From cfbde60480cddec2000726db75ebe8df3ae530ba Mon Sep 17 00:00:00 2001
From: "Stephen M. McQuay" <smcquay@fusionio.com>
Date: Wed, 30 May 2012 22:57:56 -0600
Subject: [PATCH] added vertex calcs for simple butterfly

---
 surf/subd/butterfly.py | 55 +++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 54 insertions(+), 1 deletion(-)

diff --git a/surf/subd/butterfly.py b/surf/subd/butterfly.py
index 2a5196c..3c4acfd 100644
--- a/surf/subd/butterfly.py
+++ b/surf/subd/butterfly.py
@@ -1,2 +1,55 @@
+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):
-    pass
+    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)