def unpack_segments(segments: Sequence[Segment],
context: Context) -> Union[Empty, Multisegment, Segment]:
return ((context.multisegment_cls(segments)
if len(segments) > 1
else segments[0])
if segments
else context.empty)
def unpack_polygons(polygons: Sequence[Polygon],
context: Context) -> Union[Empty, Multipolygon, Polygon]:
return ((context.multipolygon_cls(polygons)
if len(polygons) > 1
else polygons[0])
if polygons
else context.empty)
def coupled_with_polygon(box: Box, polygon: Polygon, context: Context) -> bool:
"""
Checks if the box intersects the polygon in continuous points set.
"""
border = polygon.border
polygon_box = context.contour_box(border)
if not coupled_with(polygon_box, box):
return False
elif (is_subset_of(polygon_box, box)
or any(covers_point(box, vertex) for vertex in border.vertices)):
return True
locations = [
point_in_region(vertex, border)
for vertex in to_vertices(box, context)
]
if any(location is Location.INTERIOR for location in locations):
return (not all(location is Location.INTERIOR
for location in locations)
or not is_subset_of_multiregion(box, polygon.holes, context))
else:
return (not is_subset_of_multiregion(box, polygon.holes, context) if
(is_subset_of(box, polygon_box)
and is_subset_of_region(box, border, context)) else any(
segment_in_contour(segment, border) is Relation.OVERLAP
or segment_in_region(segment, border) in (
Relation.CROSS, Relation.COMPONENT, Relation.ENCLOSED)
for segment in to_edges(box, context)))
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 _relate_region(goal_regions: Iterable[Region], region: Region,
region_bounding_box: Box, context: Context) -> Relation:
all_disjoint, none_disjoint, goal_regions_max_x, events_queue = (True,
True,
None,
None)
for goal_region in goal_regions:
goal_region_bounding_box = context.contour_box(goal_region)
if box.disjoint_with(region_bounding_box, goal_region_bounding_box):
if none_disjoint:
none_disjoint = False
else:
if all_disjoint:
all_disjoint = False
goal_regions_max_x = goal_region_bounding_box.max_x
events_queue = CompoundEventsQueue(context)
events_queue.register(region_to_oriented_segments(
region, context),
from_test=True)
else:
goal_regions_max_x = max(goal_regions_max_x,
goal_region_bounding_box.max_x)
events_queue.register(region_to_oriented_segments(
goal_region, context),
from_test=False)
if all_disjoint:
return Relation.DISJOINT
relation = process_compound_queue(
events_queue, min(goal_regions_max_x, region_bounding_box.max_x))
return (relation if none_disjoint else (
Relation.COMPONENT if relation is Relation.EQUAL else
(Relation.OVERLAP if relation in (Relation.COVER, Relation.ENCLOSES,
Relation.COMPOSITE) else relation)))
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 unpack_regions(regions: Sequence[Contour],
context: Context) -> Union[Empty, Polygon, Multipolygon]:
polygon_cls = context.polygon_cls
return ((context.multipolygon_cls([polygon_cls(region, [])
for region in regions])
if len(regions) > 1
else polygon_cls(regions[0], []))
if regions
else context.empty)
def unpack_linear_mix(discrete: Maybe[Multipoint],
linear: Maybe[Linear],
context: Context
) -> Union[Empty, Mix, Multipoint, Linear]:
return (linear
if discrete is context.empty
else (discrete
if linear is context.empty
else context.mix_cls(discrete, linear, context.empty)))
def is_subset_of_multiregion(box: Box, multiregion: Multiregion,
context: Context) -> bool:
"""
Checks if the box is the subset of the multiregion.
"""
return any(
is_subset_of(box, context.contour_box(region))
and is_subset_of_region(box, region, context)
for region in multiregion)
def relate_multipolygon(goal: Multipolygon, test: Multipolygon,
context: Context) -> Relation:
goal_bounding_box = context.polygons_box(goal.polygons)
test_bounding_box = context.polygons_box(test.polygons)
events_queue = CompoundEventsQueue(context)
events_queue.register(to_oriented_segments(goal, context), from_test=False)
events_queue.register(to_oriented_segments(test, context), from_test=True)
return process_compound_queue(
events_queue, min(goal_bounding_box.max_x, test_bounding_box.max_x))
def test_step(context: Context, segments: List[Segment]) -> None:
first_segment, *rest_segments = segments
result = segments_cross_or_overlap(rest_segments)
next_result = segments_cross_or_overlap(segments)
assert (next_result is (result or any(
context.segments_relation(first_segment, segment) in
(Relation.COMPONENT, Relation.COMPOSITE, Relation.CROSS,
Relation.EQUAL, Relation.OVERLAP) for segment in rest_segments)))
def _locate_point_in_indexed_polygons(tree: r.Tree,
polygons: Sequence[Polygon],
point: Point,
context: Context) -> Location:
candidates_indices = tree.find_supersets_indices(
context.box_cls(point.x, point.x, point.y, point.y))
for candidate_index in candidates_indices:
location = polygons[candidate_index].locate(point)
if location is not Location.EXTERIOR:
return location
return Location.EXTERIOR
def relate_multisegment(goal: Multisegment, test: Multisegment,
context: Context) -> Relation:
goal_bounding_box = context.segments_box(goal.segments)
test_bounding_box = context.segments_box(test.segments)
if box.disjoint_with(goal_bounding_box, test_bounding_box):
return Relation.DISJOINT
events_queue = LinearEventsQueue(context)
events_queue.register(to_segments_endpoints(goal), from_test=False)
events_queue.register(to_segments_endpoints(test), from_test=True)
return process_open_linear_queue(
events_queue, min(goal_bounding_box.max_x, test_bounding_box.max_x))
def relate_contour(multipolygon: Multipolygon, contour: Contour,
context: Context) -> Relation:
contour_bounding_box = context.contour_box(contour)
disjoint, multipolygon_max_x, events_queue = True, None, None
for polygon in multipolygon.polygons:
polygon_bounding_box = context.polygon_box(polygon)
if not box.disjoint_with(polygon_bounding_box, contour_bounding_box):
if disjoint:
disjoint = False
multipolygon_max_x = polygon_bounding_box.max_x
events_queue = CompoundEventsQueue(context)
events_queue.register(contour_to_edges_endpoints(contour),
from_test=True)
else:
multipolygon_max_x = max(multipolygon_max_x,
polygon_bounding_box.max_x)
events_queue.register(polygon_to_oriented_segments(
polygon, context),
from_test=False)
return (Relation.DISJOINT if disjoint else process_linear_compound_queue(
events_queue, min(contour_bounding_box.max_x, multipolygon_max_x)))
def symmetric_subtract_segments(first: Segment,
second: Segment,
context: Context
) -> Union_[Empty, Multisegment, Segment]:
relation = context.segments_relation(first, second)
if relation is Relation.DISJOINT:
return context.multisegment_cls([first, second])
elif relation is Relation.EQUAL:
return context.empty
else:
return (_unite_segments_touch(first, second, context)
if relation is Relation.TOUCH
else
(_unite_segments_cross(first, second, context)
if relation is Relation.CROSS
else
(_symmetric_subtract_segments_overlap(first, second, context)
if relation is Relation.OVERLAP
else (_subtract_segments_composite(first, second, context)
if relation is Relation.COMPOSITE
else _subtract_segments_composite(second, first,
context)))))
def relate_multiregion(goal: Multiregion, test: Multiregion,
context: Context) -> Relation:
goal_bounding_box = context.contours_box(goal)
test_bounding_box = context.contours_box(test)
if box.disjoint_with(goal_bounding_box, test_bounding_box):
return Relation.DISJOINT
events_queue = CompoundEventsQueue(context)
events_queue.register(to_oriented_edges_endpoints(goal, context),
from_test=False)
events_queue.register(to_oriented_edges_endpoints(test, context),
from_test=True)
return process_compound_queue(
events_queue, min(goal_bounding_box.max_x, test_bounding_box.max_x))
def _subtract_segment_from_multisegment(multisegment: Multisegment,
segment: Segment,
context: Context) -> List[Segment]:
result = []
segment_cls = context.segment_cls
for index, sub_segment in enumerate(multisegment.segments):
relation = context.segments_relation(segment, sub_segment)
if relation is Relation.EQUAL:
result.extend(multisegment.segments[index + 1:])
break
elif relation is Relation.COMPONENT:
left_start, left_end, right_start, right_end = sorted([
sub_segment.start, sub_segment.end, segment.start,
segment.end])
result.extend(
[segment_cls(right_start, right_end)]
if left_start == segment.start or left_start == segment.end
else
((([segment_cls(left_start, left_end)]
if right_start == right_end
else [segment_cls(left_start, left_end),
segment_cls(right_start, right_end)])
if (right_start == segment.start
or right_start == segment.end)
else [segment_cls(left_start, left_end)])
if left_end == segment.start or left_end == segment.end
else [segment_cls(left_start, right_start)]))
result.extend(multisegment.segments[index + 1:])
break
elif relation is Relation.CROSS:
cross_point = context.segments_intersection(sub_segment, segment)
result.append(segment_cls(sub_segment.start, cross_point))
result.append(segment_cls(cross_point, sub_segment.end))
elif relation is Relation.OVERLAP:
result.append(_subtract_segments_overlap(sub_segment, segment,
context))
elif relation is not Relation.COMPOSITE:
result.append(sub_segment)
return result
def test_step(context: Context, contour: Contour) -> None:
first_vertex, *rest_vertices = contour.vertices
rest_contour = Contour(rest_vertices)
result = edges_intersect(rest_contour)
next_result = edges_intersect(contour)
first_edge, last_edge = (Segment(first_vertex, rest_vertices[0]),
Segment(rest_vertices[-1], first_vertex))
rest_edges = contour_to_edges(rest_contour)
overlap_relations = (Relation.COMPONENT, Relation.COMPOSITE,
Relation.EQUAL, Relation.OVERLAP)
assert (next_result is (result and len(rest_vertices) > 2 and (any(
segments_pair_intersections(
rest_edges[index].start, rest_edges[index].end,
rest_edges[other_index].start, rest_edges[other_index].end)
for index in range(len(rest_edges) - 1)
for other_index in chain(range(index -
1), range(index + 2,
len(rest_edges) - 1))
) or any(
segments_pair_intersections(edge.start, edge.end, other_edge.start,
other_edge.end) in overlap_relations
for edge, other_edge in combinations(rest_edges[:-1], 2))) or any(
segments_pair_intersections(first_edge.start, first_edge.end,
edge.start, edge.end)
for edge in rest_edges[1:-1]) or any(
segments_pair_intersections(last_edge.start, last_edge.end,
edge.start, edge.end)
for edge in rest_edges[:-2]) or len(rest_vertices) > 1 and (
context.segments_relation(
first_edge.start, first_edge.end, rest_edges[0].start,
rest_edges[0].end) in overlap_relations or
context.segments_relation(first_edge.start, first_edge.end,
last_edge.start, last_edge.end)
in overlap_relations or context.segments_relation(
last_edge.start, last_edge.end, rest_edges[0].start,
rest_edges[0].end) in overlap_relations)))
def test_step(context: Context, segments: List[Segment]) -> None:
*rest_segments, last_segment = segments
result = segments_intersections(rest_segments)
next_result = segments_intersections(segments)
assert (next_result.keys() == (
result.keys()
| {(index, len(segments) - 1)
for index, segment in enumerate(rest_segments) if context.
segments_relation(segment, last_segment) is not Relation.DISJOINT}))
assert result.items() <= next_result.items()
assert all(segment_id < next_segment_id == len(segments) - 1
for segment_id, next_segment_id in (next_result.keys() -
result.keys()))
assert all(
context.segments_intersection(
segments[segment_id], segments[next_segment_id]) == next_result[(
segment_id, next_segment_id)][0] if len(next_result[(
segment_id,
next_segment_id)]) == 1 else context.segments_intersection(
segments[segment_id], segments[next_segment_id]) not in
(Relation.DISJOINT, Relation.TOUCH, Relation.CROSS) and (
to_sorted_pair(*next_result[(segment_id, next_segment_id)]) ==
next_result[(segment_id, next_segment_id)]) and all(
context.segment_contains_point(segments[segment_id], point)
for point in next_result[(segment_id, next_segment_id)])
and all(
context.segment_contains_point(segments[next_segment_id], point)
for point in next_result[(segment_id, next_segment_id)])
for segment_id, next_segment_id in (next_result.keys() -
result.keys()))
assert all(
context.segments_relation(segments[segment_id],
segments[next_segment_id])
is not Relation.DISJOINT
for segment_id, next_segment_id in (next_result.keys() -
result.keys()))
def _relate_contour(region: Region, contour: Contour,
contour_bounding_box: Box, context: Context) -> Relation:
region_bounding_box = context.contour_box(region)
if box.disjoint_with(contour_bounding_box, region_bounding_box):
return Relation.DISJOINT
if equal(region, contour, context):
return Relation.COMPONENT
events_queue = CompoundEventsQueue(context)
events_queue.register(to_oriented_segments(region, context),
from_test=False)
events_queue.register(contour_to_edges_endpoints(contour), from_test=True)
return process_linear_compound_queue(
events_queue, min(contour_bounding_box.max_x,
region_bounding_box.max_x))
def relate_contour(goal: Contour, test: Contour, context: Context) -> Relation:
goal_bounding_box, test_bounding_box = (context.contour_box(goal),
context.contour_box(test))
if box.disjoint_with(goal_bounding_box, test_bounding_box):
return Relation.DISJOINT
if equal(goal, test, context):
return Relation.EQUAL
events_queue = CompoundEventsQueue(context)
events_queue.register(to_oriented_edges_endpoints(goal, context),
from_test=False)
events_queue.register(to_oriented_edges_endpoints(test, context),
from_test=True)
return process_closed_linear_queue(
events_queue, min(goal_bounding_box.max_x, test_bounding_box.max_x))
def subtract_segments(minuend: Segment,
subtrahend: Segment,
context: Context
) -> Union_[Empty, Multisegment, Segment]:
relation = context.segments_relation(minuend, subtrahend)
if relation is Relation.COMPONENT or relation is Relation.EQUAL:
return context.empty
elif (relation is Relation.DISJOINT
or relation is Relation.TOUCH
or relation is Relation.CROSS):
return minuend
else:
return (_subtract_segments_overlap(minuend, subtrahend, context)
if relation is Relation.OVERLAP
else _subtract_segments_composite(minuend, subtrahend,
context))
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)
def _intersect_segment_with_multisegment(segment: Segment,
multisegment: Multisegment,
context: Context) -> List[Segment]:
result = []
for sub_segment in multisegment.segments:
relation = context.segments_relation(segment, sub_segment)
if (relation is not Relation.DISJOINT
and relation is not Relation.TOUCH
and relation is not Relation.CROSS):
result.append(segment
if (relation is Relation.EQUAL
or relation is Relation.COMPONENT)
else (sub_segment
if relation is Relation.COMPOSITE
else _intersect_segments_overlap(segment,
sub_segment,
context)))
return result
def coupled_with_region(box: Box, region: Region, context: Context) -> bool:
"""
Checks if the box intersects the region in continuous points set.
"""
region_box = context.contour_box(region)
if not coupled_with(region_box, box):
return False
elif (is_subset_of(region_box, box)
or any(covers_point(box, vertex) for vertex in region.vertices)):
return True
return (any(
point_in_region(vertex, region) is Location.INTERIOR
for vertex in to_vertices(box, context))
or is_subset_of(box, region_box)
and is_subset_of_region(box, region, context) or any(
segment_in_contour(segment, region) is Relation.OVERLAP
or segment_in_region(segment, region) in
(Relation.CROSS, Relation.COMPONENT, Relation.ENCLOSED)
for segment in to_edges(box, context)))
def from_points(points: Iterable[Point],
*,
context: Context) -> Box:
"""
Builds box from points.
"""
points = iter(points)
point = next(points)
min_x, min_y = max_x, max_y = point.x, point.y
for point in points:
x, y = point.x, point.y
if x < min_x:
min_x = x
elif x > max_x:
max_x = x
if y < min_y:
min_y = y
elif y > max_y:
max_y = y
return context.box_cls(min_x, max_x, min_y, max_y)
def _relate_multisegment(multiregion: Multiregion, multisegment: Multisegment,
multisegment_bounding_box: Box,
context: Context) -> Relation:
disjoint, multiregion_max_x, events_queue = True, None, None
for region in multiregion:
region_bounding_box = context.contour_box(region)
if not box.disjoint_with(region_bounding_box,
multisegment_bounding_box):
if disjoint:
disjoint = False
multiregion_max_x = region_bounding_box.max_x
events_queue = CompoundEventsQueue(context)
events_queue.register(to_segments_endpoints(multisegment),
from_test=True)
else:
multiregion_max_x = max(multiregion_max_x,
region_bounding_box.max_x)
events_queue.register(region_to_oriented_segments(region, context),
from_test=False)
return (Relation.DISJOINT if disjoint else process_linear_compound_queue(
events_queue, min(multisegment_bounding_box.max_x, multiregion_max_x)))
def _subtract_segments_composite(minuend: Segment,
subtrahend: Segment,
context: Context
) -> Union_[Multisegment, Segment]:
left_start, left_end, right_start, right_end = sorted([
minuend.start, minuend.end, subtrahend.start, subtrahend.end])
return (context.segment_cls(right_start, right_end)
if left_start == subtrahend.start or left_start == subtrahend.end
else (((context.segment_cls(left_start, left_end)
if right_start == right_end
else
context.multisegment_cls([context.segment_cls(left_start,
left_end),
context.segment_cls(right_start,
right_end)]))
if (right_start == subtrahend.start
or right_start == subtrahend.end)
else context.segment_cls(left_start, left_end))
if left_end == subtrahend.start or left_end == subtrahend.end
else context.segment_cls(left_start, right_start)))
def _unite_segments_touch(first: Segment,
second: Segment,
context: Context) -> Union_[Multisegment, Segment]:
return (context.multisegment_cls([first, second])
if ((first.start != second.start
or (context.angle_orientation(first.start, first.end,
second.end)
is not Orientation.COLLINEAR))
and (first.start != second.end
or (context.angle_orientation(first.start, first.end,
second.start)
is not Orientation.COLLINEAR))
and (first.end != second.start
or (context.angle_orientation(first.end, first.start,
second.end)
is not Orientation.COLLINEAR))
and (first.end != second.end
or (context.angle_orientation(first.end, first.start,
second.start)
is not Orientation.COLLINEAR)))
else context.segment_cls(min(first.start, first.end,
second.start, second.end),
max(first.start, first.end,
second.start, second.end)))
def relate_segment(goal: Segment, test: Segment, context: Context) -> Relation:
return context.segments_relation(test, goal)
