def __init__(self, degree=3, topomesh=None, **kwds):
self._successors = [IdDict(idgenerator = "set") for i in xrange(degree+1)]
self._predecessors = [IdDict(idgenerator = "set") for i in xrange(degree+1)]
PropertyTopomesh.__init__(self, degree, topomesh, **kwds)
if topomesh is not None:
for d in xrange(degree+1):
for w in self.wisps(d):
self._successors[d][w] = array("L")
self._predecessors[d][w] = array("L")
def vertex_topomesh(positions, **kwargs):
positions = array_dict(positions)
start_time = time()
print "--> Generating vertex topomesh"
vertex_topomesh = PropertyTopomesh(3)
for c in positions.keys():
vertex_topomesh.add_wisp(0,c)
vertex_topomesh.update_wisp_property('barycenter',0,positions.values(positions.keys()),keys=positions.keys())
end_time = time()
print "<-- Generating vertex topomesh [",end_time-start_time,"s]"
return vertex_topomesh
def edge_topomesh(edges, positions, **kwargs):
positions = array_dict(positions)
start_time = time()
print "--> Generating edge topomesh"
edge_topomesh = PropertyTopomesh(3)
for c in np.unique(edges):
edge_topomesh.add_wisp(0,c)
for e in edges:
eid = edge_topomesh.add_wisp(1)
for pid in e:
edge_topomesh.link(1,eid,pid)
edge_topomesh.update_wisp_property('barycenter',0,positions.values(np.unique(edges)),keys=np.unique(edges))
end_time = time()
print "<-- Generating edge topomesh [",end_time-start_time,"s]"
return edge_topomesh
def layer_triangle_topomesh_construction(layer_edge_topomesh, positions, omega_criteria = {'distance':1.0,'wall_surface':2.0,'clique':10.0}, **kwargs):
compute_topomesh_property(layer_edge_topomesh,'length',1)
edge_weights = np.zeros(layer_edge_topomesh.nb_wisps(1))
if omega_criteria.has_key('distance'):
edge_weights += omega_criteria['distance']*np.exp(-np.power(layer_edge_topomesh.wisp_property('length',1).values()/15.0,1))
if omega_criteria.has_key('wall_surface'):
img_wall_surfaces = kwargs.get('wall_surfaces',None)
img_volumes = kwargs.get('cell_volumes',dict(zip(positions.keys(),np.ones_like(positions.keys()))))
assert layer_edge_topomesh.has_wisp_property('wall_surface',1) or img_wall_surfaces is not None
if not layer_edge_topomesh.has_wisp_property('wall_surface',1):
layer_edge_vertices = np.sort([list(layer_edge_topomesh.borders(1,e)) for e in layer_edge_topomesh.wisps(1)])
layer_edge_wall_surface = np.array([img_wall_surfaces[tuple(e)]/np.power(img_volumes.values(e).mean(),2./3.) for e in layer_edge_vertices])
layer_edge_topomesh.update_wisp_property('wall_surface',1,array_dict(layer_edge_wall_surface,list(layer_edge_topomesh.wisps(1))))
edge_weights += omega_criteria['wall_surface']*layer_edge_topomesh.wisp_property('wall_surface',1).values()
edge_weights = array_dict(edge_weights,list(layer_edge_topomesh.wisps(1)))
edge_neighbor_vertices = [np.concatenate([list(set(layer_edge_topomesh.region_neighbors(0,c)))+[c] for c in layer_edge_topomesh.borders(1,e)]) for e in layer_edge_topomesh.wisps(1)]
edge_neighbor_vertices_edges = [np.concatenate([list(layer_edge_topomesh.regions(0,n_v)) for n_v in n_vertices]) for n_vertices in edge_neighbor_vertices]
edge_triangle_edges = [np.unique(e)[nd.sum(np.ones_like(e),e,index=np.unique(e))>3] for e in edge_neighbor_vertices_edges]
if omega_criteria.has_key('clique'):
edge_neighbor_weights = array_dict([edge_weights.values(e).min() - omega_criteria['clique']*(len(e)>3) for e in edge_triangle_edges],list(layer_edge_topomesh.wisps(1)))
else:
edge_neighbor_weights = array_dict([edge_weights.values(e).min() for e in edge_triangle_edges],list(layer_edge_topomesh.wisps(1)))
edge_triangle_edges = array_dict(edge_triangle_edges,list(layer_edge_topomesh.wisps(1)))
triangulation_edges = np.array(list(layer_edge_topomesh.wisps(1)))[np.array(map(len,edge_triangle_edges))>=3]
layer_triangulation_topomesh = PropertyTopomesh(3)
layer_triangulation_topomesh.add_wisp(3,1)
initial_edge = np.array(list(layer_edge_topomesh.wisps(1)))[triangulation_edges][np.argmax(edge_neighbor_weights.values(triangulation_edges))]
free_edges = [initial_edge]
while len(free_edges) > 0:
eid_to_add = free_edges.pop(0)
print "--> Edge",list(layer_edge_topomesh.borders(1,eid_to_add))," : ",edge_neighbor_weights[eid_to_add]
edge_vertex_edges = np.concatenate([list(set(layer_edge_topomesh.regions(0,c)).difference({eid_to_add})) for c in layer_edge_topomesh.borders(1,eid_to_add)])
edge_vertex_edge_vertices = np.concatenate([c*np.ones(layer_edge_topomesh.nb_regions(0,c)-1) for c in layer_edge_topomesh.borders(1,eid_to_add)])
edge_vertex_edge_neighbor_vertices = np.array([list(set(layer_edge_topomesh.borders(1,e)).difference({v}))[0] for e,v in zip(edge_vertex_edges,edge_vertex_edge_vertices)])
candidate_triangle_vertices = np.unique(edge_vertex_edge_neighbor_vertices)[nd.sum(np.ones_like(edge_vertex_edge_neighbor_vertices),edge_vertex_edge_neighbor_vertices,index=np.unique(edge_vertex_edge_neighbor_vertices))==2]
candidate_triangle_edges = np.array([np.concatenate([[eid_to_add],edge_vertex_edges[edge_vertex_edge_neighbor_vertices==c]]) for c in candidate_triangle_vertices])
if len(candidate_triangle_edges)>0:
candidate_triangle_free_edges = np.array([np.sum([e in free_edges for e in triangle_edges]) for triangle_edges in candidate_triangle_edges])
candidate_triangle_edge_weights = edge_weights.values(candidate_triangle_edges[:,1:]).min(axis=1)
if (candidate_triangle_free_edges ==candidate_triangle_free_edges.max()).sum() == 1:
sorted_candidate_triangle_edges = candidate_triangle_edges[np.argsort(-candidate_triangle_free_edges)]
else:
sorted_candidate_triangle_edges = candidate_triangle_edges[np.argsort(-candidate_triangle_edge_weights)]
for triangle_edges in sorted_candidate_triangle_edges:
if np.all(np.array([0 if not layer_triangulation_topomesh.has_wisp(1,e) else layer_triangulation_topomesh.nb_regions(1,e) for e in triangle_edges])<2):
triangle_vertices = np.unique([list(layer_edge_topomesh.borders(1,e)) for e in triangle_edges])
if layer_triangulation_topomesh.nb_wisps(2)!=1 or vq(np.sort([triangle_vertices]),np.sort([list(layer_triangulation_topomesh.borders(2,t,2)) for t in layer_triangulation_topomesh.wisps(2)]))[1][0]>0:
fid = layer_triangulation_topomesh.add_wisp(2)
layer_triangulation_topomesh.link(3,1,fid)
print " --> Triangle",fid,triangle_vertices," : ",edge_weights.values(triangle_edges[1:]).min()
for c in triangle_vertices:
if not layer_triangulation_topomesh.has_wisp(0,c):
layer_triangulation_topomesh.add_wisp(0,c)
for e in triangle_edges:
if not layer_triangulation_topomesh.has_wisp(1,e):
layer_triangulation_topomesh.add_wisp(1,e)
for c in layer_edge_topomesh.borders(1,e):
layer_triangulation_topomesh.link(1,e,c)
layer_triangulation_topomesh.link(2,fid,e)
if layer_triangulation_topomesh.nb_regions(1,e)<2:
if not e in free_edges:
free_edges.append(e)
edge_future_triangle_edges = list(set(edge_triangle_edges[e]).difference(set(layer_triangulation_topomesh.wisps(1)).difference(set(free_edges))))
if omega_criteria.has_key('clique'):
edge_neighbor_weights[e] = np.min(edge_weights.values(edge_future_triangle_edges)) - omega_criteria['clique']*(len(edge_future_triangle_edges)>3)
else:
edge_neighbor_weights[e] = np.min(edge_weights.values(edge_future_triangle_edges))
print free_edges
if len(free_edges)>0:
free_edges = list(np.array(free_edges)[np.argsort(-edge_neighbor_weights.values(free_edges))])
layer_triangulation_topomesh.update_wisp_property('barycenter',0,array_dict(positions.values(list(layer_triangulation_topomesh.wisps(0))),list(layer_triangulation_topomesh.wisps(0))))
return layer_triangulation_topomesh
def layered_tetrahedra_topomesh_construction(layer_triangle_topomesh, positions, cell_layer, omega_criteria = {'distance':1.0,'wall_surface':2.0,'clique':10.0}, **kwargs):
compute_topomesh_property(layer_triangle_topomesh,'length',1)
compute_topomesh_property(layer_triangle_topomesh,'borders',2)
compute_topomesh_property(layer_triangle_topomesh,'perimeter',2)
if omega_criteria.has_key('wall_surface'):
img_wall_surfaces = kwargs.get('wall_surfaces',None)
img_volumes = kwargs.get('cell_volumes',dict(zip(positions.keys(),np.ones_like(positions.keys()))))
assert layer_triangle_topomesh.has_wisp_property('wall_surface',1) or img_wall_surfaces is not None
if not layer_triangle_topomesh.has_wisp_property('wall_surface',1):
L1_L2_triangle_edge_vertices = np.array([np.sort([list(layer_triangle_topomesh.borders(1,e)) for e in layer_triangle_topomesh.borders(2,t)]) for t in layer_triangle_topomesh.wisps(2)])
L1_L2_triangle_edge_wall_surface = np.array([[-1. if tuple(e) not in img_wall_surfaces.keys() else img_wall_surfaces[tuple(e)]/np.power(img_volumes.values(e).mean(),2./3.) for e in t] for t in L1_L2_triangle_edge_vertices])
layer_triangle_topomesh.update_wisp_property('wall_surface',2,array_dict(L1_L2_triangle_edge_wall_surface.min(axis=1),list(layer_triangle_topomesh.wisps(2))))
layer_triangle_topomesh = layer_triangle_topomesh
triangle_weights = np.zeros(layer_triangle_topomesh.nb_wisps(2))
if omega_criteria.has_key('distance'):
triangle_weights += omega_criteria['distance']*np.exp(-np.power(layer_triangle_topomesh.wisp_property('length',1).values(layer_triangle_topomesh.wisp_property('borders',2).values()).max(axis=1)/15.0,1))
if omega_criteria.has_key('wall_surface'):
triangle_weights += omega_criteria['wall_surface']*layer_triangle_topomesh.wisp_property('wall_surface',2).values()
triangle_weights = array_dict(triangle_weights,list(layer_triangle_topomesh.wisps(2)))
triangle_neighbor_edges = [np.concatenate([list(set(layer_triangle_topomesh.region_neighbors(1,e)))+[e] for e in layer_triangle_topomesh.borders(2,t)]) for t in layer_triangle_topomesh.wisps(2)]
triangle_neighbor_edge_triangles = [np.concatenate([list(layer_triangle_topomesh.regions(1,n_e)) for n_e in n_edges]) for n_edges in triangle_neighbor_edges]
triangle_tetrahedra_triangles = [np.unique(t)[nd.sum(np.ones_like(t),t,index=np.unique(t))>5] for t in triangle_neighbor_edge_triangles]
if omega_criteria.has_key('clique'):
triangle_neighbor_weights = array_dict([triangle_weights.values(t).min() - omega_criteria['clique']*(len(t)-4) for t in triangle_tetrahedra_triangles],list(layer_triangle_topomesh.wisps(2)))
else:
triangle_neighbor_weights = array_dict([triangle_weights.values(t).min() for t in triangle_tetrahedra_triangles],list(layer_triangle_topomesh.wisps(2)))
triangle_tetrahedra_triangles = array_dict(triangle_tetrahedra_triangles,list(layer_triangle_topomesh.wisps(2)))
tetrahedrization_triangles = np.array(list(layer_triangle_topomesh.wisps(2)))[np.array(map(len,triangle_tetrahedra_triangles))>=4]
constructed_triangulation_topomesh = PropertyTopomesh(3)
initial_triangle = np.array(list(layer_triangle_topomesh.wisps(2)))[tetrahedrization_triangles][np.argmax(triangle_neighbor_weights.values(tetrahedrization_triangles))]
free_triangles = [initial_triangle]
while len(free_triangles) > 0:
fid_to_add = free_triangles.pop(0)
print "--> Triangle",list(layer_triangle_topomesh.borders(2,fid_to_add))," : ",triangle_neighbor_weights[fid_to_add]
triangle_vertex_edges = np.concatenate([list(set(layer_triangle_topomesh.regions(0,c)).difference(set(layer_triangle_topomesh.borders(2,fid_to_add)))) for c in layer_triangle_topomesh.borders(2,fid_to_add,2)])
triangle_vertex_edge_vertices = np.concatenate([c*np.ones(layer_triangle_topomesh.nb_regions(0,c)-2) for c in layer_triangle_topomesh.borders(2,fid_to_add,2)])
triangle_vertex_edge_neighbor_vertices = np.array([list(set(layer_triangle_topomesh.borders(1,e)).difference({v}))[0] for e,v in zip(triangle_vertex_edges,triangle_vertex_edge_vertices)])
candidate_tetra_vertices = np.unique(triangle_vertex_edge_neighbor_vertices)[nd.sum(np.ones_like(triangle_vertex_edge_neighbor_vertices),triangle_vertex_edge_neighbor_vertices,index=np.unique(triangle_vertex_edge_neighbor_vertices))==3]
candidate_tetra_edges = np.array([triangle_vertex_edges[triangle_vertex_edge_neighbor_vertices==c] for c in candidate_tetra_vertices])
candidate_tetra_edge_triangles = [np.concatenate([list(set(layer_triangle_topomesh.regions(1,e)).difference({fid_to_add})) for e in candidate_edges]) for candidate_edges in candidate_tetra_edges]
candidate_tetra_triangles = np.array([np.concatenate([[fid_to_add],np.unique(t)[nd.sum(np.ones_like(t),t,index=np.unique(t))==2]]) for t in candidate_tetra_edge_triangles])
if len(candidate_tetra_triangles)>0:
candidate_tetra_free_triangles = np.array([np.sum([t in free_triangles for t in tetra_triangles]) for tetra_triangles in candidate_tetra_triangles])
candidate_tetra_triangle_weights = triangle_weights.values(candidate_tetra_triangles[:,1:]).min(axis=1)
if (candidate_tetra_free_triangles == candidate_tetra_free_triangles.max()).sum() == 1:
sorted_candidate_tetra_triangles = candidate_tetra_triangles[np.argsort(-candidate_tetra_free_triangles)]
else:
sorted_candidate_tetra_triangles = candidate_tetra_triangles[np.argsort(-candidate_tetra_triangle_weights)]
for tetra_triangles in sorted_candidate_tetra_triangles:
if np.all(np.array([0 if not constructed_triangulation_topomesh.has_wisp(2,t) else constructed_triangulation_topomesh.nb_regions(2,t) for t in tetra_triangles])<2):
tetra_vertices = np.unique([list(layer_triangle_topomesh.borders(2,t,2)) for t in tetra_triangles])
tetra_edges = np.unique([list(layer_triangle_topomesh.borders(2,t)) for t in tetra_triangles])
if constructed_triangulation_topomesh.nb_wisps(3)!=1 or vq(np.sort([tetra_vertices]),np.sort([list(constructed_triangulation_topomesh.borders(3,t,3)) for t in constructed_triangulation_topomesh.wisps(3)]))[1][0]>0:
if len(np.unique(cell_layer.values(tetra_vertices)))==2:
#tetra_triangle_tetras = np.unique([list(constructed_triangulation_topomesh.regions(2,t)) for t in tetra_triangles if constructed_triangulation_topomesh.has_wisp(2,t)])
tetra_triangle_tetras = np.array(list(constructed_triangulation_topomesh.wisps(3)))
if len(tetra_triangle_tetras)>0:
tetra_triangle_tetra_edges = np.unique([list(constructed_triangulation_topomesh.borders(3,t,2)) for t in tetra_triangle_tetras])
tetra_triangle_points = positions.values(np.array([list(layer_triangle_topomesh.borders(2,t,2)) for t in tetra_triangles]))
tetra_triangle_tetra_edge_points = positions.values(np.array([list(layer_triangle_topomesh.borders(1,e)) for e in tetra_triangle_tetra_edges]))
tetra_triangle_intersection = np.ravel([intersecting_triangle(edge_points,tetra_triangle_points) for edge_points in tetra_triangle_tetra_edge_points])
tetra_triangle_edges = np.unique([list(layer_triangle_topomesh.borders(2,t)) for t in tetra_triangles])
tetra_triangle_tetra_triangles = np.unique([list(constructed_triangulation_topomesh.borders(3,t)) for t in tetra_triangle_tetras])
tetra_triangle_edge_points = positions.values(np.array([list(layer_triangle_topomesh.borders(1,e)) for e in tetra_triangle_edges]))
tetra_triangle_tetra_triangle_points = positions.values(np.array([list(layer_triangle_topomesh.borders(2,t,2)) for t in tetra_triangle_tetra_triangles]))
tetra_edge_intersection = np.ravel([intersecting_triangle(edge_points,tetra_triangle_tetra_triangle_points) for edge_points in tetra_triangle_edge_points])
tetra_triangle_intersection = np.concatenate([tetra_triangle_intersection,tetra_edge_intersection])
else:
tetra_triangle_intersection = [False]
if not np.any(tetra_triangle_intersection):
tid = constructed_triangulation_topomesh.add_wisp(3)
print " --> Tetrahedron",tid,tetra_vertices," : ", triangle_weights.values(tetra_triangles[1:]).min()
for c in tetra_vertices:
if not constructed_triangulation_topomesh.has_wisp(0,c):
constructed_triangulation_topomesh.add_wisp(0,c)
for e in tetra_edges:
if not constructed_triangulation_topomesh.has_wisp(1,e):
constructed_triangulation_topomesh.add_wisp(1,e)
for c in layer_triangle_topomesh.borders(1,e):
constructed_triangulation_topomesh.link(1,e,c)
for t in tetra_triangles:
if not constructed_triangulation_topomesh.has_wisp(2,t):
constructed_triangulation_topomesh.add_wisp(2,t)
for e in layer_triangle_topomesh.borders(2,t):
constructed_triangulation_topomesh.link(2,t,e)
constructed_triangulation_topomesh.link(3,tid,t)
if constructed_triangulation_topomesh.nb_regions(2,t)<2 and len(np.unique(cell_layer.values(list(constructed_triangulation_topomesh.borders(2,t,2)))))==2:
if not t in free_triangles:
free_triangles.append(t)
triangle_future_tetra_triangles = list(set(triangle_tetrahedra_triangles[t]).difference(set(constructed_triangulation_topomesh.wisps(2)).difference(set(free_triangles))))
if omega_criteria.has_key('clique'):
triangle_neighbor_weights[t] = np.min(triangle_weights.values(triangle_future_tetra_triangles)) - omega_criteria['clique']*(len(triangle_future_tetra_triangles)-4)
else:
triangle_neighbor_weights[t] = np.min(triangle_weights.values(triangle_future_tetra_triangles))
# print free_triangles
if len(free_triangles)>0:
free_triangles = list(np.array(free_triangles)[np.argsort(-triangle_neighbor_weights.values(free_triangles))])
constructed_triangulation_topomesh.update_wisp_property('barycenter',0,array_dict(positions.values(list(constructed_triangulation_topomesh.wisps(0))),list(constructed_triangulation_topomesh.wisps(0))))
return constructed_triangulation_topomesh
def save_property_topomesh(topomesh, path, cells_to_save=None, properties_to_save=dict([(0,['barycenter']),(1,[]),(2,[]),(3,[])]),**kwargs):
if cells_to_save is None:
cells_to_save = np.array(list(topomesh.wisps(3)))
triangles_to_save = np.array(np.unique(np.concatenate([np.array(list(topomesh.borders(3,c))) for c in cells_to_save])),int)
edges_to_save = np.array(np.unique(np.concatenate([np.array(list(topomesh.borders(2,t))) for t in triangles_to_save])),int)
vertices_to_save = np.array(np.unique(np.concatenate([np.array(list(topomesh.borders(1,e))) for e in edges_to_save])),int)
original_pids = kwargs.get('original_pids',False)
original_eids = kwargs.get('original_eids',False)
original_fids = kwargs.get('original_fids',False)
original_cids = kwargs.get('original_cids',True)
sub_topomesh = PropertyTopomesh(3)
vertices_to_pids = {}
for v in vertices_to_save:
if original_pids:
pid = sub_topomesh.add_wisp(0,v)
else:
pid = sub_topomesh.add_wisp(0)
vertices_to_pids[v] = pid
edges_to_eids = {}
for e in edges_to_save:
if original_eids:
eid = sub_topomesh.add_wisp(1,e)
else:
eid = sub_topomesh.add_wisp(1)
edges_to_eids[e] = eid
for v in topomesh.borders(1,e):
sub_topomesh.link(1,eid,vertices_to_pids[v])
triangles_to_fids = {}
for t in triangles_to_save:
if original_fids:
fid = sub_topomesh.add_wisp(2,t)
else:
fid = sub_topomesh.add_wisp(2)
triangles_to_fids[t] = fid
for e in topomesh.borders(2,t):
sub_topomesh.link(2,fid,edges_to_eids[e])
cells_to_cids = {}
for c in cells_to_save:
if original_cids:
cid = sub_topomesh.add_wisp(3,c)
else:
cid = sub_topomesh.add_wisp(3,c)
cells_to_cids[c] = cid
for t in topomesh.borders(3,c):
sub_topomesh.link(3,cid,triangles_to_fids[t])
wisps_to_save = {}
wisps_to_save[0] = vertices_to_save
wisps_to_save[1] = edges_to_save
wisps_to_save[2] = triangles_to_save
wisps_to_save[3] = cells_to_save
wisps_to_wids = {}
wisps_to_wids[0] = vertices_to_pids
wisps_to_wids[1] = edges_to_eids
wisps_to_wids[2] = triangles_to_fids
wisps_to_wids[3] = cells_to_cids
if not 0 in properties_to_save.keys():
properties_to_save[0] = []
if not 'barycenter' in properties_to_save[0]:
properties_to_save[0].append('barycenter')
for degree in properties_to_save.keys():
for property_name in properties_to_save[degree]:
print "Property ",property_name,'(',degree,')'
if topomesh.has_wisp_property(property_name,degree=degree,is_computed=True):
wids_to_save = array_dict(wisps_to_wids[degree]).values(wisps_to_save[degree])
sub_topomesh.update_wisp_property(property_name,degree,array_dict(topomesh.wisp_property(property_name,degree).values(wisps_to_save[degree]),wids_to_save))
pickle.dump(sub_topomesh,open(path,"wb"))
for f in element_properties['volume'][c]['face_index']:
face_cells[triangle_matching[f]] = face_cells[triangle_matching[f]].union({cell_matching[c]})
else:
for f in xrange(len(unique_triangles)):
face_cells[triangle_matching[f]] = {0}
else:
cell_matching[0] = 0
for f in xrange(len(unique_triangles)):
face_cells[triangle_matching[f]] = {0}
element_matching['volume'] = cell_matching
if verbose: print len(cell_matching)," Cells"
if timecheck: print 'cell unicity test:',time()-check_time
if timecheck: check_time =time()
topomesh = PropertyTopomesh(3)
for pid in xrange(len(unique_points)):
topomesh.add_wisp(0,pid)
for fid in xrange(len(unique_triangles)):
topomesh.add_wisp(2,fid)
for cid in face_cells[fid]:
if not topomesh.has_wisp(3, cid):
topomesh.add_wisp(3,cid)
topomesh.link(3,cid,fid)
for eid,e in enumerate(unique_edges):
topomesh.add_wisp(1,eid)
for pid in e:
topomesh.link(1,eid,pid)
def implicit_surface_topomesh(density_field,size,resolution,iso=0.5,center=True):
import numpy as np
from scipy.cluster.vq import kmeans, vq
from openalea.container import array_dict, PropertyTopomesh
surface_points, surface_triangles = vtk_marching_cubes(density_field,iso)
surface_points = (np.array(surface_points))*(size*resolution/np.array(density_field.shape))
if center:
surface_points -= np.array(density_field.shape)*resolution/2.
# points_ids = np.arange(len(surface_points))
# points_to_delete = []
# for p,point in enumerate(surface_points):
# matching_points = np.sort(np.where(vq(surface_points,np.array([point]))[1] == 0)[0])
# if len(matching_points) > 1:
# points_to_fuse = matching_points[1:]
# for m_p in points_to_fuse:
# surface_triangles[np.where(surface_triangles==m_p)] = matching_points[0]
# points_to_delete.append(m_p)
# points_to_delete = np.unique(points_to_delete)
# print len(points_to_delete),"points deleted"
# surface_points = np.delete(surface_points,points_to_delete,0)
# points_ids = np.delete(points_ids,points_to_delete,0)
# surface_triangles = array_dict(np.arange(len(surface_points)),points_ids).values(surface_triangles)
# for p,point in enumerate(surface_points):
# matching_points = np.where(vq(surface_points,np.array([point]))[1] == 0)[0]
# if len(matching_points) > 1:
# print p,point
# raw_input()
# triangles_to_delete = []
# for t,triangle in enumerate(surface_triangles):
# if len(np.unique(triangle)) < 3:
# triangles_to_delete.append(t)
# # elif triangle.max() >= len(surface_points):
# # triangles_to_delete.append(t)
# surface_triangles = np.delete(surface_triangles,triangles_to_delete,0)
surface_topomesh = PropertyTopomesh(3)
for p in surface_points:
pid = surface_topomesh.add_wisp(0)
triangle_edge_list = np.array([[1, 2],[0, 2],[0, 1]])
surface_edges = np.sort(np.concatenate(surface_triangles[:,triangle_edge_list]))
_,unique_edges = np.unique(np.ascontiguousarray(surface_edges).view(np.dtype((np.void,surface_edges.dtype.itemsize * surface_edges.shape[1]))),return_index=True)
surface_edges = surface_edges[unique_edges]
for e in surface_edges:
eid = surface_topomesh.add_wisp(1)
for pid in e:
surface_topomesh.link(1,eid,pid)
surface_triangle_edges = np.sort(np.concatenate(surface_triangles[:,triangle_edge_list]))
surface_triangle_edge_matching = vq(surface_triangle_edges,surface_edges)[0].reshape(surface_triangles.shape[0],3)
for t in surface_triangles:
fid = surface_topomesh.add_wisp(2)
for eid in surface_triangle_edge_matching[fid]:
surface_topomesh.link(2,fid,eid)
cid = surface_topomesh.add_wisp(3)
for fid in surface_topomesh.wisps(2):
surface_topomesh.link(3,cid,fid)
surface_topomesh.update_wisp_property('barycenter',0,array_dict(surface_points),keys=list(surface_topomesh.wisps(0)))
return surface_topomesh
def triangle_topomesh(triangles, positions, **kwargs):
triangles = np.array(triangles)
positions = array_dict(positions)
edges = array_unique(np.sort(np.concatenate(triangles[:,triangle_edge_list],axis=0)))
triangle_edges = np.sort(np.concatenate(triangles[:,triangle_edge_list]))
start_time = time()
print "--> Generating triangle topomesh"
triangle_edge_matching = vq(triangle_edges,edges)[0]
triangle_topomesh = PropertyTopomesh(3)
for c in np.unique(triangles):
triangle_topomesh.add_wisp(0,c)
for e in edges:
eid = triangle_topomesh.add_wisp(1)
for pid in e:
triangle_topomesh.link(1,eid,pid)
for t in triangles:
fid = triangle_topomesh.add_wisp(2)
for eid in triangle_edge_matching[3*fid:3*fid+3]:
triangle_topomesh.link(2,fid,eid)
triangle_topomesh.add_wisp(3,0)
for fid in triangle_topomesh.wisps(2):
triangle_topomesh.link(3,0,fid)
triangle_topomesh.update_wisp_property('barycenter',0,positions.values(np.unique(triangles)),keys=np.unique(triangles))
end_time = time()
print "<-- Generating triangle topomesh [",end_time-start_time,"s]"
return triangle_topomesh
def tetrahedra_topomesh(tetrahedra, positions, **kwargs):
tetrahedra = np.array(tetrahedra)
positions = array_dict(positions)
tetrahedra_triangles = array_unique(np.concatenate(np.sort(tetrahedra[:,tetra_triangle_list])))
tetrahedra_triangle_edges = tetrahedra_triangles[:,triangle_edge_list]
tetrahedra_triangle_vectors = positions.values(tetrahedra_triangle_edges[...,1]) - positions.values(tetrahedra_triangle_edges[...,0])
tetrahedra_triangle_lengths = np.linalg.norm(tetrahedra_triangle_vectors,axis=2)
tetrahedra_triangle_perimeters = tetrahedra_triangle_lengths.sum(axis=1)
tetrahedra_edges = array_unique(np.concatenate(tetrahedra_triangles[:,triangle_edge_list],axis=0))
start_time = time()
print "--> Generating tetrahedra topomesh"
triangle_edges = np.concatenate(tetrahedra_triangles[:,triangle_edge_list],axis=0)
triangle_edge_matching = vq(triangle_edges,tetrahedra_edges)[0]
tetrahedra_faces = np.concatenate(np.sort(tetrahedra[:,tetra_triangle_list]))
tetrahedra_triangle_matching = vq(tetrahedra_faces,tetrahedra_triangles)[0]
tetrahedra_topomesh = PropertyTopomesh(3)
for c in np.unique(tetrahedra_triangles):
tetrahedra_topomesh.add_wisp(0,c)
for e in tetrahedra_edges:
eid = tetrahedra_topomesh.add_wisp(1)
for pid in e:
tetrahedra_topomesh.link(1,eid,pid)
for t in tetrahedra_triangles:
fid = tetrahedra_topomesh.add_wisp(2)
for eid in triangle_edge_matching[3*fid:3*fid+3]:
tetrahedra_topomesh.link(2,fid,eid)
for t in tetrahedra:
cid = tetrahedra_topomesh.add_wisp(3)
for fid in tetrahedra_triangle_matching[4*cid:4*cid+4]:
tetrahedra_topomesh.link(3,cid,fid)
tetrahedra_topomesh.update_wisp_property('barycenter',0,positions.values(np.unique(tetrahedra_triangles)),keys=np.unique(tetrahedra_triangles))
end_time = time()
print "<-- Generating tetrahedra topomesh [",end_time-start_time,"s]"
return tetrahedra_topomesh
def dual_topomesh(topomesh,degree=2,vertex_positions='barycenter'):
dual_topomesh = PropertyTopomesh(topomesh.degree())
if degree == 2:
for d in xrange(3):
if d<2:
dual_topomesh._regions[d] = deepcopy(topomesh._borders[2-d])
if d>0:
dual_topomesh._borders[d] = deepcopy(topomesh._regions[2-d])
dual_topomesh._borders[3] = dict(zip(dual_topomesh._borders[2].keys(),[[w] for w in dual_topomesh._borders[2].keys()]))
dual_topomesh._regions[2] = dict(zip(dual_topomesh._borders[2].keys(),[[w] for w in dual_topomesh._borders[2].keys()]))
edges_to_remove = [e for e in dual_topomesh.wisps(1) if len(list(dual_topomesh.borders(1,e)))<2]
faces_to_remove = [f for f in dual_topomesh.wisps(2) if np.any([e in edges_to_remove for e in dual_topomesh.borders(2,f)])]
cells_to_remove = faces_to_remove
for e in edges_to_remove:
dual_topomesh.remove_wisp(1,e)
for f in faces_to_remove:
dual_topomesh.remove_wisp(2,f)
for c in cells_to_remove:
dual_topomesh.remove_wisp(3,c)
if 'voronoi' in vertex_positions:
assert is_triangular(topomesh)
if degree==2:
from openalea.cellcomplex.property_topomesh.utils.geometry_tools import triangle_geometric_features
compute_topomesh_property(topomesh,'vertices',2)
triangles = topomesh.wisp_property('vertices',2).values(list(dual_topomesh.wisps(0)))
positions = topomesh.wisp_property('barycenter',0)
if vertex_positions == 'projected_voronoi':
centers = triangle_geometric_features(triangles,positions,features=['projected_circumscribed_circle_center'])[:,0]
else:
centers = triangle_geometric_features(triangles,positions,features=['circumscribed_circle_center'])[:,0]
dual_positions = array_dict(centers,list(dual_topomesh.wisps(0)))
else:
compute_topomesh_property(topomesh,'barycenter',degree)
dual_positions = array_dict(topomesh.wisp_property('barycenter',degree).values(list(dual_topomesh.wisps(0))),list(dual_topomesh.wisps(0)))
dual_topomesh.update_wisp_property('barycenter',0,dual_positions)
return dual_topomesh
def poly_topomesh(polys, positions, faces_as_cells=False, **kwargs):
polys = np.array(polys)
positions = array_dict(positions)
poly_lengths = np.array(map(len,polys))
poly_edge_list = [np.transpose([np.arange(l),(np.arange(l)+1)%l]) for l in poly_lengths]
edges = array_unique(np.sort(np.concatenate([np.array(p)[l] for p,l in zip(polys,poly_edge_list)],axis=0)))
poly_edges = np.sort(np.concatenate([np.array(p)[l] for p,l in zip(polys,poly_edge_list)],axis=0))
start_time = time()
print "--> Generating poly topomesh"
poly_edge_matching = vq(poly_edges,edges)[0]
poly_topomesh = PropertyTopomesh(3)
for c in np.unique(polys):
poly_topomesh.add_wisp(0,c)
for e in edges:
eid = poly_topomesh.add_wisp(1)
for pid in e:
poly_topomesh.link(1,eid,pid)
total_poly_length = 0
for q,l in zip(polys,poly_lengths):
fid = poly_topomesh.add_wisp(2)
for eid in poly_edge_matching[total_poly_length:total_poly_length+l]:
poly_topomesh.link(2,fid,eid)
total_poly_length += l
if not faces_as_cells:
poly_topomesh.add_wisp(3,0)
for fid in poly_topomesh.wisps(2):
poly_topomesh.link(3,0,fid)
else:
for fid in poly_topomesh.wisps(2):
poly_topomesh.add_wisp(3,fid)
poly_topomesh.link(3,fid,fid)
poly_topomesh.update_wisp_property('barycenter',0,positions.values(np.unique(polys)),keys=np.unique(polys))
end_time = time()
print "<-- Generating poly topomesh [",end_time-start_time,"s]"
return poly_topomesh
def quad_topomesh(quads, positions, faces_as_cells=False, **kwargs):
quads = np.array(quads)
positions = array_dict(positions)
edges = array_unique(np.sort(np.concatenate(quads[:,quad_edge_list],axis=0)))
quad_edges = np.sort(np.concatenate(quads[:,quad_edge_list]))
start_time = time()
print "--> Generating quad topomesh"
quad_edge_matching = vq(quad_edges,edges)[0]
quad_topomesh = PropertyTopomesh(3)
for c in np.unique(quads):
quad_topomesh.add_wisp(0,c)
for e in edges:
eid = quad_topomesh.add_wisp(1)
for pid in e:
quad_topomesh.link(1,eid,pid)
for q in quads:
fid = quad_topomesh.add_wisp(2)
for eid in quad_edge_matching[4*fid:4*fid+4]:
quad_topomesh.link(2,fid,eid)
if not faces_as_cells:
quad_topomesh.add_wisp(3,0)
for fid in quad_topomesh.wisps(2):
quad_topomesh.link(3,0,fid)
else:
for fid in quad_topomesh.wisps(2):
quad_topomesh.add_wisp(3,fid)
quad_topomesh.link(3,fid,fid)
quad_topomesh.update_wisp_property('barycenter',0,positions.values(np.unique(quads)),keys=np.unique(quads))
end_time = time()
print "<-- Generating quad topomesh [",end_time-start_time,"s]"
return quad_topomesh