361 lines
15 KiB
Python
361 lines
15 KiB
Python
# modified from https://github.com/Profactor/continuous-remeshing
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import torch
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import torch.nn.functional as tfunc
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import torch_scatter
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from typing import Tuple
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def prepend_dummies(
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vertices:torch.Tensor, #V,D
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faces:torch.Tensor, #F,3 long
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)->Tuple[torch.Tensor,torch.Tensor]:
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"""prepend dummy elements to vertices and faces to enable "masked" scatter operations"""
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V,D = vertices.shape
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vertices = torch.concat((torch.full((1,D),fill_value=torch.nan,device=vertices.device),vertices),dim=0)
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faces = torch.concat((torch.zeros((1,3),dtype=torch.long,device=faces.device),faces+1),dim=0)
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return vertices,faces
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def remove_dummies(
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vertices:torch.Tensor, #V,D - first vertex all nan and unreferenced
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faces:torch.Tensor, #F,3 long - first face all zeros
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)->Tuple[torch.Tensor,torch.Tensor]:
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"""remove dummy elements added with prepend_dummies()"""
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return vertices[1:],faces[1:]-1
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def calc_edges(
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faces: torch.Tensor, # F,3 long - first face may be dummy with all zeros
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with_edge_to_face: bool = False
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) -> Tuple[torch.Tensor, ...]:
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"""
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returns Tuple of
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- edges E,2 long, 0 for unused, lower vertex index first
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- face_to_edge F,3 long
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- (optional) edge_to_face shape=E,[left,right],[face,side]
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o-<-----e1 e0,e1...edge, e0<e1
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| /A L,R....left and right face
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| L / | both triangles ordered counter clockwise
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| / R | normals pointing out of screen
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V/ |
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e0---->-o
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"""
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F = faces.shape[0]
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# make full edges, lower vertex index first
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face_edges = torch.stack((faces,faces.roll(-1,1)),dim=-1) #F*3,3,2
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full_edges = face_edges.reshape(F*3,2)
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sorted_edges,_ = full_edges.sort(dim=-1) #F*3,2
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# make unique edges
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edges,full_to_unique = torch.unique(input=sorted_edges,sorted=True,return_inverse=True,dim=0) #(E,2),(F*3)
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E = edges.shape[0]
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face_to_edge = full_to_unique.reshape(F,3) #F,3
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if not with_edge_to_face:
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return edges, face_to_edge
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is_right = full_edges[:,0]!=sorted_edges[:,0] #F*3
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edge_to_face = torch.zeros((E,2,2),dtype=torch.long,device=faces.device) #E,LR=2,S=2
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scatter_src = torch.cartesian_prod(torch.arange(0,F,device=faces.device),torch.arange(0,3,device=faces.device)) #F*3,2
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edge_to_face.reshape(2*E,2).scatter_(dim=0,index=(2*full_to_unique+is_right)[:,None].expand(F*3,2),src=scatter_src) #E,LR=2,S=2
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edge_to_face[0] = 0
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return edges, face_to_edge, edge_to_face
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def calc_edge_length(
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vertices:torch.Tensor, #V,3 first may be dummy
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edges:torch.Tensor, #E,2 long, lower vertex index first, (0,0) for unused
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)->torch.Tensor: #E
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full_vertices = vertices[edges] #E,2,3
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a,b = full_vertices.unbind(dim=1) #E,3
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return torch.norm(a-b,p=2,dim=-1)
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def calc_face_normals(
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vertices:torch.Tensor, #V,3 first vertex may be unreferenced
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faces:torch.Tensor, #F,3 long, first face may be all zero
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normalize:bool=False,
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)->torch.Tensor: #F,3
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"""
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n
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c0 corners ordered counterclockwise when
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/ \ looking onto surface (in neg normal direction)
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c1---c2
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"""
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full_vertices = vertices[faces] #F,C=3,3
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v0,v1,v2 = full_vertices.unbind(dim=1) #F,3
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face_normals = torch.cross(v1-v0,v2-v0, dim=1) #F,3
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if normalize:
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face_normals = tfunc.normalize(face_normals, eps=1e-6, dim=1)
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return face_normals #F,3
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def calc_vertex_normals(
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vertices:torch.Tensor, #V,3 first vertex may be unreferenced
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faces:torch.Tensor, #F,3 long, first face may be all zero
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face_normals:torch.Tensor=None, #F,3, not normalized
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)->torch.Tensor: #F,3
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F = faces.shape[0]
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if face_normals is None:
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face_normals = calc_face_normals(vertices,faces)
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vertex_normals = torch.zeros((vertices.shape[0],3,3),dtype=vertices.dtype,device=vertices.device) #V,C=3,3
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vertex_normals.scatter_add_(dim=0,index=faces[:,:,None].expand(F,3,3),src=face_normals[:,None,:].expand(F,3,3))
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vertex_normals = vertex_normals.sum(dim=1) #V,3
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return tfunc.normalize(vertex_normals, eps=1e-6, dim=1)
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def calc_face_ref_normals(
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faces:torch.Tensor, #F,3 long, 0 for unused
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vertex_normals:torch.Tensor, #V,3 first unused
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normalize:bool=False,
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)->torch.Tensor: #F,3
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"""calculate reference normals for face flip detection"""
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full_normals = vertex_normals[faces] #F,C=3,3
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ref_normals = full_normals.sum(dim=1) #F,3
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if normalize:
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ref_normals = tfunc.normalize(ref_normals, eps=1e-6, dim=1)
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return ref_normals
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def pack(
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vertices:torch.Tensor, #V,3 first unused and nan
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faces:torch.Tensor, #F,3 long, 0 for unused
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)->Tuple[torch.Tensor,torch.Tensor]: #(vertices,faces), keeps first vertex unused
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"""removes unused elements in vertices and faces"""
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V = vertices.shape[0]
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# remove unused faces
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used_faces = faces[:,0]!=0
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used_faces[0] = True
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faces = faces[used_faces] #sync
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# remove unused vertices
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used_vertices = torch.zeros(V,3,dtype=torch.bool,device=vertices.device)
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used_vertices.scatter_(dim=0,index=faces,value=True,reduce='add')
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used_vertices = used_vertices.any(dim=1)
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used_vertices[0] = True
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vertices = vertices[used_vertices] #sync
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# update used faces
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ind = torch.zeros(V,dtype=torch.long,device=vertices.device)
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V1 = used_vertices.sum()
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ind[used_vertices] = torch.arange(0,V1,device=vertices.device) #sync
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faces = ind[faces]
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return vertices,faces
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def split_edges(
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vertices:torch.Tensor, #V,3 first unused
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faces:torch.Tensor, #F,3 long, 0 for unused
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edges:torch.Tensor, #E,2 long 0 for unused, lower vertex index first
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face_to_edge:torch.Tensor, #F,3 long 0 for unused
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splits, #E bool
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pack_faces:bool=True,
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)->Tuple[torch.Tensor,torch.Tensor]: #(vertices,faces)
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# c2 c2 c...corners = faces
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# . . . . s...side_vert, 0 means no split
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# . . .N2 . S...shrunk_face
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# . . . . Ni...new_faces
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# s2 s1 s2|c2...s1|c1
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# . . . . .
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# . . . S . .
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# . . . . N1 .
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# c0...(s0=0)....c1 s0|c0...........c1
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#
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# pseudo-code:
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# S = [s0|c0,s1|c1,s2|c2] example:[c0,s1,s2]
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# split = side_vert!=0 example:[False,True,True]
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# N0 = split[0]*[c0,s0,s2|c2] example:[0,0,0]
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# N1 = split[1]*[c1,s1,s0|c0] example:[c1,s1,c0]
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# N2 = split[2]*[c2,s2,s1|c1] example:[c2,s2,s1]
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V = vertices.shape[0]
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F = faces.shape[0]
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S = splits.sum().item() #sync
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if S==0:
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return vertices,faces
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edge_vert = torch.zeros_like(splits, dtype=torch.long) #E
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edge_vert[splits] = torch.arange(V,V+S,dtype=torch.long,device=vertices.device) #E 0 for no split, sync
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side_vert = edge_vert[face_to_edge] #F,3 long, 0 for no split
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split_edges = edges[splits] #S sync
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#vertices
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split_vertices = vertices[split_edges].mean(dim=1) #S,3
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vertices = torch.concat((vertices,split_vertices),dim=0)
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#faces
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side_split = side_vert!=0 #F,3
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shrunk_faces = torch.where(side_split,side_vert,faces) #F,3 long, 0 for no split
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new_faces = side_split[:,:,None] * torch.stack((faces,side_vert,shrunk_faces.roll(1,dims=-1)),dim=-1) #F,N=3,C=3
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faces = torch.concat((shrunk_faces,new_faces.reshape(F*3,3))) #4F,3
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if pack_faces:
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mask = faces[:,0]!=0
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mask[0] = True
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faces = faces[mask] #F',3 sync
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return vertices,faces
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def collapse_edges(
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vertices:torch.Tensor, #V,3 first unused
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faces:torch.Tensor, #F,3 long 0 for unused
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edges:torch.Tensor, #E,2 long 0 for unused, lower vertex index first
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priorities:torch.Tensor, #E float
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stable:bool=False, #only for unit testing
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)->Tuple[torch.Tensor,torch.Tensor]: #(vertices,faces)
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V = vertices.shape[0]
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# check spacing
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_,order = priorities.sort(stable=stable) #E
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rank = torch.zeros_like(order)
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rank[order] = torch.arange(0,len(rank),device=rank.device)
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vert_rank = torch.zeros(V,dtype=torch.long,device=vertices.device) #V
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edge_rank = rank #E
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for i in range(3):
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torch_scatter.scatter_max(src=edge_rank[:,None].expand(-1,2).reshape(-1),index=edges.reshape(-1),dim=0,out=vert_rank)
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edge_rank,_ = vert_rank[edges].max(dim=-1) #E
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candidates = edges[(edge_rank==rank).logical_and_(priorities>0)] #E',2
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# check connectivity
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vert_connections = torch.zeros(V,dtype=torch.long,device=vertices.device) #V
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vert_connections[candidates[:,0]] = 1 #start
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edge_connections = vert_connections[edges].sum(dim=-1) #E, edge connected to start
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vert_connections.scatter_add_(dim=0,index=edges.reshape(-1),src=edge_connections[:,None].expand(-1,2).reshape(-1))# one edge from start
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vert_connections[candidates] = 0 #clear start and end
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edge_connections = vert_connections[edges].sum(dim=-1) #E, one or two edges from start
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vert_connections.scatter_add_(dim=0,index=edges.reshape(-1),src=edge_connections[:,None].expand(-1,2).reshape(-1)) #one or two edges from start
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collapses = candidates[vert_connections[candidates[:,1]] <= 2] # E" not more than two connections between start and end
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# mean vertices
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vertices[collapses[:,0]] = vertices[collapses].mean(dim=1)
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# update faces
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dest = torch.arange(0,V,dtype=torch.long,device=vertices.device) #V
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dest[collapses[:,1]] = dest[collapses[:,0]]
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faces = dest[faces] #F,3
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c0,c1,c2 = faces.unbind(dim=-1)
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collapsed = (c0==c1).logical_or_(c1==c2).logical_or_(c0==c2)
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faces[collapsed] = 0
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return vertices,faces
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def calc_face_collapses(
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vertices:torch.Tensor, #V,3 first unused
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faces:torch.Tensor, #F,3 long, 0 for unused
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edges:torch.Tensor, #E,2 long 0 for unused, lower vertex index first
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face_to_edge:torch.Tensor, #F,3 long 0 for unused
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edge_length:torch.Tensor, #E
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face_normals:torch.Tensor, #F,3
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vertex_normals:torch.Tensor, #V,3 first unused
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min_edge_length:torch.Tensor=None, #V
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area_ratio = 0.5, #collapse if area < min_edge_length**2 * area_ratio
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shortest_probability = 0.8
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)->torch.Tensor: #E edges to collapse
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E = edges.shape[0]
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F = faces.shape[0]
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# face flips
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ref_normals = calc_face_ref_normals(faces,vertex_normals,normalize=False) #F,3
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face_collapses = (face_normals*ref_normals).sum(dim=-1)<0 #F
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# small faces
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if min_edge_length is not None:
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min_face_length = min_edge_length[faces].mean(dim=-1) #F
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min_area = min_face_length**2 * area_ratio #F
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face_collapses.logical_or_(face_normals.norm(dim=-1) < min_area*2) #F
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face_collapses[0] = False
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# faces to edges
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face_length = edge_length[face_to_edge] #F,3
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if shortest_probability<1:
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#select shortest edge with shortest_probability chance
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randlim = round(2/(1-shortest_probability))
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rand_ind = torch.randint(0,randlim,size=(F,),device=faces.device).clamp_max_(2) #selected edge local index in face
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sort_ind = torch.argsort(face_length,dim=-1,descending=True) #F,3
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local_ind = sort_ind.gather(dim=-1,index=rand_ind[:,None])
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else:
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local_ind = torch.argmin(face_length,dim=-1)[:,None] #F,1 0...2 shortest edge local index in face
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edge_ind = face_to_edge.gather(dim=1,index=local_ind)[:,0] #F 0...E selected edge global index
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edge_collapses = torch.zeros(E,dtype=torch.long,device=vertices.device)
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edge_collapses.scatter_add_(dim=0,index=edge_ind,src=face_collapses.long())
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return edge_collapses.bool()
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def flip_edges(
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vertices:torch.Tensor, #V,3 first unused
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faces:torch.Tensor, #F,3 long, first must be 0, 0 for unused
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edges:torch.Tensor, #E,2 long, first must be 0, 0 for unused, lower vertex index first
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edge_to_face:torch.Tensor, #E,[left,right],[face,side]
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with_border:bool=True, #handle border edges (D=4 instead of D=6)
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with_normal_check:bool=True, #check face normal flips
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stable:bool=False, #only for unit testing
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):
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V = vertices.shape[0]
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E = edges.shape[0]
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device=vertices.device
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vertex_degree = torch.zeros(V,dtype=torch.long,device=device) #V long
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vertex_degree.scatter_(dim=0,index=edges.reshape(E*2),value=1,reduce='add')
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neighbor_corner = (edge_to_face[:,:,1] + 2) % 3 #go from side to corner
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neighbors = faces[edge_to_face[:,:,0],neighbor_corner] #E,LR=2
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edge_is_inside = neighbors.all(dim=-1) #E
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if with_border:
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# inside vertices should have D=6, border edges D=4, so we subtract 2 for all inside vertices
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# need to use float for masks in order to use scatter(reduce='multiply')
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vertex_is_inside = torch.ones(V,2,dtype=torch.float32,device=vertices.device) #V,2 float
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src = edge_is_inside.type(torch.float32)[:,None].expand(E,2) #E,2 float
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vertex_is_inside.scatter_(dim=0,index=edges,src=src,reduce='multiply')
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vertex_is_inside = vertex_is_inside.prod(dim=-1,dtype=torch.long) #V long
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vertex_degree -= 2 * vertex_is_inside #V long
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neighbor_degrees = vertex_degree[neighbors] #E,LR=2
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edge_degrees = vertex_degree[edges] #E,2
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#
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# loss = Sum_over_affected_vertices((new_degree-6)**2)
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# loss_change = Sum_over_neighbor_vertices((degree+1-6)**2-(degree-6)**2)
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# + Sum_over_edge_vertices((degree-1-6)**2-(degree-6)**2)
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# = 2 * (2 + Sum_over_neighbor_vertices(degree) - Sum_over_edge_vertices(degree))
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#
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loss_change = 2 + neighbor_degrees.sum(dim=-1) - edge_degrees.sum(dim=-1) #E
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candidates = torch.logical_and(loss_change<0, edge_is_inside) #E
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loss_change = loss_change[candidates] #E'
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if loss_change.shape[0]==0:
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return
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edges_neighbors = torch.concat((edges[candidates],neighbors[candidates]),dim=-1) #E',4
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_,order = loss_change.sort(descending=True, stable=stable) #E'
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rank = torch.zeros_like(order)
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rank[order] = torch.arange(0,len(rank),device=rank.device)
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vertex_rank = torch.zeros((V,4),dtype=torch.long,device=device) #V,4
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torch_scatter.scatter_max(src=rank[:,None].expand(-1,4),index=edges_neighbors,dim=0,out=vertex_rank)
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vertex_rank,_ = vertex_rank.max(dim=-1) #V
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neighborhood_rank,_ = vertex_rank[edges_neighbors].max(dim=-1) #E'
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flip = rank==neighborhood_rank #E'
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if with_normal_check:
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# cl-<-----e1 e0,e1...edge, e0<e1
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# | /A L,R....left and right face
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# | L / | both triangles ordered counter clockwise
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# | / R | normals pointing out of screen
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# V/ |
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# e0---->-cr
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v = vertices[edges_neighbors] #E",4,3
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v = v - v[:,0:1] #make relative to e0
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e1 = v[:,1]
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cl = v[:,2]
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cr = v[:,3]
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n = torch.cross(e1,cl,dim=-1) + torch.cross(cr,e1,dim=-1) #sum of old normal vectors
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flip.logical_and_(torch.sum(n*torch.cross(cr,cl,dim=-1),dim=-1)>0) #first new face
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flip.logical_and_(torch.sum(n*torch.cross(cl-e1,cr-e1,dim=-1),dim=-1)>0) #second new face
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flip_edges_neighbors = edges_neighbors[flip] #E",4
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flip_edge_to_face = edge_to_face[candidates,:,0][flip] #E",2
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flip_faces = flip_edges_neighbors[:,[[0,3,2],[1,2,3]]] #E",2,3
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faces.scatter_(dim=0,index=flip_edge_to_face.reshape(-1,1).expand(-1,3),src=flip_faces.reshape(-1,3))
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