],
	) -> np.ndarray:
	"""Keep valid projections; place invalid indices from a scaled gripper template."""
	out = wrist_gripper_template_pixels(image_hw).astype(np.float32, copy=True)
	valid = np.asarray(valid, dtype=bool).reshape(-1)
	q = np.asarray(queries, dtype=np.float32)
	if valid.any():
	vpts = q[valid]
	vmin, vmax = vpts.min(axis=0), vpts.max(axis=0)
	tmpl = out.copy()
	tmin, tmax = tmpl.min(axis=0), tmpl.max(axis=0)
	scale = (vmax - vmin) / np.maximum(tmax - tmin, 1e-3)
	out = (tmpl - tmin) * scale + vmin
	out[valid] = q[valid]
	return out


	# Wrist mesh indices that usually project onto visible finger geometry (not the EEF center line).
	WRIST_FINGER_MESH_INDICES = (1, 2, 3, 4)


	def _clamp_queries_to_image(queries: np.ndarray, image_hw: tuple[int, int]) -> np.ndarray:
	h, w = image_hw
	out = np.asarray(queries, dtype=np.float32).copy()
	out[..., 0] = np.clip(out[..., 0], 0.0, float(w - 1))
	out[..., 1] = np.clip(out[..., 1], 0.0, float(h - 1))
	return out


	def complete_wrist_mesh_queries(
	pix: np.ndarray,
	vis: np.ndarray,
	image_hw: tuple[int, int],
	) -> np.ndarray:
	"""
	Build 7 CoTracker seeds from wrist projection.

	Center mesh points (0/5/6) often miss the image on wrist cam; finger points (1-4) are
	reliable. Interpolate missing indices in 2D from finger projections instead of warping
	a fixed template (which caused straight-line / off-gripper seeds).
	"""
	h, w = image_hw
	out = np.asarray(pix, dtype=np.float32).copy()
	valid = gripper_queries_in_image(out, vis, image_hw)
	finger_ok = [i for i in WRIST_FINGER_MESH_INDICES if valid[i]]

	if len(finger_ok) >= 2:
	if not valid[0]:
	out[0] = out[finger_ok].mean(axis=0)
	if not valid[2] and valid[1]:
	out[2] = 2.0 * out[0] - out[1]
	if not valid[1] and valid[2]:
	out[1] = 2.0 * out[0] - out[2]
	if not valid[4] and valid[3]:
	out[4] = 2.0 * out[0] - out[3]
	if not valid[3] and valid[4]:
	out[3] = 2.0 * out[0] - out[4]
	if not valid[5]:
	if valid[3] and valid[4]:
	mid = 0.5 * (out[3] + out[4])
	elif valid[1] and valid[2]:
	mid = 0.5 * (out[1] + out[2])
	else:
	mid = out[finger_ok].mean(axis=0)
	out[5] = 0.6 * out[0] + 0.4 * mid
	if not valid[6]:
	tip_dir = out[5] - out[0]
	if float(np.linalg.norm(tip_dir)) > 2.0:
	out[6] = out[5] + 0.5 * tip_dir
	else:
	out[6] = out[5] + np.array([0.0, 0.1 * h], dtype=np.float32)
	return _clamp_queries_to_image(out, image_hw)

	if int(valid.sum()) >= 3:
	return _clamp_queries_to_image(out, image_hw)

	return wrist_gripper_template_pixels(image_hw).astype(np.float32)


	def scale_pixels_between_hw(
	pixels: np.ndarray,
	src_hw: tuple[int, int],
	dst_hw: tuple[int, int],
	) -> np.ndarray:
	"""Affine scale pixel coords when resizing images src_hw -> dst_hw."""
	href, wref = src_hw
	hnew, wnew = dst_hw
	out = np.asarray(pixels, dtype=np.float64).copy()
	sx = wnew / float(wref)
	sy = hnew / float(href)
	out[..., 0] *= sx
	out[..., 1] *= sy
	return out


	def project_gripper_mesh_wrist(
	cartesian6: np.ndarray,
	extrinsic_6d: np.ndarray,
	gripper_offset_6d: np.ndarray,
	*,
	K: np.ndarray,
	dist: np.ndarray \| None = None,
	native_hw: tuple[int, int] = DROID_NATIVE_HW,
	gripper_open: float \| None = None,
	) -> tuple[np.ndarray, np.ndarray]:
	"""
	Wrist-view gripper mesh: same chain as :func:`project_gripper_mesh`.

	h5 ``{serial}_left_gripper_offset`` is the camera mount (``T_c2w ≈ T_eef @ T_offset``)
	and is already reflected in ``extrinsic_6d``; mesh points live in the EEF frame and
	must not be premultiplied by ``T_gripper_offset``. ``gripper_offset_6d`` is kept for
	API compatibility only.
	"""
	del gripper_offset_6d
	return project_gripper_mesh(
	cartesian6,
	extrinsic_6d,
	K=K,
	dist=dist,
	native_hw=native_hw,
	gripper_open=gripper_open,
	)


	def project_gripper_mesh(
	cartesian6: np.ndarray,
	extrinsic_6d: np.ndarray,
	*,
	K: np.ndarray,
	dist: np.ndarray \| None = None,
	native_hw: tuple[int, int] = DROID_NATIVE_HW,
	gripper_open: float \| None = None,
	) -> tuple[np.ndarray, np.ndarray]:
	"""7 gripper points -> (7,2) pixels and visibility at ``native_hw`` resolution."""
	c = np.asarray(cartesian6, dtype=np.float64).reshape(-1)
	R_wg = Rotation.from_euler(DROID_EULER_CONVENTION, c[3:6]).as_matrix()
	offsets = (
	gripper_offsets_for_opening(gripper_open)
	if gripper_open is not None
	else GRIPPER_OFFSETS
	)
	world = (R_wg @ offsets.T).T + c[:3].reshape(1, 3)

	K = np.asarray(K, dtype=np.float64).reshape(3, 3)
	w2c = world_to_cam_matrix(extrinsic_6d)
	R = w2c[:3, :3]
	t = w2c[:3, 3].reshape(3, 1)

	pixels = np.zeros((7, 2), dtype=np.float64)
	vis = np.zeros((7,), dtype=bool)

	dist_use = None
	if dist is not None:
	dist_use = np.asarray(dist, dtype=np.float64).reshape(-1)
	if dist_use.size >= 5 and np.allclose(dist_use[:5], 0.0):
	dist_use = None

	href, wref = native_hw
	cam_z = np.zeros((7,), dtype=np.float64)

	if dist_use is not None:
	import cv2

	rvec, _ = cv2.Rodrigues(R)
	pts, _ = cv2.projectPoints(
	world.reshape(-1, 1, 3).astype(np.float64),
	rvec,
	t,
	K,
	dist_use[:5],
	)
	pixels = pts.reshape(-1, 2)
	cam_z = (R @ world.T + t).T[:, 2]
	else:
	for i, p in enumerate(world):
	cam3d = (w2c @ np.concatenate([p, [1.0]]))[:3]
	cam_z[i] = cam3d[2]
	if cam_z[i] <= 1e-5:
	pixels[i] = np.nan
	vis[i] = False
	continue
	proj = K @ cam3d
	if abs(proj[2]) < 1e-8:
	pixels[i] = np.nan
	vis[i] = False
	else:
	pixels[i] = (proj / proj[2])[:2]

	for i in range(7):
	if cam_z[i] <= 0.02:
	vis[i] = False
	pixels[i] = np.nan
	continue
	if not (
	np.isfinite(pixels[i, 0])
	and np.isfinite(pixels[i, 1])
	and 0.0 <= pixels[i, 0] < float(wref)
	and 0.0 <= pixels[i, 1] < float(href)
	):
	vis[i] = False
	pixels[i] = np.nan
	else:
	vis[i] = True
	return pixels.astype(np.float64), vis.astype(np.float64)


	def gripper_offsets_for_opening(gripper_open: float) -> np.ndarray:
	"""Scale finger keypoint offsets by gripper opening (0=closed, 1=open)."""
	g = float(np.clip(gripper_open, 0.0, 1.0))
	offsets = GRIPPER_OFFSETS.copy()
	# Finger tips (indices 1-4): spread with opening; center / palm points stay fixed.
	for i in (1, 2, 3, 4):
	offsets[i, 1] = 0.35 + 0.65 g
	offsets[i, 2] = 0.55 + 0.45 g
	return offsets


	def _score_wrist_seed_queries(queries: np.ndarray, image_hw: tuple[int, int]) -> float:
	h, w = image_hw
	q = np.asarray(queries, dtype=np.float64).reshape(7, 2)
	cy = float(q[:, 1].mean() / max(h, 1))
	cx_spread = float(q[:, 0].std())
	y_spread = float(q[:, 1].std())
	if cy < 0.28 or cy > 0.92:
	return -1.0
	if cx_spread < 12.0 or y_spread < 8.0:
	return -1.0
	finger = q[list(WRIST_FINGER_MESH_INDICES)]
	finger_spread = float(finger.std(axis=0).mean())
	return finger_spread + cx_spread * 0.08 + (0.68 - abs(cy - 0.58)) * 3.0


	def make_wrist_gripper_mesh_queries(
	cartesian: np.ndarray,
	wrist_extrinsics: np.ndarray,
	wrist_gripper_offset: np.ndarray,
	gripper_open: np.ndarray,
	*,
	K: np.ndarray,
	dist: np.ndarray \| None,
	out_hw: tuple[int, int],
	K_candidates: list[tuple[np.ndarray, np.ndarray \| None]] \| None = None,
	) -> np.ndarray:
	"""
	CoTracker seeds for 7 wrist gripper points.

	Uses the same chain as exterior: ``inv(cam2world) @ T_eef @ mesh`` (see
	:func:`project_gripper_mesh`). Tries KarlP vs ZED intrinsics and several timesteps.
	"""
	t_len = int(cartesian.shape[0])
	if t_len < 1:
	return wrist_gripper_template_pixels(out_hw).astype(np.float32)

	seed_times = sorted({0, t_len // 4, t_len // 2, max(0, t_len - 1)})
	k_list: list[tuple[np.ndarray, np.ndarray \| None]] = (
	list(K_candidates) if K_candidates else [(K, dist)]
	)
	best_queries: np.ndarray \| None = None
	best_score = -1.0
	del wrist_gripper_offset # mount calib is in wrist_extrinsics, not applied to mesh

	for t_seed in seed_times:
	ext6 = wrist_extrinsics[t_seed]
	for K_use, dist_use in k_list:
	# Wrist seeds: nominal finger mesh only (gripper_open scaling pushes points OOB).
	pix, vis = project_gripper_mesh(
	cartesian[t_seed],
	ext6,
	K=K_use,
	dist=None,
	native_hw=DROID_NATIVE_HW,
	gripper_open=None,
	)
	pix_out = scale_pixels_between_hw(pix, DROID_NATIVE_HW, out_hw)
	cand = complete_wrist_mesh_queries(pix_out, vis, out_hw)
	score = _score_wrist_seed_queries(cand, out_hw)
	if score > best_score:
	best_score = score
	best_queries = cand
	if best_score >= 25.0:
	return best_queries.astype(np.float32)

	if best_queries is not None and best_score >= 5.0:
	return best_queries.astype(np.float32)
	return wrist_gripper_template_pixels(out_hw).astype(np.float32)


	def make_image_grid(img_h: int, img_w: int, grid_size: int = 5) -> np.ndarray:
	xs = np.linspace(0.0, float(img_w - 1), grid_size, dtype=np.float64)
	ys = np.linspace(0.0, float(img_h - 1), grid_size, dtype=np.float64)
	return np.stack(np.meshgrid(xs, ys, indexing="xy"), axis=-1).reshape(-1, 2)