def triangulate_polygon (pids, pos) :
"""Sort pids in tuples of 3 points
.. seealso:: Compared to `topo_triangulate_polygon`, this function will use
geometrical informations to produce nice triangles
:Parameters:
- `pids` (list of pid) - ordered list of points that form a closed polygon
- `pos` (dict of (pid|Vector) ) - position of points in the mesh.
:Returns Type: list of (pid,pid,pid)
"""
triangles = topo_triangulate_polygon(pids)
if len(triangles) == 1 :
return triangles
#change triangles to tends towards equilateral one
#local triangulated mesh
mesh = Topomesh(2)
for pid in pids :
mesh.add_wisp(0,pid)
edge = {}
for pid1,pid2,pid3 in triangles :
tid = mesh.add_wisp(2)
for pida,pidb in [(pid1,pid2),(pid2,pid3),(pid3,pid1)] :
key = (min(pida,pidb),max(pida,pidb) )
try :
eid = edge[key]
except KeyError :
eid = mesh.add_wisp(1)
mesh.link(1,eid,pida)
mesh.link(1,eid,pidb)
edge[key] = eid
mesh.link(2,tid,eid)
#flip edges
test = True
while test :
test = False
for eid in tuple(mesh.wisps(1) ) :
if flip_necessary(mesh,eid,pos) :
flip_edge(mesh,eid)
test = True
return [tuple(mesh.borders(2,fid,2) ) for fid in mesh.wisps(2)]
def triangulate_polygon(pids, pos):
"""Sort pids in tuples of 3 points
.. seealso:: Compared to `topo_triangulate_polygon`, this function will use
geometrical informations to produce nice triangles
:Parameters:
- `pids` (list of pid) - ordered list of points that form a closed polygon
- `pos` (dict of (pid|Vector) ) - position of points in the mesh.
:Returns Type: list of (pid,pid,pid)
"""
triangles = topo_triangulate_polygon(pids)
if len(triangles) == 1:
return triangles
#change triangles to tends towards equilateral one
#local triangulated mesh
mesh = Topomesh(2)
for pid in pids:
mesh.add_wisp(0, pid)
edge = {}
for pid1, pid2, pid3 in triangles:
tid = mesh.add_wisp(2)
for pida, pidb in [(pid1, pid2), (pid2, pid3), (pid3, pid1)]:
key = (min(pida, pidb), max(pida, pidb))
try:
eid = edge[key]
except KeyError:
eid = mesh.add_wisp(1)
mesh.link(1, eid, pida)
mesh.link(1, eid, pidb)
edge[key] = eid
mesh.link(2, tid, eid)
#flip edges
test = True
while test:
test = False
for eid in tuple(mesh.wisps(1)):
if flip_necessary(mesh, eid, pos):
flip_edge(mesh, eid)
test = True
return [tuple(mesh.borders(2, fid, 2)) for fid in mesh.wisps(2)]
def triangulate (mesh, fid) :
"""Triangulate the given face of a mesh
:Parameters:
- `mesh` (Mesh)
- `fid` (did) - id of face to triangulate. Must be of
degree 2
:Warning: Modify mesh in place.
:Note: This method does not introduce new points in the
mesh.
"""
#store info
edges = tuple(mesh.borders(fid) )
if len(edges) == 3 :#face is already a triangle
return
if len(edges) < 3 :
raise UserWarning("face is not geometricaly defined")
cells = tuple(mesh.regions(fid) )
#remove face
mesh.remove_dart(fid)
#walk along edges
edge_pool = list(edges)
front_eid = edge_pool.pop()
ref_pid, front_pid = mesh.borders(front_eid)
ref_pos = mesh.position(ref_pid)
new_edges = []
while len(edge_pool) > 2 :#remaining two edges will
#naturally form a triangle
#find next edge
next_eid, = (eid for eid in edge_pool \
if front_pid in mesh.borders(eid) )
next_pid, = (pid for pid in mesh.borders(next_eid) \
if pid != front_pid)
#triangulate, create an edge between ref_pid and
#next_pid
new_eid = mesh.add_dart(1)
mesh.link(new_eid, ref_pid)
mesh.link(new_eid, next_pid)
l = norm(mesh.position(next_pid) - ref_pos)
new_edges.append( (l, new_eid) )
#create new facet
fid = mesh.add_dart(2)
for cid in cells :
mesh.link(cid, fid)
for eid in (front_eid, next_eid, new_eid) :
mesh.link(fid, eid)
#increment step
edge_pool.remove(next_eid)
front_eid = new_eid
front_pid = next_pid
#create last facet
fid = mesh.add_dart(2)
for cid in cells :
mesh.link(cid, fid)
for eid in edge_pool + [front_eid] :
mesh.link(fid, eid)
#improve triangulation quality
new_edges.sort()
for l, eid in new_edges :
if is_flip_better(mesh, eid) :
flip_edge(mesh, eid)
