class EventsQueue:
__slots__ = 'context', 'key', '_queue'
def __init__(self, context: Context) -> None:
self.context = context
key = self.key = partial(EventsQueueKey, context.angle_orientation)
self._queue = PriorityQueue(key=key)
__repr__ = generate_repr(__init__)
def __bool__(self) -> bool:
return bool(self._queue)
def peek(self) -> Event:
return self._queue.peek()
@abstractmethod
def register(self, segments_endpoints: Iterable[SegmentEndpoints], *,
from_test: bool) -> None:
"""
Registers segments in the events queue.
"""
@abstractmethod
def sweep(self, stop_x: Scalar) -> Iterable[LeftEvent]:
"""
Sweeps plane and emits processed segments' events.
"""
def _divide_segment(self, event: LeftEvent, break_point: Point) -> None:
self._queue.push(event.divide(break_point))
self._queue.push(event.right)
class Builder:
__slots__ = ('index', '_beach_line', '_circle_events', '_end_points',
'site_events', '_site_event_index')
def __init__(self,
index: int = 0,
site_events: Optional[List[SiteEvent]] = None) -> None:
self.index = index
self._beach_line = red_black.Tree.from_components([])
self._circle_events = PriorityQueue(key=itemgetter(0))
self._end_points = PriorityQueue(key=itemgetter(0))
self.site_events = [] if site_events is None else site_events
self._site_event_index = None
__repr__ = generate_repr(__init__)
@property
def beach_line(self) -> List[Tuple[BeachLineKey, BeachLineValue]]:
return [node.item for node in self._beach_line]
@property
def site_event(self) -> SiteEvent:
return self.site_events[self._site_event_index]
@property
def site_event_index(self) -> int:
return (len(self.site_events)
if self._site_event_index is None else self._site_event_index)
def activate_circle_event(self, first_site: SiteEvent,
second_site: SiteEvent, third_site: SiteEvent,
bisector_node: red_black.Node) -> None:
event = CircleEvent(0., 0., 0.)
# check if the three input sites create a circle event
if compute_circle_event(event, first_site, second_site, third_site):
# add the new circle event to the circle events queue;
# update bisector's circle event iterator to point
# to the new circle event in the circle event queue
self._circle_events.push((event, bisector_node))
bisector_node.value.circle_event = event
def construct(self, output: 'Diagram') -> None:
self.init_sites_queue()
self.init_beach_line(output)
while (self._circle_events
or self._site_event_index < len(self.site_events)):
if (not self._circle_events
or (self._site_event_index < len(self.site_events)
and self.site_event < self._circle_events.peek()[0])):
self.process_site_event(output)
else:
self.process_circle_event(output)
while (self._circle_events
and not self._circle_events.peek()[0].is_active):
self._circle_events.pop()
self._beach_line.clear()
output._build()
@staticmethod
def deactivate_circle_event(value: BeachLineValue) -> None:
if value.circle_event is not None:
value.circle_event.deactivate()
value.circle_event = None
def init_beach_line(self, diagram: 'Diagram') -> None:
if not self.site_events:
return
elif len(self.site_events) == 1:
# handle single site event case
diagram._process_single_site(self.site_events[0])
self._site_event_index += 1
else:
skip = 0
while (self._site_event_index < len(self.site_events)
and are_vertical_endpoints(self.site_event.start,
self.site_events[0].start)
and self.site_event.is_vertical):
self._site_event_index += 1
skip += 1
if skip == 1:
# init beach line with the first two sites
self.init_beach_line_default(diagram)
else:
# init beach line with collinear vertical sites
self.init_beach_line_collinear_sites(diagram)
def init_beach_line_collinear_sites(self, diagram: 'Diagram') -> None:
first_index, second_index = 0, 1
while second_index != self._site_event_index:
# create a new beach line node
first_site, second_site = (self.site_events[first_index],
self.site_events[second_index])
new_node = BeachLineKey(first_site, second_site)
# update the diagram
edge, _ = diagram._insert_new_edge(first_site, second_site)
# insert a new bisector into the beach line
self._beach_line.insert(new_node, BeachLineValue(edge))
first_index += 1
second_index += 1
def init_beach_line_default(self, diagram: 'Diagram') -> None:
# get the first and the second site event
self.insert_new_arc(self.site_events[0], self.site_events[0],
self.site_events[1], diagram)
# the second site was already processed, move the position
self._site_event_index += 1
def insert_new_arc(self, first_arc_site: SiteEvent,
second_arc_site: SiteEvent, site_event: SiteEvent,
output: 'Diagram') -> red_black.Node:
# create two new bisectors with opposite directions
new_left_node = BeachLineKey(first_arc_site, site_event)
new_right_node = BeachLineKey(site_event, second_arc_site)
# set correct orientation for the first site of the second node
if site_event.is_segment:
new_right_node.left_site.inverse()
# update the output
edges = output._insert_new_edge(second_arc_site, site_event)
self._beach_line.insert(new_right_node, BeachLineValue(edges[1]))
if site_event.is_segment:
# update the beach line with temporary bisector,
# that will # disappear after processing site event
# corresponding to the second endpoint of the segment site
new_node = BeachLineKey(site_event, site_event)
new_node.right_site.inverse()
node = self._beach_line.insert(new_node, BeachLineValue(None))
# update the data structure that holds temporary bisectors
self._end_points.push((site_event.end, node))
return self._beach_line.insert(new_left_node, BeachLineValue(edges[0]))
def init_sites_queue(self) -> None:
self.site_events.sort()
self.site_events = to_unique_just_seen(self.site_events)
for index, event in enumerate(self.site_events):
event.sorted_index = index
self._site_event_index = 0
def insert_point(self, point: Point) -> int:
index = self.index
self.site_events.append(
SiteEvent.from_point(point,
initial_index=index,
source_category=SourceCategory.SINGLE_POINT))
self.index += 1
return index
def insert_segment(self, segment: Segment) -> int:
site_events = self.site_events
index = self.index
start, end = segment.start, segment.end
site_events.append(
SiteEvent.from_point(
start,
initial_index=index,
source_category=SourceCategory.SEGMENT_START_POINT))
site_events.append(
SiteEvent.from_point(
end,
initial_index=index,
source_category=SourceCategory.SEGMENT_END_POINT))
site_events.append(
SiteEvent(start,
end,
source_category=SourceCategory.INITIAL_SEGMENT,
initial_index=index) if start < end else SiteEvent(
end,
start,
source_category=SourceCategory.REVERSE_SEGMENT,
initial_index=index))
self.index += 1
return index
def process_circle_event(self, output: 'Diagram') -> None:
circle_event, first_node = self._circle_events.pop()
last_node = first_node
second_site = copy(first_node.key.right_site)
second_bisector = first_node.value.edge
first_node = self._beach_line.predecessor(first_node)
first_bisector = first_node.value.edge
first_site = copy(first_node.key.left_site)
if (not first_site.is_segment and second_site.is_segment
and second_site.end == first_site.start):
second_site.inverse()
first_node.key.right_site = second_site
first_node.value.edge, _ = output._insert_new_edge_from_intersection(
first_site, second_site, circle_event, first_bisector,
second_bisector)
self._beach_line.remove(last_node)
last_node = first_node
if first_node is not self._beach_line.min():
self.deactivate_circle_event(first_node.value)
first_node = self._beach_line.predecessor(first_node)
self.activate_circle_event(first_node.key.left_site, first_site,
second_site, last_node)
last_node = self._beach_line.successor(last_node)
if last_node is not red_black.NIL:
self.deactivate_circle_event(last_node.value)
self.activate_circle_event(first_site, second_site,
last_node.key.right_site, last_node)
def process_site_event(self, output: 'Diagram') -> None:
last_index = self._site_event_index + 1
if not self.site_event.is_segment:
while (self._end_points
and self._end_points.peek()[0] == self.site_event.start):
_, node = self._end_points.pop()
self._beach_line.remove(node)
else:
while (last_index < len(self.site_events)
and self.site_events[last_index].is_segment
and (self.site_events[last_index].start
== self.site_event.start)):
last_index += 1
# find the node in the binary search tree
# with left arc lying above the new site point
new_key = BeachLineKey(self.site_event, self.site_event)
right_node = self._beach_line.supremum(new_key)
while self._site_event_index < last_index:
site_event = copy(self.site_event)
left_node = right_node
if right_node is red_black.NIL:
# the above arc corresponds to the second arc of the last node,
# move the iterator to the last node
left_node = self._beach_line.max()
# get the second site of the last node
arc_site = left_node.key.right_site
# insert new nodes into the beach line, update the output
right_node = self.insert_new_arc(arc_site, arc_site,
site_event, output)
# add a candidate circle to the circle event queue;
# there could be only one new circle event
# formed by a new bisector and the one on the left
self.activate_circle_event(left_node.key.left_site,
left_node.key.right_site,
site_event, right_node)
elif right_node is self._beach_line.min():
# the above arc corresponds to the first site of the first node
arc_site = right_node.key.left_site
# Insert new nodes into the beach line. Update the output.
left_node = self.insert_new_arc(arc_site, arc_site, site_event,
output)
# if the site event is a segment, update its direction
if site_event.is_segment:
site_event.inverse()
# add a candidate circle to the circle event queue;
# there could be only one new circle event
# formed by a new bisector and the one on the right
self.activate_circle_event(site_event,
right_node.key.left_site,
right_node.key.right_site,
right_node)
right_node = left_node
else:
# the above arc corresponds neither to the first,
# nor to the last site in the beach line
second_arc_site = right_node.key.left_site
third_site = right_node.key.right_site
# remove the candidate circle from the event queue
self.deactivate_circle_event(right_node.value)
left_node = self._beach_line.predecessor(left_node)
first_arc_site = left_node.key.right_site
first_site = left_node.key.left_site
# insert new nodes into the beach line. Update the output
new_node = self.insert_new_arc(first_arc_site, second_arc_site,
site_event, output)
# add candidate circles to the circle event queue;
# there could be up to two circle events
# formed by a new bisector and the one on the left or right
self.activate_circle_event(first_site, first_arc_site,
site_event, new_node)
# if the site event is a segment, update its direction
if site_event.is_segment:
site_event.inverse()
self.activate_circle_event(site_event, second_arc_site,
third_site, right_node)
right_node = new_node
self._site_event_index += 1
class Operation:
__slots__ = ('_left', '_right', '_type', '_events_queue', '_resultant',
'_already_run')
def __init__(self, left: Polygon, right: Polygon,
type_: OperationType) -> None:
self._left = left
self._right = right
self._type = type_
self._events_queue = PriorityQueue(key=EventsQueueKey, reverse=True)
self._resultant = Polygon([])
self._already_run = False
__repr__ = generate_repr(__init__, field_seeker=seekers.complex_)
def __eq__(self, other: 'Operation') -> bool:
return (self._left == other._left and self._right == other._right
and self._type is other._type
if isinstance(other, Operation) else NotImplemented)
@property
def left(self) -> Polygon:
return self._left
@property
def right(self) -> Polygon:
return self._right
@property
def events(self) -> List[SweepEvent]:
events_queue = copy(self._events_queue)
return [events_queue.pop() for _ in range(len(events_queue))]
@property
def resultant(self) -> Polygon:
return self._resultant
@property
def type(self) -> OperationType:
return self._type
@property
def is_trivial(self) -> bool:
# test 1 for trivial result case
if not (self._left.contours and self._right.contours):
# at least one of the polygons is empty
if self._type is OperationType.DIFFERENCE:
self._resultant = self._left
if (self._type is OperationType.UNION
or self._type is OperationType.XOR):
self._resultant = (self._left
if self._left.contours else self._right)
self._already_run = True
return True
# test 2 for trivial result case
left_bounding_box = self._left.bounding_box
right_bounding_box = self._right.bounding_box
if (left_bounding_box.x_min > right_bounding_box.x_max
or right_bounding_box.x_min > left_bounding_box.x_max
or left_bounding_box.y_min > right_bounding_box.y_max
or right_bounding_box.y_min > left_bounding_box.y_max):
# the bounding boxes do not overlap
if self._type is OperationType.DIFFERENCE:
self._resultant = self._left
elif (self._type is OperationType.UNION
or self._type is OperationType.XOR):
self._resultant = self._left
self._resultant.join(self._right)
self._already_run = True
return True
return False
@staticmethod
def collect_events(events: List[SweepEvent]) -> List[SweepEvent]:
result = [
event for event in events if event.is_left and event.in_result
or not event.is_left and event.other_event.in_result
]
is_sorted = False
while not is_sorted:
is_sorted = True
for index in range(len(result) - 1):
if (EventsQueueKey(result[index]) < EventsQueueKey(
result[index + 1])):
result[index], result[index + 1] = (result[index + 1],
result[index])
is_sorted = False
for index, event in enumerate(result):
event.position = index
if not event.is_left:
event.position, event.other_event.position = (
event.other_event.position, event.position)
return result
def connect_edges(self, events: List[SweepEvent]) -> None:
self.process_events(self.collect_events(events))
def divide_segment(self, event: SweepEvent, point: Point) -> None:
# "left event" of the "right line segment"
# resulting from dividing event.segment
left_event = SweepEvent(True, point, event.other_event,
event.polygon_type, EdgeType.NORMAL)
# "right event" of the "left line segment"
# resulting from dividing event.segment
right_event = SweepEvent(False, point, event, event.polygon_type,
EdgeType.NORMAL)
if EventsQueueKey(left_event) < EventsQueueKey(event.other_event):
# avoid a rounding error,
# the left event would be processed after the right event
event.other_event.is_left = True
left_event.is_left = False
event.other_event.other_event = left_event
event.other_event = right_event
self._events_queue.push(left_event)
self._events_queue.push(right_event)
def in_result(self, event: SweepEvent) -> bool:
operation_type = self._type
edge_type = event.edge_type
if edge_type is EdgeType.NORMAL:
if operation_type is OperationType.INTERSECTION:
return not event.other_in_out
elif operation_type is OperationType.UNION:
return event.other_in_out
elif operation_type is OperationType.DIFFERENCE:
return (event.polygon_type is PolygonType.SUBJECT
and event.other_in_out
or event.polygon_type is PolygonType.CLIPPING
and not event.other_in_out)
else:
return operation_type is OperationType.XOR
elif edge_type is EdgeType.SAME_TRANSITION:
return (operation_type is OperationType.INTERSECTION
or operation_type is OperationType.UNION)
elif edge_type is EdgeType.DIFFERENT_TRANSITION:
return operation_type is OperationType.DIFFERENCE
else:
return False
def possible_intersection(self, first_event: SweepEvent,
second_event: SweepEvent) -> int:
intersections_count, first_point, second_point = find_intersections(
first_event.segment, second_event.segment)
if not intersections_count:
# no intersection
return 0
if ((intersections_count == 1)
and (first_event.point == second_event.point or
(first_event.other_event.point
== second_event.other_event.point))):
# the line segments intersect at an endpoint of both line segments
return 0
if (intersections_count == 2
and first_event.polygon_type is second_event.polygon_type):
raise ValueError("Edges of the same polygon should not overlap.")
# The line segments associated to le1 and le2 intersect
if intersections_count == 1:
if (first_event.point != first_point
and first_event.other_event.point != first_point):
# if the intersection point is not an endpoint of le1.segment
self.divide_segment(first_event, first_point)
if (second_event.point != first_point
and second_event.other_event.point != first_point):
# if the intersection point is not an endpoint of le2.segment
self.divide_segment(second_event, first_point)
return 1
# The line segments associated to le1 and le2 overlap
sorted_events = []
if first_event.point == second_event.point:
sorted_events.append(None)
elif EventsQueueKey(first_event) < EventsQueueKey(second_event):
sorted_events.append(second_event)
sorted_events.append(first_event)
else:
sorted_events.append(first_event)
sorted_events.append(second_event)
if first_event.other_event.point == second_event.other_event.point:
sorted_events.append(None)
elif (EventsQueueKey(first_event.other_event) < EventsQueueKey(
second_event.other_event)):
sorted_events.append(second_event.other_event)
sorted_events.append(first_event.other_event)
else:
sorted_events.append(first_event.other_event)
sorted_events.append(second_event.other_event)
if (len(sorted_events) == 2
or len(sorted_events) == 3 and sorted_events[2]):
# both line segments are equal or share the left endpoint
first_event.edge_type = EdgeType.NON_CONTRIBUTING
second_event.edge_type = (EdgeType.SAME_TRANSITION if
first_event.in_out is second_event.in_out
else EdgeType.DIFFERENT_TRANSITION)
if len(sorted_events) == 3:
self.divide_segment(sorted_events[2].other_event,
sorted_events[1].point)
return 2
if len(sorted_events) == 3:
# the line segments share the right endpoint
self.divide_segment(sorted_events[0], sorted_events[1].point)
return 3
if sorted_events[0] is not sorted_events[3].other_event:
# no line segment includes totally the other one
self.divide_segment(sorted_events[0], sorted_events[1].point)
self.divide_segment(sorted_events[1], sorted_events[2].point)
return 3
# one line segment includes the other one
self.divide_segment(sorted_events[0], sorted_events[1].point)
self.divide_segment(sorted_events[3].other_event,
sorted_events[2].point)
return 3
def process_events(self, events: List[SweepEvent]) -> None:
depth, hole_of = [], []
processed = [False] * len(events)
contours = self._resultant.contours
for index, event in enumerate(events):
if processed[index]:
continue
contour = Contour([], [], True)
contour_id = len(contours)
contours.append(contour)
depth.append(0)
hole_of.append(-1)
if event.prev_in_result_event is not None:
lower_contour_id = event.prev_in_result_event.contour_id
if not event.prev_in_result_event.result_in_out:
contours[lower_contour_id].add_hole(contour_id)
hole_of[contour_id] = lower_contour_id
depth[contour_id] = depth[lower_contour_id] + 1
contour.is_external = False
elif not contours[lower_contour_id].is_external:
contours[hole_of[lower_contour_id]].add_hole(contour_id)
hole_of[contour_id] = hole_of[lower_contour_id]
depth[contour_id] = depth[lower_contour_id]
contour.is_external = False
position = index
initial = event.point
contour.add(initial)
event = events[position]
while event.other_event.point != initial:
processed[position] = True
if event.is_left:
event.result_in_out = False
event.contour_id = contour_id
else:
event.other_event.result_in_out = True
event.other_event.contour_id = contour_id
position = event.position
processed[position] = True
contour.add(events[position].point)
position = self.to_next_position(position, events, processed)
event = events[position]
processed[position] = processed[event.position] = True
event.other_event.result_in_out = True
event.other_event.contour_id = contour_id
if depth[contour_id] & 1:
contour.reverse()
def process_segments(self) -> None:
for contour in self._left.contours:
for segment in to_segments(contour.points):
self._process_segment(segment, PolygonType.SUBJECT)
for contour in self._right.contours:
for segment in to_segments(contour.points):
self._process_segment(segment, PolygonType.CLIPPING)
def _process_segment(self, segment: Segment,
polygon_type: PolygonType) -> None:
source_event = SweepEvent(True, segment.source, None, polygon_type,
EdgeType.NORMAL)
target_event = SweepEvent(True, segment.target, source_event,
polygon_type, EdgeType.NORMAL)
source_event.other_event = target_event
if segment.min == segment.source:
target_event.is_left = False
else:
source_event.is_left = False
self._events_queue.push(source_event)
self._events_queue.push(target_event)
def sweep(self) -> List[SweepEvent]:
min_max_x = min(self._left.bounding_box.x_max,
self._right.bounding_box.x_max)
result = []
events_queue = self._events_queue
sweep_line = red_black.set_(key=SweepLineKey)
while events_queue:
event = events_queue.peek()
if (self._type is OperationType.INTERSECTION
and event.point.x > min_max_x
or self._type is OperationType.DIFFERENCE
and event.point.x > self._left.bounding_box.x_max):
break
result.append(event)
events_queue.pop()
if event.is_left:
sweep_line.add(event)
try:
next_event = sweep_line.next(event)
except ValueError:
next_event = None
try:
previous_event = sweep_line.prev(event)
except ValueError:
previous_event = None
self.compute_fields(event, previous_event)
if next_event is not None:
if self.possible_intersection(event, next_event) == 2:
self.compute_fields(event, previous_event)
self.compute_fields(next_event, event)
if previous_event is not None:
if self.possible_intersection(previous_event, event) == 2:
try:
pre_previous_event = sweep_line.prev(
previous_event)
except ValueError:
pre_previous_event = None
self.compute_fields(previous_event, pre_previous_event)
self.compute_fields(event, previous_event)
else:
event = event.other_event
if event not in sweep_line:
continue
try:
next_event = sweep_line.next(event)
except ValueError:
next_event = None
try:
previous_event = sweep_line.prev(event)
except ValueError:
previous_event = None
sweep_line.remove(event)
if next_event is not None and previous_event is not None:
self.possible_intersection(previous_event, next_event)
return result
def compute_fields(self, event: SweepEvent,
previous_event: Optional[SweepEvent]) -> None:
if previous_event is None:
event.in_out = False
event.other_in_out = True
else:
if event.polygon_type is previous_event.polygon_type:
event.in_out = not previous_event.in_out
event.other_in_out = previous_event.other_in_out
else:
event.in_out = not previous_event.other_in_out
event.other_in_out = (not previous_event.in_out
if previous_event.is_vertical else
previous_event.in_out)
event.prev_in_result_event = (
previous_event.prev_in_result_event if
(not self.in_result(previous_event)
or previous_event.is_vertical) else previous_event)
event.in_result = self.in_result(event)
def run(self) -> None:
if self._already_run:
return
if self.is_trivial:
return
self.process_segments()
self.connect_edges(self.sweep())
self._already_run = True
@staticmethod
def to_next_position(position: int, events: List[SweepEvent],
processed: List[bool]) -> int:
result = position + 1
while (result < len(events)
and events[result].point == events[position].point):
if not processed[result]:
return result
else:
result += 1
if not position:
return 0
result = position - 1
while processed[result]:
if not result:
break
result -= 1
return result
class ShapedEventsQueue(Generic[LeftShapedEvent]):
__slots__ = 'context', 'event_cls', '_queue'
def __init__(self,
event_cls: Type[LeftShapedEvent],
context: Context) -> None:
self.event_cls, self.context = event_cls, context
self._queue = PriorityQueue(key=partial(BinaryEventsQueueKey,
context.angle_orientation))
__repr__ = generate_repr(__init__)
def __bool__(self) -> bool:
return bool(self._queue)
@property
def key(self) -> Callable[[ShapedEvent], BinaryEventsQueueKey]:
return self._queue.key
def detect_intersection(self,
below_event: LeftShapedEvent,
event: LeftShapedEvent) -> bool:
relation = self.context.segments_relation(below_event, event)
if relation is Relation.CROSS or relation is Relation.TOUCH:
if (event.start != below_event.start
and event.end != below_event.end):
# segments do not intersect_multipolygons at endpoints
point = self.context.segments_intersection(below_event, event)
if point != below_event.start and point != below_event.end:
self._divide_segment(below_event, point)
if point != event.start and point != event.end:
self._divide_segment(event, point)
elif relation is not Relation.DISJOINT:
# segments overlap
if below_event.from_first is event.from_first:
raise ValueError('Edges of the same geometry '
'should not overlap.')
starts_equal = below_event.start == event.start
if starts_equal:
start_min = start_max = None
elif self.key(event) < self.key(below_event):
start_min, start_max = event, below_event
else:
start_min, start_max = below_event, event
ends_equal = event.end == below_event.end
if ends_equal:
end_min = end_max = None
elif self.key(event.opposite) < self.key(below_event.opposite):
end_min, end_max = event.opposite, below_event.opposite
else:
end_min, end_max = below_event.opposite, event.opposite
if starts_equal:
# both line segments are equal or share the left endpoint
below_event.overlap_kind = event.overlap_kind = (
OverlapKind.SAME_ORIENTATION
if event.interior_to_left is below_event.interior_to_left
else OverlapKind.DIFFERENT_ORIENTATION)
if not ends_equal:
self._divide_segment(end_max.opposite, end_min.start)
return True
elif ends_equal:
# the line segments share the right endpoint
self._divide_segment(start_min, start_max.start)
elif start_min is end_max.opposite:
# one line segment includes the other one
self._divide_segment(start_min, end_min.start)
self._divide_segment(start_min, start_max.start)
else:
# no line segment includes the other one
self._divide_segment(start_max, end_min.start)
self._divide_segment(start_min, start_max.start)
return False
def pop(self) -> ShapedEvent:
return self._queue.pop()
def register(self,
segments_endpoints: Iterable[SegmentEndpoints],
from_first: bool) -> None:
event_cls, push = self.event_cls, self._queue.push
for segment_endpoints in segments_endpoints:
event = event_cls.from_endpoints(segment_endpoints, from_first)
push(event)
push(event.opposite)
def _divide_segment(self, event: LeftShapedEvent, point: Point) -> None:
tail = event.divide(point)
self._queue.push(tail)
self._queue.push(event.opposite)
class NaryEventsQueue:
__slots__ = 'context', '_queue'
def __init__(self, context: Context) -> None:
self.context = context
self._queue = PriorityQueue(key=partial(NaryEventsQueueKey,
context.angle_orientation))
__repr__ = generate_repr(__init__)
def __bool__(self) -> bool:
return bool(self._queue)
@property
def key(self) -> Callable[[NaryEvent], NaryEventsQueueKey]:
return self._queue.key
def detect_intersection(self,
below_event: LeftNaryEvent,
event: LeftNaryEvent) -> None:
relation = self.context.segments_relation(below_event, event)
if relation is Relation.CROSS or relation is Relation.TOUCH:
if (event.start != below_event.start
and event.end != below_event.end):
# segments do not intersect_multipolygons at endpoints
point = self.context.segments_intersection(below_event, event)
if point != below_event.start and point != below_event.end:
self._divide_segment(below_event, point)
if point != event.start and point != event.end:
self._divide_segment(event, point)
elif relation is not Relation.DISJOINT:
# segments overlap
starts_equal = below_event.start == event.start
if starts_equal:
start_min = start_max = None
elif self.key(event) < self.key(below_event):
start_min, start_max = event, below_event
else:
start_min, start_max = below_event, event
ends_equal = event.end == below_event.end
if ends_equal:
end_min = end_max = None
elif self.key(event.opposite) < self.key(below_event.opposite):
end_min, end_max = event.opposite, below_event.opposite
else:
end_min, end_max = below_event.opposite, event.opposite
if starts_equal:
# both line segments are equal or share the left endpoint
if not ends_equal:
self._divide_segment(end_max.opposite, end_min.start)
elif ends_equal:
# the line segments share the right endpoint
self._divide_segment(start_min, start_max.start)
elif start_min is end_max.opposite:
# one line segment includes the other one
self._divide_segment(start_min, end_min.start)
self._divide_segment(start_min, start_max.start)
else:
# no line segment includes the other one
self._divide_segment(start_max, end_min.start)
self._divide_segment(start_min, start_max.start)
def pop(self) -> NaryEvent:
return self._queue.pop()
def register(self, segments_endpoints: Iterable[SegmentEndpoints]) -> None:
push = self._queue.push
for segment_endpoints in segments_endpoints:
event = LeftNaryEvent.from_segment_endpoints(segment_endpoints)
push(event)
push(event.opposite)
def _divide_segment(self, event: LeftNaryEvent, point: Point) -> None:
tail = LeftNaryEvent.divide(event, point)
self._queue.push(tail)
self._queue.push(event.opposite)
class MixedEventsQueue:
__slots__ = 'context', '_queue'
def __init__(self, context: Context) -> None:
self.context = context
self._queue = PriorityQueue(key=partial(BinaryEventsQueueKey,
context.angle_orientation))
@property
def key(self) -> Callable[[MixedEvent], BinaryEventsQueueKey]:
return self._queue.key
__repr__ = generate_repr(__init__)
def __bool__(self) -> bool:
return bool(self._queue)
def detect_intersection(self,
below_event: LeftMixedEvent,
event: LeftMixedEvent) -> bool:
relation = self.context.segments_relation(below_event, event)
if relation is Relation.CROSS or relation is Relation.TOUCH:
if (event.start != below_event.start
and event.end != below_event.end):
# segments do not intersect_multipolygons at endpoints
point = self.context.segments_intersection(below_event, event)
if point != below_event.start and point != below_event.end:
self._divide_segment(below_event, point)
if point != event.start and point != event.end:
self._divide_segment(event, point)
elif relation is not Relation.DISJOINT:
# segments overlap
if below_event.from_first is event.from_first:
raise ValueError('Edges of the {geometry} '
'should not overlap.'
.format(geometry=('multisegment'
if event.from_first
else 'multipolygon')))
event.is_overlap = below_event.is_overlap = True
starts_equal = below_event.start == event.start
if starts_equal:
start_min = start_max = None
elif self.key(event) < self.key(below_event):
start_min, start_max = event, below_event
else:
start_min, start_max = below_event, event
ends_equal = event.end == below_event.end
if ends_equal:
end_min = end_max = None
elif self.key(event.opposite) < self.key(below_event.opposite):
end_min, end_max = event.opposite, below_event.opposite
else:
end_min, end_max = below_event.opposite, event.opposite
if starts_equal:
# both line segments are equal or share the left endpoint
if not ends_equal:
self._divide_segment(end_max.opposite, end_min.start)
return True
elif ends_equal:
# the line segments share the right endpoint
self._divide_segment(start_min, start_max.start)
elif start_min is end_max.opposite:
# one line segment includes the other one
self._divide_segment(start_min, end_min.start)
self._divide_segment(start_min, start_max.start)
else:
# no line segment includes the other one
self._divide_segment(start_max, end_min.start)
self._divide_segment(start_min, start_max.start)
return False
def pop(self) -> MixedEvent:
return self._queue.pop()
def register(self,
segments_endpoints: Iterable[SegmentEndpoints],
from_first: bool) -> None:
push = self._queue.push
for segment_endpoints in segments_endpoints:
event = LeftMixedEvent.from_endpoints(segment_endpoints,
from_first)
push(event)
push(event.opposite)
def _divide_segment(self, event: LeftMixedEvent, point: Point) -> None:
tail = event.divide(point)
self._queue.push(tail)
self._queue.push(event.opposite)
class EventsQueue:
__slots__ = 'context', '_queue'
def __init__(self, context: Context) -> None:
self.context = context
self._queue = PriorityQueue(key=partial(EventsQueueKey,
context.angle_orientation))
@staticmethod
def compute_position(below_event: Optional[LeftEvent],
event: LeftEvent) -> None:
if below_event is not None:
event.other_interior_to_left = (below_event.other_interior_to_left
if (event.from_first
is below_event.from_first)
else below_event.interior_to_left)
def detect_intersection(self,
below_event: LeftEvent,
event: LeftEvent) -> bool:
"""
Populates events queue with intersection events.
Checks if events' segments overlap and have the same start.
"""
relation = self.context.segments_relation(below_event, event)
if relation is Relation.CROSS or relation is Relation.TOUCH:
point = self.context.segments_intersection(below_event, event)
if point != below_event.start and point != below_event.end:
self.divide_segment(below_event, point)
if point != event.start and point != event.end:
self.divide_segment(event, point)
elif relation is not Relation.DISJOINT:
# segments overlap
if below_event.from_first is event.from_first:
raise ValueError('Edges of the same polygon '
'should not overlap.')
starts_equal = below_event.start == event.start
ends_equal = below_event.end == event.end
start_min, start_max = (
(event, below_event)
if starts_equal or (self._queue.key(event)
< self._queue.key(below_event))
else (below_event, event))
end_min, end_max = (
(event.right, below_event.right)
if ends_equal or (self._queue.key(event.right)
< self._queue.key(below_event.right))
else (below_event.right, event.right))
if starts_equal:
# both line segments are equal or share the left endpoint
event.is_overlap = below_event.is_overlap = True
if not ends_equal:
self.divide_segment(end_max.left, end_min.start)
return True
elif ends_equal:
# the line segments share the right endpoint
self.divide_segment(start_min, start_max.start)
else:
self.divide_segment(start_min
# one line segment includes the other one
if start_min is end_max.left
# no line segment includes the other one
else start_max,
end_min.start)
self.divide_segment(start_min, start_max.start)
return False
def divide_segment(self, event: LeftEvent, point: Point) -> None:
self.push(event.divide(point))
self.push(event.right)
def push(self, event: Event) -> None:
self._queue.push(event)
def register_edge(self,
edge: QuadEdge,
*,
from_first: bool,
is_counterclockwise_contour: bool) -> None:
start_event = LeftEvent.from_segment_endpoints(
to_endpoints(edge), from_first, is_counterclockwise_contour)
start_event.edge = edge
self.push(start_event)
self.push(start_event.right)
def register_segment(self,
endpoints: SegmentEndpoints,
*,
from_first: bool,
is_counterclockwise_contour: bool) -> None:
start_event = LeftEvent.from_segment_endpoints(
endpoints, from_first, is_counterclockwise_contour)
self.push(start_event)
self.push(start_event.right)
def sweep(self) -> Iterable[LeftEvent]:
sweep_line = SweepLine(self.context)
queue = self._queue
while queue:
event = queue.pop()
if event.is_left:
sweep_line.add(event)
above_event, below_event = (sweep_line.above(event),
sweep_line.below(event))
self.compute_position(below_event, event)
if (above_event is not None
and self.detect_intersection(event, above_event)):
self.compute_position(event, above_event)
if (below_event is not None
and self.detect_intersection(below_event, event)):
self.compute_position(sweep_line.below(below_event),
below_event)
else:
event = event.left
if event in sweep_line:
above_event, below_event = (sweep_line.above(event),
sweep_line.below(event))
sweep_line.remove(event)
if above_event is not None and below_event is not None:
self.detect_intersection(below_event, above_event)
yield event
class EventsQueue:
__slots__ = 'context', '_queue'
def __init__(self, context: Context) -> None:
self.context = context
self._queue = PriorityQueue(key=EventsQueueKey)
__repr__ = generate_repr(__init__)
def __bool__(self) -> bool:
return bool(self._queue)
def detect_intersection(self, below_event: Event, event: Event) -> None:
relation = self.context.segments_relation(below_event.start,
below_event.end, event.start,
event.end)
if relation is Relation.TOUCH or relation is Relation.CROSS:
# segments touch or cross
point = self.context.segments_intersection(below_event.start,
below_event.end,
event.start, event.end)
if point != below_event.start and point != below_event.end:
self._divide_segment(below_event, point)
if point != event.start and point != event.end:
self._divide_segment(event, point)
event.set_both_relations(max(event.relation, relation))
below_event.set_both_relations(max(below_event.relation, relation))
elif relation is not Relation.DISJOINT:
# segments overlap
starts_equal = event.start == below_event.start
start_min, start_max = ((None, None) if starts_equal else (
(event, below_event)
if EventsQueueKey(event) < EventsQueueKey(below_event) else
(below_event, event)))
ends_equal = event.end == below_event.end
end_min, end_max = ((None, None) if ends_equal else
((event.complement, below_event.complement) if
(EventsQueueKey(event.complement) <
EventsQueueKey(below_event.complement)) else
(below_event.complement, event.complement)))
if starts_equal:
if ends_equal:
# segments are equal
event.set_both_relations(relation)
below_event.set_both_relations(relation)
else:
# segments share the left endpoint
end_min.set_both_relations(relation)
end_max.complement.relation = relation
self._divide_segment(end_max.complement, end_min.start)
elif ends_equal:
# segments share the right endpoint
start_max.set_both_relations(relation)
start_min.complement.relation = relation
self._divide_segment(start_min, start_max.start)
elif start_min is end_max.complement:
# one line segment includes the other one
start_max.set_both_relations(relation)
start_min_original_relationship = start_min.relation
start_min.relation = relation
self._divide_segment(start_min, end_min.start)
start_min.relation = start_min_original_relationship
start_min.complement.relation = relation
self._divide_segment(start_min, start_max.start)
else:
# no line segment includes the other one
start_max.relation = relation
self._divide_segment(start_max, end_min.start)
start_min.complement.relation = relation
self._divide_segment(start_min, start_max.start)
def peek(self) -> Event:
return self._queue.peek()
def pop(self) -> Event:
return self._queue.pop()
def push(self, event: Event) -> None:
if event.start == event.end:
raise ValueError('Degenerate segment found '
'with both endpoints being: {}.'.format(
event.start))
self._queue.push(event)
def _divide_segment(self, event: Event, break_point: Point) -> None:
left_event = event.complement.complement = Event(
start=break_point,
complement=event.complement,
is_left_endpoint=True,
relation=event.complement.relation,
segments_ids=event.segments_ids)
right_event = event.complement = Event(
start=break_point,
complement=event,
is_left_endpoint=False,
relation=event.relation,
segments_ids=event.complement.segments_ids)
self.push(left_event)
self.push(right_event)
class EventsQueue:
@classmethod
def from_segments(cls, segments: Sequence[Segment], *,
context: Context) -> 'EventsQueue':
result = cls(context)
for index, segment in enumerate(segments):
event = LeftEvent.from_segment(segment, index)
result.push(event)
result.push(event.right)
return result
__slots__ = 'context', '_queue'
def __init__(self, context: Context) -> None:
self.context = context
self._queue = PriorityQueue(key=EventsQueueKey)
__repr__ = generate_repr(__init__)
def __bool__(self) -> bool:
return bool(self._queue)
def detect_intersection(self, below_event: LeftEvent, event: LeftEvent,
sweep_line: SweepLine) -> None:
relation = self.context.segments_relation(below_event, event)
if relation is Relation.DISJOINT:
return
elif relation is Relation.TOUCH or relation is Relation.CROSS:
# segments touch or cross
point = self.context.segments_intersection(below_event, event)
assert event.segments_ids.isdisjoint(below_event.segments_ids)
if point != below_event.start and point != below_event.end:
below_below = sweep_line.below(below_event)
assert not (below_below is not None and below_below.start
== below_event.start and below_below.end == point)
self.push(below_event.divide(point))
self.push(below_event.right)
if point != event.start and point != event.end:
above_event = sweep_line.above(event)
if (above_event is not None
and above_event.start == event.start
and above_event.end == point):
sweep_line.remove(above_event)
self.push(event.divide(point))
self.push(event.right)
event.merge_with(above_event)
else:
self.push(event.divide(point))
self.push(event.right)
else:
# segments overlap
starts_equal = event.start == below_event.start
start_min, start_max = ((event, below_event) if (
starts_equal
or EventsQueueKey(event) < EventsQueueKey(below_event)) else
(below_event, event))
ends_equal = event.end == below_event.end
end_min, end_max = ((event.right,
below_event.right) if ends_equal or
(EventsQueueKey(event.right) < EventsQueueKey(
below_event.right)) else
(below_event.right, event.right))
if starts_equal:
assert not ends_equal
# segments share the left endpoint
sweep_line.remove(end_max.left)
self.push(end_max.left.divide(end_min.start))
event.merge_with(below_event)
elif ends_equal:
# segments share the right endpoint
start_max.merge_with(start_min.divide(start_max.start))
self.push(start_min.right)
elif start_min is end_max.left:
# one line segment includes the other one
self.push(start_min.divide(end_min.start))
self.push(start_min.right)
start_max.merge_with(start_min.divide(start_max.start))
self.push(start_min.right)
else:
# no line segment includes the other one
self.push(start_max.divide(end_min.start))
start_max.merge_with(start_min.divide(start_max.start))
self.push(start_max.right)
self.push(start_min.right)
def peek(self) -> Event:
return self._queue.peek()
def pop(self) -> Event:
return self._queue.pop()
def push(self, event: Event) -> None:
if event.start == event.end:
raise ValueError('Degenerate segment found '
'with both endpoints being: {}.'.format(
event.start))
self._queue.push(event)
class EventsQueue:
__slots__ = '_queue',
def __init__(self) -> None:
self._queue = PriorityQueue(key=EventsQueueKey)
@staticmethod
def compute_position(below_event: Optional[Event], event: Event) -> None:
if below_event is not None:
event.other_interior_to_left = (
below_event.other_interior_to_left if
(event.from_left is below_event.from_left) else
below_event.interior_to_left)
def detect_intersection(self, below_event: Event, event: Event) -> bool:
"""
Populates events queue with intersection events.
Checks if events' segments overlap and have the same start.
"""
below_segment, segment = below_event.segment, event.segment
relationship = segments_relationship(below_segment, segment)
if relationship is SegmentsRelationship.OVERLAP:
# segments overlap
if below_event.from_left is event.from_left:
raise ValueError('Edges of the same polygon '
'should not overlap.')
starts_equal = below_event.start == event.start
ends_equal = below_event.end == event.end
start_min, start_max = ((None, None) if starts_equal else (
(event, below_event) if
(EventsQueueKey(event) < EventsQueueKey(below_event)) else
(below_event, event)))
end_min, end_max = ((None, None) if ends_equal else
((event.complement, below_event.complement) if
(EventsQueueKey(event.complement) <
EventsQueueKey(below_event.complement)) else
(below_event.complement, event.complement)))
if starts_equal:
# both line segments are equal or share the left endpoint
event.is_overlap = below_event.is_overlap = True
if not ends_equal:
self.divide_segment(end_max.complement, end_min.start)
return True
elif ends_equal:
# the line segments share the right endpoint
self.divide_segment(start_min, start_max.start)
else:
self.divide_segment(
start_min
# one line segment includes the other one
if start_min is end_max.complement
# no line segment includes the other one
else start_max,
end_min.start)
self.divide_segment(start_min, start_max.start)
elif (relationship is not SegmentsRelationship.NONE
and below_event.start != event.start
and below_event.end != event.end):
# segments do not intersect at endpoints
point = segments_intersection(below_segment, segment)
if point != below_event.start and point != below_event.end:
self.divide_segment(below_event, point)
if point != event.start and point != event.end:
self.divide_segment(event, point)
return False
def divide_segment(self, event: Event, point: Point) -> None:
left_event = Event(True, point, event.complement, event.from_left,
event.interior_to_left, event.edge)
right_event = Event(False, point, event, event.from_left,
event.interior_to_left, event.edge)
event.complement.complement, event.complement = left_event, right_event
self._queue.push(left_event)
self._queue.push(right_event)
def register_edge(self, edge: QuadEdge, *, from_left: bool,
is_counterclockwise_contour: bool) -> None:
start, end = edge.start, edge.end
interior_to_left = is_counterclockwise_contour
if start > end:
start, end = end, start
interior_to_left = not interior_to_left
start_event = Event(True, start, None, from_left, interior_to_left,
edge)
end_event = Event(False, end, start_event, from_left, interior_to_left,
edge)
start_event.complement = end_event
self._queue.push(start_event)
self._queue.push(end_event)
def register_segment(self, segment: Segment, *, from_left: bool,
is_counterclockwise_contour: bool) -> None:
start, end = segment
interior_to_left = is_counterclockwise_contour
if start > end:
start, end = end, start
interior_to_left = not interior_to_left
start_event = Event(True, start, None, from_left, interior_to_left)
end_event = Event(False, end, start_event, from_left, interior_to_left)
start_event.complement = end_event
self._queue.push(start_event)
self._queue.push(end_event)
def sweep(self) -> Iterable[Event]:
sweep_line = SweepLine()
while self._queue:
event = self._queue.pop()
if event.is_left_endpoint:
sweep_line.add(event)
above_event, below_event = (sweep_line.above(event),
sweep_line.below(event))
self.compute_position(below_event, event)
if (above_event is not None
and self.detect_intersection(event, above_event)):
self.compute_position(event, above_event)
if (below_event is not None
and self.detect_intersection(below_event, event)):
self.compute_position(sweep_line.below(below_event),
below_event)
else:
event = event.complement
if event in sweep_line:
above_event, below_event = (sweep_line.above(event),
sweep_line.below(event))
sweep_line.remove(event)
if above_event is not None and below_event is not None:
self.detect_intersection(below_event, above_event)
yield event