from collections import defaultdict

from surf.geometry import PolygonMesh, centroid


def refine(mesh):
    new_vertices = list(mesh.vertices)

    # this can be used to both get to fvid in new_vertices and to offest
    # mesh.faces to be dealing with the fvid generated from that face
    f_vert_offset = len(new_vertices)

    # this doesn't need to be calculated, but it is conceptually convenient to
    # have along the way. Alternatively one could get this by doing a:
    # >>> [e + e_vert_offset for e in mesh.edges_for_face[fvid]
    # (fvid for all faces)
    evid_for_fvid = defaultdict(list)

    new_edges = []
    new_faces = []

    # For each face, add a face Vertex
    for old_fid, old_face in enumerate(mesh.faces):
        # Set each face Vertex to be the centroid of all original Vertices for
        # the respective face.

        # here we have already created a list that is a copy of the original
        # verts. we append the new face Vertices to that same list, and simply
        # keep track of offsets into the new vert list ... see f_vert_offset
        # above and e_vert_offset below
        new_face_vertex = mesh.centroid(old_face)
        new_vertices.append(new_face_vertex)

    # edge verts will be new_vertices[e_vert_offset:]. Also, this can be used
    # to both get to evid in new_vertices and to offest mesh.edges to be
    # dealing with the evid generated from that edge
    e_vert_offset = len(new_vertices)

    # For each edge, add an edge Vertex.
    for old_eid, old_edge in enumerate(mesh.edges):
        tmp_verts = []

        # Set each edge Vertex to be the average of the two neighbouring, (very
        # recently calculated) face Vertices ...
        tmp_verts.extend([new_vertices[f + f_vert_offset]
            for f in mesh.faces_for_edge[old_eid]])

        # ... and its two original endpoints.
        tmp_verts.extend([mesh.vertices[vid] for vid in old_edge])

        # centroid == average
        new_vertices.append(centroid(tmp_verts))

        # make mapping from evid -> fvid for later
        for old_fid in mesh.faces_for_edge[old_eid]:
            fvid = old_fid + f_vert_offset
            evid = old_eid + e_vert_offset
            evid_for_fvid[fvid].append(evid)

    # For each original Vertex P, move the original Vertex to a new location
    # Here we mimic the F, R, and P spelling in the wiki article
    for old_vid in xrange(f_vert_offset):
        # take the average F of all n face Vertices for faces touching P ...
        F_verts = []
        for old_fid in mesh.faces_for_vert[old_vid]:
            F_verts.append(new_vertices[f_vert_offset + old_fid])
        F = centroid(F_verts)

        # and take the average R of all n new edge Vertices for edges adjacent
        # to P
        edges = [mesh.edges[eid] for eid in mesh.edges_for_vert[old_vid]]
        e_verts = []
        for edge in edges:
            e_verts.extend([mesh.vertices[vid] for vid in edge])
        R = centroid(e_verts)

        # where each edge midpoint is the average of its two endpoint vertices.
        # *Move* each original point to the point (or replace it in new_verts)
        new_vertex_point = (F + 2 * R
                              + (len(edges) - 3) * new_vertices[old_vid]
                            ) / len(edges)
        new_vertices[old_vid] = new_vertex_point

        # Connect each new Vertex point (with original id) to the new edge
        # points of all original edges incident on the original vertex.
        for old_eid in mesh.edges_for_vert[old_vid]:
            new_edges.append([old_vid, old_eid + e_vert_offset])

    # For each face point, add an edge connecting the new face point to each
    # new edge point
    for fvid, evids in evid_for_fvid.iteritems():
        for evid in evids:
            new_edges.append([fvid, evid])

    # to define new faces need to know the following for each new face:
    for fvid in xrange(f_vert_offset, e_vert_offset):
        # new face_vid (1 vid)

        # vid connected to fvid (iterate over, use 1 vid periteration)
        connected_vids = mesh.faces[fvid - f_vert_offset]
        evids_for_current_face = evid_for_fvid[fvid]
        for connected_vid in connected_vids:
            # evid connected to both the vid and the fvid (2 vids)
            evids_for_vid = [e + e_vert_offset for e in
                    mesh.edges_for_vert[connected_vid]]
            common_ids = list(set(evids_for_vid) & set(evids_for_current_face))
            assert len(common_ids) == 2
            # then connect the (4) vids together ...
            new_faces.append([fvid, common_ids[0], connected_vid, common_ids[1]])

    return PolygonMesh(vertices=new_vertices, edges=new_edges, faces=new_faces)