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

tests/test_laplacian_matrices.py

@@ -0,0 +1,119 @@
+# Copyright (c) Facebook, Inc. and its affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the BSD-style license found in the
+# LICENSE file in the root directory of this source tree.
+
+import unittest
+
+import torch
+from common_testing import TestCaseMixin, get_random_cuda_device
+from pytorch3d.ops import laplacian, norm_laplacian, cot_laplacian
+from pytorch3d.structures.meshes import Meshes
+
+
+class TestLaplacianMatrices(TestCaseMixin, unittest.TestCase):
+    def setUp(self) -> None:
+        super().setUp()
+        torch.manual_seed(1)
+
+    def init_mesh(self) -> Meshes:
+        V, F = 32, 64
+        device = get_random_cuda_device()
+        # random vertices
+        verts = torch.rand((V, 3), dtype=torch.float32, device=device)
+        # random valid faces (no self circles, e.g. (v0, v0, v1))
+        faces = torch.stack([torch.randperm(V) for f in range(F)], dim=0)[:, :3]
+        faces = faces.to(device=device)
+        return Meshes(verts=[verts], faces=[faces])
+
+    def test_laplacian(self):
+        mesh = self.init_mesh()
+        verts = mesh.verts_packed()
+        edges = mesh.edges_packed()
+        V, E = verts.shape[0], edges.shape[0]
+
+        L = laplacian(verts, edges)
+
+        Lnaive = torch.zeros((V, V), dtype=torch.float32, device=verts.device)
+        for e in range(E):
+            e0, e1 = edges[e]
+            Lnaive[e0, e1] = 1
+            # symetric
+            Lnaive[e1, e0] = 1
+
+        deg = Lnaive.sum(1).view(-1, 1)
+        deg[deg > 0] = 1.0 / deg[deg > 0]
+        Lnaive = Lnaive * deg
+        diag = torch.eye(V, dtype=torch.float32, device=mesh.device)
+        Lnaive.masked_fill_(diag > 0, -1)
+
+        self.assertClose(L.to_dense(), Lnaive)
+
+    def test_cot_laplacian(self):
+        mesh = self.init_mesh()
+        verts = mesh.verts_packed()
+        faces = mesh.faces_packed()
+        V, F = verts.shape[0], faces.shape[0]
+
+        eps = 1e-12
+
+        L, inv_areas = cot_laplacian(verts, faces, eps=eps)
+
+        Lnaive = torch.zeros((V, V), dtype=torch.float32, device=verts.device)
+        inv_areas_naive = torch.zeros((V, 1), dtype=torch.float32, device=verts.device)
+
+        for f in faces:
+            v0 = verts[f[0], :]
+            v1 = verts[f[1], :]
+            v2 = verts[f[2], :]
+            A = (v1 - v2).norm()
+            B = (v0 - v2).norm()
+            C = (v0 - v1).norm()
+            s = 0.5 * (A + B + C)
+
+            face_area = (s * (s - A) * (s - B) * (s - C)).clamp_(min=1e-12).sqrt()
+            inv_areas_naive[f[0]] += face_area
+            inv_areas_naive[f[1]] += face_area
+            inv_areas_naive[f[2]] += face_area
+
+            A2, B2, C2 = A * A, B * B, C * C
+            cota = (B2 + C2 - A2) / face_area / 4.0
+            cotb = (A2 + C2 - B2) / face_area / 4.0
+            cotc = (A2 + B2 - C2) / face_area / 4.0
+
+            Lnaive[f[1], f[2]] += cota
+            Lnaive[f[2], f[0]] += cotb
+            Lnaive[f[0], f[1]] += cotc
+            # symetric
+            Lnaive[f[2], f[1]] += cota
+            Lnaive[f[0], f[2]] += cotb
+            Lnaive[f[1], f[0]] += cotc
+
+        idx = inv_areas_naive > 0
+        inv_areas_naive[idx] = 1.0 / inv_areas_naive[idx]
+
+        self.assertClose(inv_areas, inv_areas_naive)
+        self.assertClose(L.to_dense(), Lnaive)
+
+    def test_norm_laplacian(self):
+        mesh = self.init_mesh()
+        verts = mesh.verts_packed()
+        edges = mesh.edges_packed()
+        V, E = verts.shape[0], edges.shape[0]
+
+        eps = 1e-12
+
+        L = norm_laplacian(verts, edges, eps=eps)
+
+        Lnaive = torch.zeros((V, V), dtype=torch.float32, device=verts.device)
+        for e in range(E):
+            e0, e1 = edges[e]
+            v0 = verts[e0]
+            v1 = verts[e1]
+
+            w01 = 1.0 / ((v0 - v1).norm() + eps)
+            Lnaive[e0, e1] += w01
+            Lnaive[e1, e0] += w01
+
+        self.assertClose(L.to_dense(), Lnaive)