112 lines
4.6 KiB
Python
112 lines
4.6 KiB
Python
from collections import defaultdict
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from surf.geometry import PolygonMesh, centroid
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def refine(mesh):
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new_vertices = list(mesh.vertices)
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# this can be used to both get to fvid in new_vertices and to offest
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# mesh.faces to be dealing with the fvid generated from that face
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f_vert_offset = len(new_vertices)
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# this doesn't need to be calculated, but it is conceptually convenient to
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# have along the way. Alternatively one could get this by doing a:
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# >>> [e + e_vert_offset for e in mesh.edges_for_face[fvid]
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# (fvid for all faces)
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evid_for_fvid = defaultdict(list)
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new_edges = []
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new_faces = []
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# For each face, add a face Vertex
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for old_fid, old_face in enumerate(mesh.faces):
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# Set each face Vertex to be the centroid of all original Vertices for
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# the respective face.
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# here we have already created a list that is a copy of the original
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# verts. we append the new face Vertices to that same list, and simply
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# keep track of offsets into the new vert list ... see f_vert_offset
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# above and e_vert_offset below
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new_face_vertex = mesh.centroid(old_face)
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new_vertices.append(new_face_vertex)
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# edge verts will be new_vertices[e_vert_offset:]. Also, this can be used
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# to both get to evid in new_vertices and to offest mesh.edges to be
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# dealing with the evid generated from that edge
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e_vert_offset = len(new_vertices)
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# For each edge, add an edge Vertex.
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for old_eid, old_edge in enumerate(mesh.edges):
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tmp_verts = []
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# Set each edge Vertex to be the average of the two neighbouring, (very
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# recently calculated) face Vertices ...
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tmp_verts.extend([new_vertices[f + f_vert_offset]
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for f in mesh.faces_for_edge[old_eid]])
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# ... and its two original endpoints.
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tmp_verts.extend([mesh.vertices[vid] for vid in old_edge])
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# centroid == average
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new_vertices.append(centroid(tmp_verts))
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# make mapping from evid -> fvid for later
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for old_fid in mesh.faces_for_edge[old_eid]:
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fvid = old_fid + f_vert_offset
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evid = old_eid + e_vert_offset
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evid_for_fvid[fvid].append(evid)
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# For each original Vertex P, move the original Vertex to a new location
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# Here we mimic the F, R, and P spelling in the wiki article
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for old_vid in xrange(f_vert_offset):
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# take the average F of all n face Vertices for faces touching P ...
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F_verts = []
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for old_fid in mesh.faces_for_vert[old_vid]:
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F_verts.append(new_vertices[f_vert_offset + old_fid])
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F = centroid(F_verts)
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# and take the average R of all n new edge Vertices for edges adjacent
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# to P
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edges = [mesh.edges[eid] for eid in mesh.edges_for_vert[old_vid]]
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e_verts = []
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for edge in edges:
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e_verts.extend([mesh.vertices[vid] for vid in edge])
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R = centroid(e_verts)
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# where each edge midpoint is the average of its two endpoint vertices.
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# *Move* each original point to the point (or replace it in new_verts)
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new_vertex_point = (F + 2 * R
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+ (len(edges) - 3) * new_vertices[old_vid]
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) / len(edges)
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new_vertices[old_vid] = new_vertex_point
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# Connect each new Vertex point (with original id) to the new edge
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# points of all original edges incident on the original vertex.
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for old_eid in mesh.edges_for_vert[old_vid]:
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new_edges.append([old_vid, old_eid + e_vert_offset])
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# For each face point, add an edge connecting the new face point to each
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# new edge point
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for fvid, evids in evid_for_fvid.iteritems():
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for evid in evids:
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new_edges.append([fvid, evid])
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# to define new faces need to know the following for each new face:
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for fvid in xrange(f_vert_offset, e_vert_offset):
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# new face_vid (1 vid)
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# vid connected to fvid (iterate over, use 1 vid periteration)
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connected_vids = mesh.faces[fvid - f_vert_offset]
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evids_for_current_face = evid_for_fvid[fvid]
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for connected_vid in connected_vids:
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# evid connected to both the vid and the fvid (2 vids)
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evids_for_vid = [e + e_vert_offset for e in
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mesh.edges_for_vert[connected_vid]]
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common_ids = list(set(evids_for_vid) & set(evids_for_current_face))
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assert len(common_ids) == 2
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# then connect the (4) vids together ...
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new_faces.append([fvid, common_ids[0], connected_vid, common_ids[1]])
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return PolygonMesh(vertices=new_vertices, edges=new_edges, faces=new_faces)
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