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65 lines
2.5 KiB
Python
65 lines
2.5 KiB
Python
import numpy
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from numpy.typing import NDArray, ArrayLike
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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)
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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))
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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, :] # vertices, along axis 0
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xydiff = ntpts - verts # Expands into (n_vertices, n_ntpts, 2)
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y0_le = xydiff[:, :, 1] >= 0 # y_point >= y_vertex (axes 0, 1 for all points & vertices)
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y1_le = numpy.roll(y0_le, -1, axis=0) # same thing for next vertex
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upward = y0_le & ~y1_le # edge passes point y coord going upwards
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downward = ~y0_le & y1_le # edge passes point y coord going downwards
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dv = numpy.roll(verts, -1, axis=0) - verts
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is_left = (dv[..., 0] * xydiff[..., 1] # >0 if left of dv, <0 if right, 0 if on the line
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- dv[..., 1] * xydiff[..., 0])
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winding_number = ((upward & (is_left > 0)).sum(axis=0)
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- (downward & (is_left < 0)).sum(axis=0))
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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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