def _unite_segments_cross(first: Segment,
second: Segment,
context: Context) -> Multisegment:
cross_point = context.segments_intersection(first, second)
segment_cls = context.segment_cls
return context.multisegment_cls([segment_cls(first.start, cross_point),
segment_cls(second.start, cross_point),
segment_cls(cross_point, first.end),
segment_cls(cross_point, second.end)])
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 intersect_segments(first: Segment,
second: Segment,
context: Context) -> Union_[Empty, Multipoint, Segment]:
relation = context.segments_relation(first, second)
if relation is Relation.DISJOINT:
return context.empty
elif relation is Relation.TOUCH or relation is Relation.CROSS:
return context.multipoint_cls([context.segments_intersection(first,
second)])
else:
return (first
if relation is Relation.EQUAL or relation is Relation.COMPONENT
else
(second
if relation is Relation.COMPOSITE
else _intersect_segments_overlap(first, second, context)))
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 relate_segment(multisegment: Multisegment, segment: Segment,
context: Context) -> Relation:
is_segment_superset = has_no_touch = has_no_cross = has_no_overlap = True
# orientations of multisegment's segments
# which touch given segment in the middle
middle_touching_orientations = {} # type: Dict[Point, Orientation]
components = []
start, end = segment_endpoints = segment.start, segment.end
if start > end:
start, end = end, start
for index, sub_segment in enumerate(multisegment.segments):
sub_segment_endpoints = sub_segment.start, sub_segment.end
relation = relate_segments(sub_segment, segment, context)
if relation is Relation.COMPONENT or relation is Relation.EQUAL:
return Relation.COMPONENT
elif relation is Relation.COMPOSITE:
if has_no_overlap:
has_no_overlap = False
if start in sub_segment_endpoints:
start = max(sub_segment_endpoints)
segment_endpoints = start, end
elif end in sub_segment_endpoints:
end = min(sub_segment_endpoints)
segment_endpoints = start, end
else:
components.append(to_sorted_pair(sub_segment_endpoints))
elif relation is Relation.OVERLAP:
if is_segment_superset:
is_segment_superset = False
if has_no_overlap:
has_no_overlap = False
start, end = segment_endpoints = _subtract_segments_overlap(
segment_endpoints, sub_segment_endpoints)
else:
if is_segment_superset:
is_segment_superset = False
if has_no_overlap:
if relation is Relation.TOUCH:
if has_no_touch:
has_no_touch = False
if has_no_cross:
intersection = context.segments_intersection(
sub_segment, segment)
if intersection != start and intersection != end:
sub_start, sub_end = sub_segment_endpoints
non_touched_endpoint = (sub_start if intersection
== sub_end else sub_end)
try:
previous_orientation = (
middle_touching_orientations[intersection])
except KeyError:
middle_touching_orientations[intersection] = (
context.angle_orientation(
start, end, non_touched_endpoint))
else:
if (context.angle_orientation(
start, end, non_touched_endpoint)
is not previous_orientation):
has_no_cross = False
elif has_no_cross and relation is Relation.CROSS:
has_no_cross = False
if has_no_overlap:
return (Relation.DISJOINT if has_no_touch and has_no_cross else
(Relation.TOUCH if has_no_cross else Relation.CROSS))
elif components:
components_iterator = iter(components)
min_component_start, max_component_end = next(components_iterator)
components_starts = {min_component_start}
for component_start, component_end in components_iterator:
components_starts.add(component_start)
if min_component_start > component_start:
min_component_start = component_start
if max_component_end < component_end:
max_component_end = component_end
return (
(Relation.EQUAL if is_segment_superset else Relation.COMPONENT) if
(min_component_start == start and max_component_end == end
and all(component_end in components_starts
or component_end == max_component_end
for _, component_end in components)) else
(Relation.COMPOSITE if is_segment_superset else Relation.OVERLAP))
else:
return (
(Relation.EQUAL if is_segment_superset else Relation.COMPONENT)
if start == end else
(Relation.COMPOSITE if is_segment_superset else Relation.OVERLAP))
def segments_intersection(context: Context, first_start, first_end,
second_start, second_end):
return context.segments_intersection(first_start, first_end, second_start,
second_end)
