Function _all_points_on_plane

lib/mpl_toolkits/mplot3d/art3d.py:1637–1675

Check if all points are on the same plane. Note that NaN values are ignored. Parameters ---------- xs, ys, zs : array-like The x, y, and z coordinates of the points. atol : float, default: 1e-8 The tolerance for the equality check.

(xs, ys, zs, atol=1e-8)

def _all_points_on_plane(xs, ys, zs, atol=1e-8):
    """
    Check if all points are on the same plane. Note that NaN values are
    ignored.

    Parameters
    ----------
    xs, ys, zs : array-like
        The x, y, and z coordinates of the points.
    atol : float, default: 1e-8
        The tolerance for the equality check.
    """
    xs, ys, zs = np.asarray(xs), np.asarray(ys), np.asarray(zs)
    points = np.column_stack([xs, ys, zs])
    points = points[~np.isnan(points).any(axis=1)]
    # Check for the case where we have less than 3 unique points
    points = np.unique(points, axis=0)
    if len(points) <= 3:
        return True
    # Calculate the vectors from the first point to all other points
    vs = (points - points[0])[1:]
    vs = vs / np.linalg.norm(vs, axis=1)[:, np.newaxis]
    # Filter out parallel vectors
    vs = np.unique(vs, axis=0)
    if len(vs) <= 2:
        return True
    # Filter out parallel and antiparallel vectors to the first vector
    cross_norms = np.linalg.norm(np.cross(vs[0], vs[1:]), axis=1)
    zero_cross_norms = np.where(np.isclose(cross_norms, 0, atol=atol))[0] + 1
    vs = np.delete(vs, zero_cross_norms, axis=0)
    if len(vs) <= 2:
        return True
    # Calculate the normal vector from the first three points
    n = np.cross(vs[0], vs[1])
    n = n / np.linalg.norm(n)
    # If the dot product of the normal vector and all other vectors is zero,
    # all points are on the same plane
    dots = np.dot(n, vs.transpose())
    return np.allclose(dots, 0, atol=atol)


def _generate_normals(polygons):