refactor laplacian matrices

Summary:
Refactor of all functions to compute laplacian matrices in one file.
Support for:
* Standard Laplacian
* Cotangent Laplacian
* Norm Laplacian

Reviewed By: nikhilaravi

Differential Revision: D29297466

fbshipit-source-id: b96b88915ce8ef0c2f5693ec9b179fd27b70abf9

pytorch3d/structures/meshes.py

@@ -1142,6 +1142,8 @@ class Meshes:
             Sparse FloatTensor of shape (V, V) where V = sum(V_n)
 
         """
+        from ..ops import laplacian
+
         if not (refresh or self._laplacian_packed is None):
             return
 
@@ -1153,39 +1155,8 @@ class Meshes:
 
         verts_packed = self.verts_packed()  # (sum(V_n), 3)
         edges_packed = self.edges_packed()  # (sum(E_n), 3)
-        V = verts_packed.shape[0]  # sum(V_n)
 
-        e0, e1 = edges_packed.unbind(1)
-
-        idx01 = torch.stack([e0, e1], dim=1)  # (sum(E_n), 2)
-        idx10 = torch.stack([e1, e0], dim=1)  # (sum(E_n), 2)
-        idx = torch.cat([idx01, idx10], dim=0).t()  # (2, 2*sum(E_n))
-
-        # First, we construct the adjacency matrix,
-        # i.e. A[i, j] = 1 if (i,j) is an edge, or
-        # A[e0, e1] = 1 &  A[e1, e0] = 1
-        ones = torch.ones(idx.shape[1], dtype=torch.float32, device=self.device)
-        A = torch.sparse.FloatTensor(idx, ones, (V, V))
-
-        # the sum of i-th row of A gives the degree of the i-th vertex
-        deg = torch.sparse.sum(A, dim=1).to_dense()
-
-        # We construct the Laplacian matrix by adding the non diagonal values
-        # i.e. L[i, j] = 1 ./ deg(i) if (i, j) is an edge
-        deg0 = deg[e0]
-        deg0 = torch.where(deg0 > 0.0, 1.0 / deg0, deg0)
-        deg1 = deg[e1]
-        deg1 = torch.where(deg1 > 0.0, 1.0 / deg1, deg1)
-        val = torch.cat([deg0, deg1])
-        L = torch.sparse.FloatTensor(idx, val, (V, V))
-
-        # Then we add the diagonal values L[i, i] = -1.
-        idx = torch.arange(V, device=self.device)
-        idx = torch.stack([idx, idx], dim=0)
-        ones = torch.ones(idx.shape[1], dtype=torch.float32, device=self.device)
-        L -= torch.sparse.FloatTensor(idx, ones, (V, V))
-
-        self._laplacian_packed = L
+        self._laplacian_packed = laplacian(verts_packed, edges_packed)
 
     def clone(self):
         """