a playground adding surface subdivision methods to scipy
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from __future__ import division
from itertools import combinations
from surf.geometry import PolygonMesh, Vertex
def _get_third_point(mesh, eid, fid):
evids = set(mesh.edges[eid])
fvids = set(mesh.faces[fid])
other_vid = fvids - evids
assert len(other_vid) == 1
other_vid = other_vid.pop()
return other_vid
def _make_edge_point(mesh, eid):
final_vert = Vertex()
a = 1 / 2
b = 1 / 8
c = -1 / 16
a_verts = [mesh.vertices[v] for v in mesh.edges[eid]]
for v in a_verts:
final_vert += a * v
for fid in mesh.faces_for_edge[eid]:
other_vid = _get_third_point(mesh, eid, fid)
final_vert += b * mesh.vertices[other_vid]
other_edges = [e for e in mesh.edges_for_face[fid] if e != eid]
for other_edge in other_edges:
wing_face = [f for f in mesh.faces_for_edge[other_edge]
if f != fid]
assert len(wing_face) == 1
vid = _get_third_point(mesh, other_edge, wing_face[0])
final_vert += c * mesh.vertices[vid]
return final_vert
def refine(mesh):
new_verts = list(mesh.vertices)
nv_offset = len(new_verts)
new_edges = []
new_faces = []
for eid, verts_for_edge in enumerate(mesh.edges):
new_vert = _make_edge_point(mesh, eid)
new_verts.append(new_vert)
# populate *some* of the new edges (missing all edges on a face ...)
new_vert_id = eid + nv_offset
for evid in mesh.edges[eid]:
new_edge = [evid, new_vert_id]
new_edges.append(new_edge)
for fid in range(len(mesh.faces)):
# join all new edge points on a face:
new_center_face = [i + nv_offset for i in mesh.edges_for_face[fid]]
inner_edges = list(combinations(new_center_face, 2))
new_edges.extend(inner_edges)
# make new faces: center face
new_faces.append(new_center_face)
# three new faces, one per old vertex:
for fvid in mesh.faces[fid]:
possible_edges = mesh.edges_for_vert[fvid]
face_edges = mesh.edges_for_face[fid]
edges_for_fvid = list(set(possible_edges) & set(face_edges))
assert len(edges_for_fvid) == 2
new_faces.append([
edges_for_fvid[0] + nv_offset,
fvid,
edges_for_fvid[1] + nv_offset
])
return PolygonMesh(new_verts, new_faces, new_edges)