def testIndependentSet(self):
n = 100
e = 5 * n
g = UndirectedGraph()
for i in range(e):
u = int(random() * n)
v = int(random() * n)
if u == v:
continue
if not g.contains(u):
g.add_node(u)
if not g.contains(v):
g.add_node(v)
g.connect(u, v)
ind_set = g.independent_set(8)
for i in ind_set:
neighbors = g.e[i]
self.assertEqual(neighbors.intersection(ind_set), set([]))
def remove_independent_set(regions):
"""
Processes a set of regions, detecting and removing an independent set
of vertices from the regions' graph representation, and re-triangulating
the resulting holes.
Arguments:
regions -- a set of non-overlapping polygons that tile some part of the plane
Returns: a new set of regions covering the same subset of the plane, with fewer vertices
"""
# Take note of which points are in which regions
points_to_regions = {}
for idx, region in enumerate(regions):
for point in region.points:
if point in points_to_regions:
points_to_regions[point].add(idx)
continue
points_to_regions[point] = set([idx])
# Connect graph
g = UndirectedGraph()
for region in regions:
for idx in range(region.n):
u = region.points[idx % region.n]
v = region.points[(idx + 1) % region.n]
if not g.contains(u):
g.add_node(u)
if not g.contains(v):
g.add_node(v)
g.connect(u, v)
# Avoid adding points from outer triangle
removal = g.independent_set(8, avoid=bounding_triangle.points)
# Track unaffected regions
unaffected_regions = set([i for i in range(len(regions))])
new_regions = []
for p in removal:
# Take note of affected regions
affected_regions = points_to_regions[p]
unaffected_regions.difference_update(points_to_regions[p])
def calculate_bounding_polygon(p, affected_regions):
edges = []
point_locations = {}
for j, i in enumerate(affected_regions):
edge = set(regions[i].points)
edge.remove(p)
edges.append(edge)
for v in edge:
if v in point_locations:
point_locations[v].add(j)
else:
point_locations[v] = set([j])
boundary = []
edge = edges.pop()
for v in edge:
point_locations[v].remove(len(edges))
boundary.append(v)
for k in range(len(affected_regions) - 2):
v = boundary[-1]
i = point_locations[v].pop()
edge = edges[i]
edge.remove(v)
u = edge.pop()
point_locations[u].remove(i)
boundary.append(u)
return shapes.Polygon(boundary)
# triangulate hole
poly = calculate_bounding_polygon(p, affected_regions)
triangles = spatial.triangulatePolygon(poly)
for triangle in triangles:
self.dag.add_node(triangle)
for j in affected_regions:
region = regions[j]
self.dag.connect(triangle, region)
new_regions.append(triangle)
for i in unaffected_regions:
new_regions.append(regions[i])
return new_regions
