def constrict_convex_hull_size(
points: Sequence[Point[Scalar]], *, context: Context,
max_size: Optional[int]) -> Sequence[Point[Scalar]]:
if max_size is None:
return points
convex_hull = context.points_convex_hull(points)
if len(convex_hull) <= max_size:
return points
sorted_convex_hull = sorted(convex_hull,
key=partial(context.points_squared_distance,
convex_hull[0]))
new_border_points = []
for index in range(max_size):
quotient, remainder = divmod(index, 2)
new_border_points.append(sorted_convex_hull[-quotient - 1] if remainder
else sorted_convex_hull[quotient])
orienteer = context.angle_orientation
new_border = list(to_max_convex_hull(new_border_points, orienteer))
new_border_extra_endpoints_pairs = tuple(
{(new_border[index - 1], new_border[index])
for index in range(len(new_border))} -
{(convex_hull[index], convex_hull[index - 1])
for index in range(len(convex_hull))})
return (new_border + [
point for point in set(points) - set(convex_hull) if all(
orienteer(start, end, point) is Orientation.COUNTERCLOCKWISE
for start, end in new_border_extra_endpoints_pairs)
])
def to_convex_vertices_sequence(points: Sequence[Point[Scalar]],
random: Random,
context: Context) -> Sequence[Point[Scalar]]:
"""
Based on Valtr algorithm by Sander Verdonschot.
Time complexity:
``O(len(points) * log len(points))``
Memory complexity:
``O(len(points))``
Reference:
http://cglab.ca/~sander/misc/ConvexGeneration/convex.html
"""
xs, ys = [point.x for point in points], [point.y for point in points]
xs, ys = sorted(xs), sorted(ys)
min_x, *xs, max_x = xs
min_y, *ys, max_y = ys
def to_vectors_coordinates(coordinates: List[Scalar],
min_coordinate: Scalar,
max_coordinate: Scalar) -> List[Scalar]:
last_min = last_max = min_coordinate
result = []
for coordinate in coordinates:
if random.getrandbits(1):
result.append(coordinate - last_min)
last_min = coordinate
else:
result.append(last_max - coordinate)
last_max = coordinate
result.extend((max_coordinate - last_min, last_max - max_coordinate))
return result
vectors_xs = to_vectors_coordinates(xs, min_x, max_x)
vectors_ys = to_vectors_coordinates(ys, min_y, max_y)
random.shuffle(vectors_ys)
def to_vector_angle(vector: Tuple[Scalar, Scalar]) -> Key:
x, y = vector
return atan2(y, x)
vectors = sorted(zip(vectors_xs, vectors_ys), key=to_vector_angle)
point_x = point_y = 0
min_polygon_x = min_polygon_y = 0
coordinates_pairs = []
for vector_x, vector_y in vectors:
coordinates_pairs.append((point_x, point_y))
point_x += vector_x
point_y += vector_y
min_polygon_x, min_polygon_y = (min(min_polygon_x, point_x),
min(min_polygon_y, point_y))
shift_x, shift_y = min_x - min_polygon_x, min_y - min_polygon_y
point_cls = context.point_cls
return context.points_convex_hull([
point_cls(min(max(x + shift_x, min_x), max_x),
min(max(y + shift_y, min_y), max_y))
for x, y in coordinates_pairs
])
def test_sizes(
context: Context,
polygon_with_extra_points: Tuple[Polygon, Sequence[Point]]) -> None:
polygon, extra_points = polygon_with_extra_points
result = Triangulation.constrained_delaunay(polygon,
extra_points=extra_points,
context=context)
triangles = result.triangles()
assert 0 < len(triangles) <= (2 * (len(
to_distinct(
chain(polygon.border.vertices, *
[hole.vertices
for hole in polygon.holes], extra_points))) - 1) - len(
context.points_convex_hull(polygon.border.vertices)))
assert all(is_contour_triangular(triangle) for triangle in triangles)