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 is_collapse_topo_allowed (mesh, eid, protected_edges) :
"""Test wether collapse of the edge is safe.
mesh: a topomesh object
eid: id of the edge to flip
"""
#collapse enabled only if faces are triangle or square
for fid in mesh.regions(1,eid) :
if mesh.nb_borders(2,fid) not in (3,4) :
return False
#construct a local copy of the mesh
#including all the faces that touch one
#of the extremity of the edge
#find relevant elements
fids = set()
for pid in mesh.borders(1,eid) :
for bid in mesh.regions(0,pid) :
fids.update(mesh.regions(1,bid))
eids = set()
pids = set()
for fid in fids :
eids.update(mesh.borders(2,fid))
pids.update(mesh.borders(2,fid,2))
elms = (pids,eids,fids)
if mesh.degree() == 3 :
cids = set()
for fid in fids :
cids.update(mesh.regions(2,fid))
elms = elms + (cids,)
#construct local mesh
lmesh = Topomesh(mesh.degree(),"max")
for deg,wids in enumerate(elms) :
for wid in wids :
lmesh.add_wisp(deg,wid)
for deg,wids in enumerate(elms[:-1]) :
for wid in wids :
for rid in set(mesh.regions(deg,wid)) & elms[deg + 1] :
lmesh.link(deg + 1,rid,wid)
#collapse edge on this local copy
try :
pid1,pid2 = collapse_edge(lmesh,eid,protected_edges)
except UserWarning :
return False
#test the result
#edges without any face
for wid in lmesh.wisps(1) :
if lmesh.nb_regions(1,wid) == 0 :
return False
#surperposed faces
#TODO optimization
for ref_fid in lmesh.wisps(2) :
ref_pids = set(lmesh.borders(2,ref_fid,2) )
for fid in [wid for wid in lmesh.wisps(2) if wid != ref_fid] :
pids = set(lmesh.borders(2,fid,2) )
if len(pids) == len(ref_pids) :
if pids == ref_pids :
return False
elif len(pids) > len(ref_pids) :
if len(pids - ref_pids) == 1 :
return False
else :
if len(ref_pids - pids) == 1 :
return False
#return
def is_collapse_topo_allowed(mesh, eid, protected_edges):
"""Test wether collapse of the edge is safe.
mesh: a topomesh object
eid: id of the edge to flip
"""
#collapse enabled only if faces are triangle or square
for fid in mesh.regions(1, eid):
if mesh.nb_borders(2, fid) not in (3, 4):
return False
#construct a local copy of the mesh
#including all the faces that touch one
#of the extremity of the edge
#find relevant elements
fids = set()
for pid in mesh.borders(1, eid):
for bid in mesh.regions(0, pid):
fids.update(mesh.regions(1, bid))
eids = set()
pids = set()
for fid in fids:
eids.update(mesh.borders(2, fid))
pids.update(mesh.borders(2, fid, 2))
elms = (pids, eids, fids)
if mesh.degree() == 3:
cids = set()
for fid in fids:
cids.update(mesh.regions(2, fid))
elms = elms + (cids, )
#construct local mesh
lmesh = Topomesh(mesh.degree(), "max")
for deg, wids in enumerate(elms):
for wid in wids:
lmesh.add_wisp(deg, wid)
for deg, wids in enumerate(elms[:-1]):
for wid in wids:
for rid in set(mesh.regions(deg, wid)) & elms[deg + 1]:
lmesh.link(deg + 1, rid, wid)
#collapse edge on this local copy
try:
pid1, pid2 = collapse_edge(lmesh, eid, protected_edges)
except UserWarning:
return False
#test the result
#edges without any face
for wid in lmesh.wisps(1):
if lmesh.nb_regions(1, wid) == 0:
return False
#surperposed faces
#TODO optimization
for ref_fid in lmesh.wisps(2):
ref_pids = set(lmesh.borders(2, ref_fid, 2))
for fid in [wid for wid in lmesh.wisps(2) if wid != ref_fid]:
pids = set(lmesh.borders(2, fid, 2))
if len(pids) == len(ref_pids):
if pids == ref_pids:
return False
elif len(pids) > len(ref_pids):
if len(pids - ref_pids) == 1:
return False
else:
if len(ref_pids - pids) == 1:
return False
#return
return True