65 lines
2.5 KiB
Python
65 lines
2.5 KiB
Python
import numpy
|
|
from numpy.typing import NDArray, ArrayLike
|
|
|
|
|
|
def poly_contains_points(
|
|
vertices: ArrayLike,
|
|
points: ArrayLike,
|
|
include_boundary: bool = True,
|
|
) -> NDArray[numpy.int_]:
|
|
"""
|
|
Tests whether the provided points are inside the implicitly closed polygon
|
|
described by the provided list of vertices.
|
|
|
|
Args:
|
|
vertices: Nx2 Arraylike of form [[x0, y0], [x1, y1], ...], describing an implicitly-
|
|
closed polygon. Note that this should include any offsets.
|
|
points: Nx2 ArrayLike of form [[x0, y0], [x1, y1], ...] containing the points to test.
|
|
include_boundary: True if points on the boundary should be count as inside the shape.
|
|
Default True.
|
|
|
|
Returns:
|
|
ndarray of booleans, [point0_is_in_shape, point1_is_in_shape, ...]
|
|
"""
|
|
points = numpy.array(points, copy=False)
|
|
vertices = numpy.array(vertices, copy=False)
|
|
|
|
if points.size == 0:
|
|
return numpy.zeros(0)
|
|
|
|
min_bounds = numpy.min(vertices, axis=0)[None, :]
|
|
max_bounds = numpy.max(vertices, axis=0)[None, :]
|
|
|
|
trivially_outside = ((points < min_bounds).any(axis=1)
|
|
| (points > max_bounds).any(axis=1))
|
|
|
|
nontrivial = ~trivially_outside
|
|
if trivially_outside.all():
|
|
inside = numpy.zeros_like(trivially_outside, dtype=bool)
|
|
return inside
|
|
|
|
ntpts = points[None, nontrivial, :] # nontrivial points, along axis 1 of ndarray
|
|
verts = vertices[:, None, :] # vertices, along axis 0
|
|
xydiff = ntpts - verts # Expands into (n_vertices, n_ntpts, 2)
|
|
|
|
y0_le = xydiff[:, :, 1] >= 0 # y_point >= y_vertex (axes 0, 1 for all points & vertices)
|
|
y1_le = numpy.roll(y0_le, -1, axis=0) # same thing for next vertex
|
|
|
|
upward = y0_le & ~y1_le # edge passes point y coord going upwards
|
|
downward = ~y0_le & y1_le # edge passes point y coord going downwards
|
|
|
|
dv = numpy.roll(verts, -1, axis=0) - verts
|
|
is_left = (dv[..., 0] * xydiff[..., 1] # >0 if left of dv, <0 if right, 0 if on the line
|
|
- dv[..., 1] * xydiff[..., 0])
|
|
|
|
winding_number = ((upward & (is_left > 0)).sum(axis=0)
|
|
- (downward & (is_left < 0)).sum(axis=0))
|
|
|
|
nontrivial_inside = winding_number != 0 # filter nontrivial points based on winding number
|
|
if include_boundary:
|
|
nontrivial_inside[(is_left == 0).any(axis=0)] = True # check if point lies on any edge
|
|
|
|
inside = nontrivial.copy()
|
|
inside[nontrivial] = nontrivial_inside
|
|
return inside
|