surfaces/surf/subd/butterfly.py

from __future__ import division

import sys

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)

    # TODO:
    new_faces = []
    # TODO:
    new_edges = []

    for eid, verts_for_edge in enumerate(mesh.edges):
        new_vert = _make_edge_point(mesh, eid)
        new_verts.append(new_vert)

    return PolygonMesh(new_verts, new_faces, new_edges)