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25a49bc | 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 | # Copyright 2023 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Authors: kmaninis@google.com (Kevis-Kokitsi Maninis), spopov@google.com (Stefan Popov)
"""Mesh utils."""
import torch as t
import torch.nn.functional as F
def sample_points_from_mesh(mesh: t.tensor, num_sample_points: int):
"""Samples points on a mesh, uniformly distributed over the surface area."""
surface_areas = (
t.norm(
t.linalg.cross(mesh[:, 0, :], mesh[:, 1, :])
+ t.linalg.cross(mesh[:, 1, :], mesh[:, 2, :])
+ t.linalg.cross(mesh[:, 2, :], mesh[:, 0, :]),
dim=-1) / 2.)
cdf = F.pad(t.cumsum(surface_areas, dim=-1), (1, 0))
cdf = cdf / cdf[-1]
rv = t.rand([num_sample_points])
triangle_index = t.searchsorted(cdf, rv, side="right") - 1
assert (
triangle_index.min() >= 0
and triangle_index.max() < mesh.shape[0]
)
sampled_tri = mesh[triangle_index, ...]
r1, r2 = t.unbind(t.rand([num_sample_points, 2]), dim=-1)
r1 = t.sqrt(r1)
u = 1 - r1
v = (1 - r2) * r1
w = r2 * r1
sampled_pts = (
sampled_tri[:, 0] * u[:, None]
+ sampled_tri[:, 1] * v[:, None]
+ sampled_tri[:, 2] * w[:, None])
return sampled_pts, triangle_index
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