test_sample_points_from_meshes.py

# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.


import unittest
from pathlib import Path
import torch

from pytorch3d.ops import sample_points_from_meshes
from pytorch3d.structures.meshes import Meshes
from pytorch3d.utils.ico_sphere import ico_sphere

from common_testing import TestCaseMixin


class TestSamplePoints(TestCaseMixin, unittest.TestCase):
    def setUp(self) -> None:
        super().setUp()
        torch.manual_seed(1)

    @staticmethod
    def init_meshes(
        num_meshes: int = 10,
        num_verts: int = 1000,
        num_faces: int = 3000,
        device: str = "cpu",
    ):
        device = torch.device(device)
        verts_list = []
        faces_list = []
        for _ in range(num_meshes):
            verts = torch.rand(
                (num_verts, 3), dtype=torch.float32, device=device
            )
            faces = torch.randint(
                num_verts, size=(num_faces, 3), dtype=torch.int64, device=device
            )
            verts_list.append(verts)
            faces_list.append(faces)
        meshes = Meshes(verts_list, faces_list)

        return meshes

    def test_all_empty_meshes(self):
        """
        Check sample_points_from_meshes raises an exception if all meshes are
        invalid.
        """
        device = torch.device("cuda:0")
        verts1 = torch.tensor([], dtype=torch.float32, device=device)
        faces1 = torch.tensor([], dtype=torch.int64, device=device)
        meshes = Meshes(
            verts=[verts1, verts1, verts1], faces=[faces1, faces1, faces1]
        )
        with self.assertRaises(ValueError) as err:
            sample_points_from_meshes(
                meshes, num_samples=100, return_normals=True
            )
        self.assertTrue("Meshes are empty." in str(err.exception))

    def test_sampling_output(self):
        """
        Check outputs of sampling are correct for different meshes.
        For an ico_sphere, the sampled vertices should lie on a unit sphere.
        For an empty mesh, the samples and normals should be 0.
        """
        device = torch.device("cuda:0")

        # Unit simplex.
        verts_pyramid = torch.tensor(
            [
                [0.0, 0.0, 0.0],
                [1.0, 0.0, 0.0],
                [0.0, 1.0, 0.0],
                [0.0, 0.0, 1.0],
            ],
            dtype=torch.float32,
            device=device,
        )
        faces_pyramid = torch.tensor(
            [[0, 1, 2], [0, 2, 3], [0, 1, 3], [1, 2, 3]],
            dtype=torch.int64,
            device=device,
        )
        sphere_mesh = ico_sphere(9, device)
        verts_sphere, faces_sphere = sphere_mesh.get_mesh_verts_faces(0)
        verts_empty = torch.tensor([], dtype=torch.float32, device=device)
        faces_empty = torch.tensor([], dtype=torch.int64, device=device)
        num_samples = 10
        meshes = Meshes(
            verts=[verts_empty, verts_sphere, verts_pyramid],
            faces=[faces_empty, faces_sphere, faces_pyramid],
        )
        samples, normals = sample_points_from_meshes(
            meshes, num_samples=num_samples, return_normals=True
        )
        samples = samples.cpu()
        normals = normals.cpu()

        self.assertEqual(samples.shape, (3, num_samples, 3))
        self.assertEqual(normals.shape, (3, num_samples, 3))

        # Empty meshes: should have all zeros for samples and normals.
        self.assertClose(samples[0, :], torch.zeros((num_samples, 3)))
        self.assertClose(normals[0, :], torch.zeros((num_samples, 3)))

        # Sphere: points should have radius 1.
        x, y, z = samples[1, :].unbind(1)
        radius = torch.sqrt(x ** 2 + y ** 2 + z ** 2)

        self.assertClose(radius, torch.ones((num_samples)))

        # Pyramid: points shoudl lie on one of the faces.
        pyramid_verts = samples[2, :]
        pyramid_normals = normals[2, :]

        self.assertClose(
            pyramid_verts.lt(1).float(), torch.ones_like(pyramid_verts)
        )
        self.assertClose(
            (pyramid_verts >= 0).float(), torch.ones_like(pyramid_verts)
        )

        # Face 1: z = 0,  x + y <= 1, normals = (0, 0, 1).
        face_1_idxs = pyramid_verts[:, 2] == 0
        face_1_verts, face_1_normals = (
            pyramid_verts[face_1_idxs, :],
            pyramid_normals[face_1_idxs, :],
        )
        self.assertTrue(
            torch.all((face_1_verts[:, 0] + face_1_verts[:, 1]) <= 1)
        )
        self.assertClose(
            face_1_normals,
            torch.tensor([0, 0, 1], dtype=torch.float32).expand(
                face_1_normals.size()
            ),
        )

        # Face 2: x = 0,  z + y <= 1, normals = (1, 0, 0).
        face_2_idxs = pyramid_verts[:, 0] == 0
        face_2_verts, face_2_normals = (
            pyramid_verts[face_2_idxs, :],
            pyramid_normals[face_2_idxs, :],
        )
        self.assertTrue(
            torch.all((face_2_verts[:, 1] + face_2_verts[:, 2]) <= 1)
        )
        self.assertClose(
            face_2_normals,
            torch.tensor([1, 0, 0], dtype=torch.float32).expand(
                face_2_normals.size()
            ),
        )

        # Face 3: y = 0, x + z <= 1, normals = (0, -1, 0).
        face_3_idxs = pyramid_verts[:, 1] == 0
        face_3_verts, face_3_normals = (
            pyramid_verts[face_3_idxs, :],
            pyramid_normals[face_3_idxs, :],
        )
        self.assertTrue(
            torch.all((face_3_verts[:, 0] + face_3_verts[:, 2]) <= 1)
        )
        self.assertClose(
            face_3_normals,
            torch.tensor([0, -1, 0], dtype=torch.float32).expand(
                face_3_normals.size()
            ),
        )

        # Face 4: x + y + z = 1, normals = (1, 1, 1)/sqrt(3).
        face_4_idxs = pyramid_verts.gt(0).all(1)
        face_4_verts, face_4_normals = (
            pyramid_verts[face_4_idxs, :],
            pyramid_normals[face_4_idxs, :],
        )
        self.assertClose(face_4_verts.sum(1), torch.ones(face_4_verts.size(0)))
        self.assertClose(
            face_4_normals,
            (
                torch.tensor([1, 1, 1], dtype=torch.float32)
                / torch.sqrt(torch.tensor(3, dtype=torch.float32))
            ).expand(face_4_normals.size()),
        )

    def test_multinomial(self):
        """
        Confirm that torch.multinomial does not sample elements which have
        zero probability.
        """
        freqs = torch.cuda.FloatTensor(
            [
                0.0,
                0.0,
                0.0,
                0.0,
                0.0,
                0.0,
                0.0,
                0.0,
                0.0,
                0.03178183361887932,
                0.027680952101945877,
                0.033176131546497345,
                0.046052902936935425,
                0.07742464542388916,
                0.11543981730937958,
                0.14148041605949402,
                0.15784293413162231,
                0.13180233538150787,
                0.08271478116512299,
                0.049702685326337814,
                0.027557924389839172,
                0.018125897273421288,
                0.011851548217236996,
                0.010252203792333603,
                0.007422595750540495,
                0.005372154992073774,
                0.0045109698548913,
                0.0036087757907807827,
                0.0035267581697553396,
                0.0018864056328311563,
                0.0024605290964245796,
                0.0022964938543736935,
                0.0018453967059031129,
                0.0010662291897460818,
                0.0009842115687206388,
                0.00045109697384759784,
                0.0007791675161570311,
                0.00020504408166743815,
                0.00020504408166743815,
                0.00020504408166743815,
                0.00012302644609007984,
                0.0,
                0.00012302644609007984,
                4.100881778867915e-05,
                0.0,
                0.0,
                0.0,
                0.0,
                0.0,
                0.0,
            ]
        )

        sample = []
        for _ in range(1000):
            torch.cuda.get_rng_state()
            sample = torch.multinomial(freqs, 1000, True)
            if freqs[sample].min() == 0:
                sample_idx = (freqs[sample] == 0).nonzero()[0][0]
                sampled = sample[sample_idx]
                print(
                    "%s th element of last sample was %s, which has probability %s"
                    % (sample_idx, sampled, freqs[sampled])
                )
                return False
        return True

    def test_multinomial_weights(self):
        """
        Confirm that torch.multinomial does not sample elements which have
        zero probability using a real example of input from a training run.
        """
        weights = torch.load(Path(__file__).resolve().parent / "weights.pt")
        S = 4096
        num_trials = 100
        for _ in range(0, num_trials):
            weights[weights < 0] = 0.0
            samples = weights.multinomial(S, replacement=True)
            sampled_weights = weights[samples]
            assert sampled_weights.min() > 0
            if sampled_weights.min() <= 0:
                return False
        return True

    def test_verts_nan(self):
        num_verts = 30
        num_faces = 50
        for device in ["cpu", "cuda:0"]:
            for invalid in ["nan", "inf"]:
                verts = torch.rand(
                    (num_verts, 3), dtype=torch.float32, device=device
                )
                # randomly assign an invalid type
                verts[torch.randperm(num_verts)[:10]] = float(invalid)
                faces = torch.randint(
                    num_verts,
                    size=(num_faces, 3),
                    dtype=torch.int64,
                    device=device,
                )
                meshes = Meshes(verts=[verts], faces=[faces])

                with self.assertRaisesRegex(
                    ValueError, "Meshes contain nan or inf."
                ):
                    sample_points_from_meshes(
                        meshes, num_samples=100, return_normals=True
                    )

    @staticmethod
    def sample_points_with_init(
        num_meshes: int,
        num_verts: int,
        num_faces: int,
        num_samples: int,
        device: str = "cpu",
    ):
        verts_list = []
        faces_list = []
        for _ in range(num_meshes):
            verts = torch.rand(
                (num_verts, 3), dtype=torch.float32, device=device
            )
            faces = torch.randint(
                num_verts, size=(num_faces, 3), dtype=torch.int64, device=device
            )
            verts_list.append(verts)
            faces_list.append(faces)
        meshes = Meshes(verts_list, faces_list)
        torch.cuda.synchronize()

        def sample_points():
            sample_points_from_meshes(
                meshes, num_samples=num_samples, return_normals=True
            )
            torch.cuda.synchronize()

        return sample_points