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