def _remove(self, site, points, triangles):
'''
Update the triangulation by removing the surrounding triangles
and then filling this cavity with new Delaunay triangles.
Challenge: Maintain neighborhood control.
Ref: Mir Abolfazl Mostafavi, Christopher Gold, and Maciej Dakowicz.
2003. Delete and insert operations in Voronoi/Delaunay methods
and applications. Comput. Geosci. 29, 4 (May 2003), 523-530.
DOI=10.1016/S0098-3004(03)00017-7
http://dx.doi.org/10.1016/S0098-3004(03)00017-7
'''
# verify compatibility of surrounding points and old triangles
if len(points) != len(triangles):
raise Exception("Triangulation has different sizes.")
# verify is the triangulation is empty (or insufficient?)
if len(points) < 3:
return
# initialize new triangulation controls
i = -1
new_triangles = {}
# while there are points to form more than the last triangle
while len(points) > 3:
# checks the possible triangles considering
# all three consecutive points (i, i1, i2 in a cycle)
# of surrounding points of the site
i += 1
npoints = len(points)
if (i >= npoints):
raise Exception("Inexists a valid ear? Is it possible?")
i1 = (i + 1) % npoints
i2 = (i1 + 1) % npoints
# verify if points represent a valid triangle to site,
# like a ear listen to the site:
# 1: gets triangle orientation (CW or CCW)
o_ear = Triangle.orientation(points[i], points[i1], points[i2])
# 2: gets direction of triangle to the site (CW or CCW)
o_ear_site = Triangle.orientation(points[i], points[i2], site)
# 3: if points are collinear, try another edge as a reference
# ??why don't take this edge at first place??
if o_ear_site == 0:
o_ear_site = Triangle.orientation(points[i], points[i1], site)
# 4: the directions is the same?
if (o_ear * o_ear_site) > 0:
# if so, this a valid ear (possible triangulation)
valid_ear = Triangle(points[i], points[i1], points[i2])
# verify if this ear is a Delaunay Triangulation
ear_is_delaunay = True
# 1. for all other surrounding points
for p in points:
# 1.1: is this other point (not in ear)?
if not valid_ear.contains(p):
# verify if ear won't circumcircle it
if valid_ear.circumscribe(p):
# if circumcircle, ear is not a Delaunay triangle
ear_is_delaunay = False
break
# if it is a Delaunay triangle...
if ear_is_delaunay:
# include to new triangle control
new_triangles[valid_ear] = None
# include to neighborhood control
self.neighborhood[valid_ear] = {}
# link to the opposite triangles from the removed vertices
self._link_ear(site, valid_ear, triangles[i],
new_triangles)
self._link_ear(site, valid_ear, triangles[i1],
new_triangles)
# change triangle related to vertex by the new one
# remove old triangle by switching the diagonal
triangles[i] = valid_ear
# remove middle point (leave the corners)
del points[i1]
del triangles[i1]
# restart cycle of surrounding points
i = -1
# if has only three neighbours remaining in the surrounding points,
# merged these three points (triangles) into last triangulation
last_ear = Triangle(points[0], points[1], points[2])
self.neighborhood[last_ear] = {}
new_triangles[last_ear] = None
# last triangle closes the triangulation and
# needs update the link with all sides (neighborhood)
self._link_ear(site, last_ear, triangles[0], new_triangles)
self._link_ear(site, last_ear, triangles[1], new_triangles)
self._link_ear(site, last_ear, triangles[2], new_triangles)
if self.main_site is not None:
if self.main_site == site:
self.main_site = None
self._new_version()
if self.check_triangulation:
if not self.valid():
print "### Removing failure"
