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116 lines
4.1 KiB
Python
116 lines
4.1 KiB
Python
"""
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Vertex list operations
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"""
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import numpy
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from numpy.typing import NDArray, ArrayLike
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def remove_duplicate_vertices(vertices: ArrayLike, closed_path: bool = True) -> NDArray[numpy.float64]:
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"""
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Given a list of vertices, remove any consecutive duplicates.
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Args:
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vertices: `[[x0, y0], [x1, y1], ...]`
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closed_path: If True, `vertices` is interpreted as an implicity-closed path
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(i.e. the last vertex will be removed if it is the same as the first)
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Returns:
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`vertices` with no consecutive duplicates.
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"""
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vertices = numpy.array(vertices)
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duplicates = (vertices == numpy.roll(vertices, 1, axis=0)).all(axis=1)
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if not closed_path:
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duplicates[0] = False
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return vertices[~duplicates]
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def remove_colinear_vertices(vertices: ArrayLike, closed_path: bool = True) -> NDArray[numpy.float64]:
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"""
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Given a list of vertices, remove any superflous vertices (i.e.
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those which lie along the line formed by their neighbors)
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Args:
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vertices: Nx2 ndarray of vertices
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closed_path: If `True`, the vertices are assumed to represent an implicitly
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closed path. If `False`, the path is assumed to be open. Default `True`.
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Returns:
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`vertices` with colinear (superflous) vertices removed.
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"""
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vertices = remove_duplicate_vertices(vertices)
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# Check for dx0/dy0 == dx1/dy1
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dv = numpy.roll(vertices, -1, axis=0) - vertices # [y1-y0, y2-y1, ...]
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dxdy = dv * numpy.roll(dv, 1, axis=0)[:, ::-1] # [[dx0*(dy_-1), (dx_-1)*dy0], dx1*dy0, dy1*dx0]]
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dxdy_diff = numpy.abs(numpy.diff(dxdy, axis=1))[:, 0]
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err_mult = 2 * numpy.abs(dxdy).sum(axis=1) + 1e-40
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slopes_equal = (dxdy_diff / err_mult) < 1e-15
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if not closed_path:
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slopes_equal[[0, -1]] = False
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return vertices[~slopes_equal]
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def poly_contains_points(
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vertices: ArrayLike,
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points: ArrayLike,
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include_boundary: bool = True,
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) -> NDArray[numpy.int_]:
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"""
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Tests whether the provided points are inside the implicitly closed polygon
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described by the provided list of vertices.
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Args:
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vertices: Nx2 Arraylike of form [[x0, y0], [x1, y1], ...], describing an implicitly-
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closed polygon. Note that this should include any offsets.
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points: Nx2 ArrayLike of form [[x0, y0], [x1, y1], ...] containing the points to test.
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include_boundary: True if points on the boundary should be count as inside the shape.
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Default True.
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Returns:
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ndarray of booleans, [point0_is_in_shape, point1_is_in_shape, ...]
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"""
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points = numpy.array(points, copy=False)
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vertices = numpy.array(vertices, copy=False)
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if points.size == 0:
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return numpy.zeros(0, dtype=numpy.int8)
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min_bounds = numpy.min(vertices, axis=0)[None, :]
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max_bounds = numpy.max(vertices, axis=0)[None, :]
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trivially_outside = ((points < min_bounds).any(axis=1)
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| (points > max_bounds).any(axis=1)) # noqa: E128
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nontrivial = ~trivially_outside
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if trivially_outside.all():
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inside = numpy.zeros_like(trivially_outside, dtype=bool)
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return inside
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ntpts = points[None, nontrivial, :] # nontrivial points, along axis 1 of ndarray
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verts = vertices[:, :, None]
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y0_le = verts[:, 1] <= ntpts[..., 1] # (axis 0) y_vertex <= y_point (axis 1)
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y1_le = numpy.roll(y0_le, -1, axis=0) # rolled by 1 vertex
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upward = y0_le & ~y1_le
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downward = ~y0_le & y1_le
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dv = numpy.roll(verts, -1, axis=0) - verts
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is_left = (dv[:, 0] * (ntpts[..., 1] - verts[:, 1]) # >0 if left of dv, <0 if right, 0 if on the line
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- dv[:, 1] * (ntpts[..., 0] - verts[:, 0])) # noqa: E128
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winding_number = ((upward & (is_left > 0)).sum(axis=0)
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- (downward & (is_left < 0)).sum(axis=0)) # noqa: E128
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nontrivial_inside = winding_number != 0 # filter nontrivial points based on winding number
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if include_boundary:
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nontrivial_inside[(is_left == 0).any(axis=0)] = True # check if point lies on any edge
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inside = nontrivial.copy()
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inside[nontrivial] = nontrivial_inside
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return inside
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