test_sample_points_from_meshes.py

#!/usr/bin/env python3
# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.


import unittest
from pathlib import Path
import torch

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


class TestSamplePoints(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.assertTrue(
            torch.allclose(samples[0, :], torch.zeros((1, num_samples, 3)))
        )
        self.assertTrue(
            torch.allclose(normals[0, :], torch.zeros((1, 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.assertTrue(torch.allclose(radius, torch.ones((num_samples))))

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

        self.assertTrue(
            torch.allclose(
                pyramid_verts.lt(1).float(), torch.ones_like(pyramid_verts)
            )
        )
        self.assertTrue(
            torch.allclose(
                (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.assertTrue(
            torch.allclose(
                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.assertTrue(
            torch.allclose(
                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.assertTrue(
            torch.allclose(
                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.assertTrue(
            torch.allclose(
                face_4_verts.sum(1), torch.ones(face_4_verts.size(0))
            )
        )
        self.assertTrue(
            torch.allclose(
                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_mutinomial(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

    @staticmethod
    def face_areas(verts, faces):
        """
        Vectorized PyTorch implementation of triangle face area function.
        """
        verts_faces = verts[faces]
        v0x = verts_faces[:, 0::3, 0]
        v0y = verts_faces[:, 0::3, 1]
        v0z = verts_faces[:, 0::3, 2]

        v1x = verts_faces[:, 1::3, 0]
        v1y = verts_faces[:, 1::3, 1]
        v1z = verts_faces[:, 1::3, 2]

        v2x = verts_faces[:, 2::3, 0]
        v2y = verts_faces[:, 2::3, 1]
        v2z = verts_faces[:, 2::3, 2]

        ax = v0x - v2x
        ay = v0y - v2y
        az = v0z - v2z

        bx = v1x - v2x
        by = v1y - v2y
        bz = v1z - v2z

        cx = ay * bz - az * by
        cy = az * bx - ax * bz
        cz = ax * by - ay * bx

        # this gives the area of the parallelogram with sides a and b
        area_sqr = cx * cx + cy * cy + cz * cz
        # the area of the triangle is half
        return torch.sqrt(area_sqr) / 2.0

    def test_face_areas(self):
        """
        Check the results from face_areas cuda and PyTorch implementions are
        the same. Check that face_areas throws an error if cpu tensors are
        given as input.
        """
        meshes = self.init_meshes(10, 1000, 3000, device="cuda:0")
        verts = meshes.verts_packed()
        faces = meshes.faces_packed()

        areas_torch = self.face_areas(verts, faces).squeeze()
        areas_cuda, _ = _C.face_areas_normals(verts, faces)
        self.assertTrue(torch.allclose(areas_torch, areas_cuda, atol=5e-8))
        with self.assertRaises(Exception) as err:
            _C.face_areas_normals(verts.cpu(), faces.cpu())
        self.assertTrue("Not implemented on the CPU" in str(err.exception))

    @staticmethod
    def packed_to_padded_tensor(inputs, first_idxs, max_size):
        """
        PyTorch implementation of cuda packed_to_padded_tensor function.
        """
        num_meshes = first_idxs.size(0)
        inputs_padded = torch.zeros((num_meshes, max_size))
        for m in range(num_meshes):
            s = first_idxs[m]
            if m == num_meshes - 1:
                f = inputs.size(0)
            else:
                f = first_idxs[m + 1]
            inputs_padded[m, :f] = inputs[s:f]

        return inputs_padded

    def test_packed_to_padded_tensor(self):
        """
        Check the results from packed_to_padded cuda and PyTorch implementions
        are the same.
        """
        meshes = self.init_meshes(1, 3, 5, device="cuda:0")
        verts = meshes.verts_packed()
        faces = meshes.faces_packed()
        mesh_to_faces_packed_first_idx = meshes.mesh_to_faces_packed_first_idx()
        max_faces = meshes.num_faces_per_mesh().max().item()

        areas, _ = _C.face_areas_normals(verts, faces)
        areas_padded = _C.packed_to_padded_tensor(
            areas, mesh_to_faces_packed_first_idx, max_faces
        ).cpu()
        areas_padded_cpu = TestSamplePoints.packed_to_padded_tensor(
            areas, mesh_to_faces_packed_first_idx, max_faces
        )
        self.assertTrue(torch.allclose(areas_padded, areas_padded_cpu))
        with self.assertRaises(Exception) as err:
            _C.packed_to_padded_tensor(
                areas.cpu(), mesh_to_faces_packed_first_idx, max_faces
            )
        self.assertTrue("Not implemented on the CPU" in str(err.exception))

    @staticmethod
    def sample_points_with_init(
        num_meshes: int,
        num_verts: int,
        num_faces: int,
        num_samples: int,
        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)
        torch.cuda.synchronize()

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

        return sample_points

    @staticmethod
    def face_areas_with_init(
        num_meshes: int, num_verts: int, num_faces: int, cuda: str = True
    ):
        device = "cuda" if cuda else "cpu"
        meshes = TestSamplePoints.init_meshes(
            num_meshes, num_verts, num_faces, device
        )
        verts = meshes.verts_packed()
        faces = meshes.faces_packed()
        torch.cuda.synchronize()

        def face_areas():
            if cuda:
                _C.face_areas_normals(verts, faces)
            else:
                TestSamplePoints.face_areas(verts, faces)
            torch.cuda.synchronize()

        return face_areas

    @staticmethod
    def packed_to_padded_with_init(
        num_meshes: int, num_verts: int, num_faces: int, cuda: str = True
    ):
        device = "cuda" if cuda else "cpu"
        meshes = TestSamplePoints.init_meshes(
            num_meshes, num_verts, num_faces, device
        )
        verts = meshes.verts_packed()
        faces = meshes.faces_packed()
        mesh_to_faces_packed_first_idx = meshes.mesh_to_faces_packed_first_idx()
        max_faces = meshes.num_faces_per_mesh().max().item()

        if cuda:
            areas, _ = _C.face_areas_normals(verts, faces)
        else:
            areas = TestSamplePoints.face_areas(verts, faces)
        torch.cuda.synchronize()

        def packed_to_padded():
            if cuda:
                _C.packed_to_padded_tensor(
                    areas, mesh_to_faces_packed_first_idx, max_faces
                )
            else:
                TestSamplePoints.packed_to_padded_tensor(
                    areas, mesh_to_faces_packed_first_idx, max_faces
                )
            torch.cuda.synchronize()

        return packed_to_padded