Spaces:
Running
Running
File size: 3,879 Bytes
7088d16 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 |
# Copyright (c) Meta Platforms, Inc. and 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 pytorch3d.ops import cot_laplacian, laplacian, norm_laplacian
from pytorch3d.structures.meshes import Meshes
from .common_testing import get_random_cuda_device, TestCaseMixin
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 = verts.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)
|