pytorch3d/tests/test_meshes.py

# 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 itertools
import random
import unittest

import numpy as np
import torch
from common_testing import TestCaseMixin
from pytorch3d.structures.meshes import Meshes


def init_mesh(
    num_meshes: int = 10,
    max_v: int = 100,
    max_f: int = 300,
    lists_to_tensors: bool = False,
    device: str = "cpu",
    requires_grad: bool = False,
):
    """
    Function to generate a Meshes object of N meshes with
    random numbers of vertices and faces.

    Args:
        num_meshes: Number of meshes to generate.
        max_v: Max number of vertices per mesh.
        max_f: Max number of faces per mesh.
        lists_to_tensors: Determines whether the generated meshes should be
                            constructed from lists (=False) or
                            a tensor (=True) of faces/verts.

    Returns:
        Meshes object.
    """
    device = torch.device(device)

    verts_list = []
    faces_list = []

    # Randomly generate numbers of faces and vertices in each mesh.
    if lists_to_tensors:
        # If we define faces/verts with tensors, f/v has to be the
        # same for each mesh in the batch.
        f = torch.randint(1, max_f, size=(1,), dtype=torch.int32)
        v = torch.randint(3, high=max_v, size=(1,), dtype=torch.int32)
        f = f.repeat(num_meshes)
        v = v.repeat(num_meshes)
    else:
        # For lists of faces and vertices, we can sample different v/f
        # per mesh.
        f = torch.randint(max_f, size=(num_meshes,), dtype=torch.int32)
        v = torch.randint(3, high=max_v, size=(num_meshes,), dtype=torch.int32)

    # Generate the actual vertices and faces.
    for i in range(num_meshes):
        verts = torch.rand(
            (v[i], 3),
            dtype=torch.float32,
            device=device,
            requires_grad=requires_grad,
        )
        faces = torch.randint(v[i], size=(f[i], 3), dtype=torch.int64, device=device)
        verts_list.append(verts)
        faces_list.append(faces)

    if lists_to_tensors:
        verts_list = torch.stack(verts_list)
        faces_list = torch.stack(faces_list)

    return Meshes(verts=verts_list, faces=faces_list)


def init_simple_mesh(device: str = "cpu"):
    """
    Returns a Meshes data structure of simple mesh examples.

    Returns:
        Meshes object.
    """
    device = torch.device(device)

    verts = [
        torch.tensor(
            [[0.1, 0.3, 0.5], [0.5, 0.2, 0.1], [0.6, 0.8, 0.7]],
            dtype=torch.float32,
            device=device,
        ),
        torch.tensor(
            [[0.1, 0.3, 0.3], [0.6, 0.7, 0.8], [0.2, 0.3, 0.4], [0.1, 0.5, 0.3]],
            dtype=torch.float32,
            device=device,
        ),
        torch.tensor(
            [
                [0.7, 0.3, 0.6],
                [0.2, 0.4, 0.8],
                [0.9, 0.5, 0.2],
                [0.2, 0.3, 0.4],
                [0.9, 0.3, 0.8],
            ],
            dtype=torch.float32,
            device=device,
        ),
    ]
    faces = [
        torch.tensor([[0, 1, 2]], dtype=torch.int64, device=device),
        torch.tensor([[0, 1, 2], [1, 2, 3]], dtype=torch.int64, device=device),
        torch.tensor(
            [
                [1, 2, 0],
                [0, 1, 3],
                [2, 3, 1],
                [4, 3, 2],
                [4, 0, 1],
                [4, 3, 1],
                [4, 2, 1],
            ],
            dtype=torch.int64,
            device=device,
        ),
    ]
    return Meshes(verts=verts, faces=faces)


def mesh_structures_equal(mesh1, mesh2) -> bool:
    """
    Two meshes are equal if they have identical verts_list and faces_list.

    Use to_sorted() before passing into this function to obtain meshes invariant to
    vertex permutations. Note that this operator treats two geometrically identical
    meshes as different if their vertices are in different coordinate frames.
    """
    if mesh1.__class__ != mesh1.__class__:
        return False

    if mesh1.textures is not None or mesh2.textures is not None:
        raise NotImplementedError(
            "mesh equality is not implemented for textured meshes."
        )

    if len(mesh1.verts_list()) != len(mesh2.verts_list()) or not all(
        torch.equal(verts_mesh1, verts_mesh2)
        for (verts_mesh1, verts_mesh2) in zip(mesh1.verts_list(), mesh2.verts_list())
    ):
        return False

    if len(mesh1.faces_list()) != len(mesh2.faces_list()) or not all(
        torch.equal(faces_mesh1, faces_mesh2)
        for (faces_mesh1, faces_mesh2) in zip(mesh1.faces_list(), mesh2.faces_list())
    ):
        return False

    if len(mesh1.verts_normals_list()) != len(mesh2.verts_normals_list()) or not all(
        torch.equal(normals_mesh1, normals_mesh2)
        for (normals_mesh1, normals_mesh2) in zip(
            mesh1.verts_normals_list(), mesh2.verts_normals_list()
        )
    ):
        return False

    return True


def to_sorted(mesh: Meshes) -> "Meshes":
    """
    Create a new Meshes object, where each sub-mesh's vertices are sorted
    alphabetically.

    Returns:
        A Meshes object with the same topology as this mesh, with vertices sorted
        alphabetically.

    Example:

    For a mesh with verts [[2.3, .2, .4], [.0, .1, .2], [.0, .0, .1]] and a single
    face [[0, 1, 2]], to_sorted will create a new mesh with verts [[.0, .0, .1],
    [.0, .1, .2], [2.3, .2, .4]] and a single face [[2, 1, 0]]. This is useful to
    create a semi-canonical representation of the mesh that is invariant to vertex
    permutations, but not invariant to coordinate frame changes.
    """
    if mesh.textures is not None:
        raise NotImplementedError(
            "to_sorted is not implemented for meshes with "
            f"{type(mesh.textures).__name__} textures."
        )

    verts_list = mesh.verts_list()
    faces_list = mesh.faces_list()
    verts_sorted_list = []
    faces_sorted_list = []

    for verts, faces in zip(verts_list, faces_list):
        # Argsort the vertices alphabetically: sort_ids[k] corresponds to the id of
        # the vertex in the non-sorted mesh that should sit at index k in the sorted mesh.
        sort_ids = torch.tensor(
            [
                idx_and_val[0]
                for idx_and_val in sorted(
                    enumerate(verts.tolist()),
                    key=lambda idx_and_val: idx_and_val[1],
                )
            ],
            device=mesh.device,
        )

        # Resort the vertices. index_select allocates new memory.
        verts_sorted = verts[sort_ids]
        verts_sorted_list.append(verts_sorted)

        # The `faces` tensor contains vertex ids. Substitute old vertex ids for the
        # new ones. new_vertex_ids is the inverse of sort_ids: new_vertex_ids[k]
        # corresponds to the id of the vertex in the sorted mesh that is the same as
        # vertex k in the non-sorted mesh.
        new_vertex_ids = torch.argsort(sort_ids)
        faces_sorted = (
            torch.gather(new_vertex_ids, 0, faces.flatten())
            .reshape(faces.shape)
            .clone()
        )
        faces_sorted_list.append(faces_sorted)

    other = mesh.__class__(verts=verts_sorted_list, faces=faces_sorted_list)
    for k in mesh._INTERNAL_TENSORS:
        v = getattr(mesh, k)
        if torch.is_tensor(v):
            setattr(other, k, v.clone())

    return other


class TestMeshes(TestCaseMixin, unittest.TestCase):
    def setUp(self) -> None:
        np.random.seed(42)
        torch.manual_seed(42)

    def test_simple(self):
        mesh = init_simple_mesh("cuda:0")

        # Check that faces/verts per mesh are set in init:
        self.assertClose(mesh._num_faces_per_mesh.cpu(), torch.tensor([1, 2, 7]))
        self.assertClose(mesh._num_verts_per_mesh.cpu(), torch.tensor([3, 4, 5]))

        # Check computed tensors
        self.assertClose(
            mesh.verts_packed_to_mesh_idx().cpu(),
            torch.tensor([0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2]),
        )
        self.assertClose(
            mesh.mesh_to_verts_packed_first_idx().cpu(), torch.tensor([0, 3, 7])
        )
        self.assertClose(
            mesh.verts_padded_to_packed_idx().cpu(),
            torch.tensor([0, 1, 2, 5, 6, 7, 8, 10, 11, 12, 13, 14]),
        )
        self.assertClose(
            mesh.faces_packed_to_mesh_idx().cpu(),
            torch.tensor([0, 1, 1, 2, 2, 2, 2, 2, 2, 2]),
        )
        self.assertClose(
            mesh.mesh_to_faces_packed_first_idx().cpu(), torch.tensor([0, 1, 3])
        )
        self.assertClose(
            mesh.num_edges_per_mesh().cpu(), torch.tensor([3, 5, 10], dtype=torch.int32)
        )
        self.assertClose(
            mesh.mesh_to_edges_packed_first_idx().cpu(),
            torch.tensor([0, 3, 8], dtype=torch.int64),
        )

    def test_init_error(self):
        # Check if correct errors are raised when verts/faces are on
        # different devices

        mesh = init_mesh(10, 10, 100)
        verts_list = mesh.verts_list()  # all tensors on cpu
        verts_list = [
            v.to("cuda:0") if random.uniform(0, 1) > 0.5 else v for v in verts_list
        ]
        faces_list = mesh.faces_list()

        with self.assertRaises(ValueError) as cm:
            Meshes(verts=verts_list, faces=faces_list)
            self.assertTrue("same device" in cm.msg)

        verts_padded = mesh.verts_padded()  # on cpu
        verts_padded = verts_padded.to("cuda:0")
        faces_padded = mesh.faces_padded()

        with self.assertRaises(ValueError) as cm:
            Meshes(verts=verts_padded, faces=faces_padded)
            self.assertTrue("same device" in cm.msg)

    def test_simple_random_meshes(self):

        # Define the test mesh object either as a list or tensor of faces/verts.
        for lists_to_tensors in (False, True):
            N = 10
            mesh = init_mesh(N, 100, 300, lists_to_tensors=lists_to_tensors)
            verts_list = mesh.verts_list()
            faces_list = mesh.faces_list()

            # Check batch calculations.
            verts_padded = mesh.verts_padded()
            faces_padded = mesh.faces_padded()
            verts_per_mesh = mesh.num_verts_per_mesh()
            faces_per_mesh = mesh.num_faces_per_mesh()
            for n in range(N):
                v = verts_list[n].shape[0]
                f = faces_list[n].shape[0]
                self.assertClose(verts_padded[n, :v, :], verts_list[n])
                if verts_padded.shape[1] > v:
                    self.assertTrue(verts_padded[n, v:, :].eq(0).all())
                self.assertClose(faces_padded[n, :f, :], faces_list[n])
                if faces_padded.shape[1] > f:
                    self.assertTrue(faces_padded[n, f:, :].eq(-1).all())
                self.assertEqual(verts_per_mesh[n], v)
                self.assertEqual(faces_per_mesh[n], f)

            # Check compute packed.
            verts_packed = mesh.verts_packed()
            vert_to_mesh = mesh.verts_packed_to_mesh_idx()
            mesh_to_vert = mesh.mesh_to_verts_packed_first_idx()
            faces_packed = mesh.faces_packed()
            face_to_mesh = mesh.faces_packed_to_mesh_idx()
            mesh_to_face = mesh.mesh_to_faces_packed_first_idx()

            curv, curf = 0, 0
            for n in range(N):
                v = verts_list[n].shape[0]
                f = faces_list[n].shape[0]
                self.assertClose(verts_packed[curv : curv + v, :], verts_list[n])
                self.assertClose(faces_packed[curf : curf + f, :] - curv, faces_list[n])
                self.assertTrue(vert_to_mesh[curv : curv + v].eq(n).all())
                self.assertTrue(face_to_mesh[curf : curf + f].eq(n).all())
                self.assertTrue(mesh_to_vert[n] == curv)
                self.assertTrue(mesh_to_face[n] == curf)
                curv += v
                curf += f

            # Check compute edges and compare with numpy unique.
            edges = mesh.edges_packed().cpu().numpy()
            edge_to_mesh_idx = mesh.edges_packed_to_mesh_idx().cpu().numpy()
            num_edges_per_mesh = mesh.num_edges_per_mesh().cpu().numpy()

            npfaces_packed = mesh.faces_packed().cpu().numpy()
            e01 = npfaces_packed[:, [0, 1]]
            e12 = npfaces_packed[:, [1, 2]]
            e20 = npfaces_packed[:, [2, 0]]
            npedges = np.concatenate((e12, e20, e01), axis=0)
            npedges = np.sort(npedges, axis=1)

            unique_edges, unique_idx = np.unique(npedges, return_index=True, axis=0)
            self.assertTrue(np.allclose(edges, unique_edges))
            temp = face_to_mesh.cpu().numpy()
            temp = np.concatenate((temp, temp, temp), axis=0)
            edge_to_mesh = temp[unique_idx]
            self.assertTrue(np.allclose(edge_to_mesh_idx, edge_to_mesh))
            num_edges = np.bincount(edge_to_mesh, minlength=N)
            self.assertTrue(np.allclose(num_edges_per_mesh, num_edges))
            mesh_to_edges_packed_first_idx = (
                mesh.mesh_to_edges_packed_first_idx().cpu().numpy()
            )
            self.assertTrue(
                np.allclose(mesh_to_edges_packed_first_idx[1:], num_edges.cumsum()[:-1])
            )
            self.assertTrue(mesh_to_edges_packed_first_idx[0] == 0)

    def test_allempty(self):
        mesh = Meshes(verts=[], faces=[])
        self.assertEqual(len(mesh), 0)
        self.assertEqual(mesh.verts_padded().shape[0], 0)
        self.assertEqual(mesh.faces_padded().shape[0], 0)
        self.assertEqual(mesh.verts_packed().shape[0], 0)
        self.assertEqual(mesh.faces_packed().shape[0], 0)
        self.assertEqual(mesh.num_faces_per_mesh().shape[0], 0)
        self.assertEqual(mesh.num_verts_per_mesh().shape[0], 0)

    def test_empty(self):
        N, V, F = 10, 100, 300
        device = torch.device("cuda:0")
        verts_list = []
        faces_list = []
        valid = torch.randint(2, size=(N,), dtype=torch.uint8, device=device)
        for n in range(N):
            if valid[n]:
                v = torch.randint(
                    3, high=V, size=(1,), dtype=torch.int32, device=device
                )[0]
                f = torch.randint(F, size=(1,), dtype=torch.int32, device=device)[0]
                verts = torch.rand((v, 3), dtype=torch.float32, device=device)
                faces = torch.randint(v, size=(f, 3), dtype=torch.int64, device=device)
            else:
                verts = torch.tensor([], dtype=torch.float32, device=device)
                faces = torch.tensor([], dtype=torch.int64, device=device)
            verts_list.append(verts)
            faces_list.append(faces)

        mesh = Meshes(verts=verts_list, faces=faces_list)
        verts_padded = mesh.verts_padded()
        faces_padded = mesh.faces_padded()
        verts_per_mesh = mesh.num_verts_per_mesh()
        faces_per_mesh = mesh.num_faces_per_mesh()
        for n in range(N):
            v = len(verts_list[n])
            f = len(faces_list[n])
            if v > 0:
                self.assertClose(verts_padded[n, :v, :], verts_list[n])
                if verts_padded.shape[1] > v:
                    self.assertTrue(verts_padded[n, v:, :].eq(0).all())
            if f > 0:
                self.assertClose(faces_padded[n, :f, :], faces_list[n])
                if faces_padded.shape[1] > f:
                    self.assertTrue(faces_padded[n, f:, :].eq(-1).all())
            self.assertTrue(verts_per_mesh[n] == v)
            self.assertTrue(faces_per_mesh[n] == f)

    def test_padding(self):
        N, V, F = 10, 100, 300
        device = torch.device("cuda:0")
        verts, faces = [], []
        valid = torch.randint(2, size=(N,), dtype=torch.uint8, device=device)
        num_verts, num_faces = (
            torch.zeros(N, dtype=torch.int32),
            torch.zeros(N, dtype=torch.int32),
        )
        for n in range(N):
            verts.append(torch.rand((V, 3), dtype=torch.float32, device=device))
            this_faces = torch.full((F, 3), -1, dtype=torch.int64, device=device)
            if valid[n]:
                v = torch.randint(
                    3, high=V, size=(1,), dtype=torch.int32, device=device
                )[0]
                f = torch.randint(F, size=(1,), dtype=torch.int32, device=device)[0]
                this_faces[:f, :] = torch.randint(
                    v, size=(f, 3), dtype=torch.int64, device=device
                )
                num_verts[n] = v
                num_faces[n] = f
            faces.append(this_faces)

        mesh = Meshes(verts=torch.stack(verts), faces=torch.stack(faces))

        # Check verts/faces per mesh are set correctly in init.
        self.assertListEqual(mesh._num_faces_per_mesh.tolist(), num_faces.tolist())
        self.assertListEqual(mesh._num_verts_per_mesh.tolist(), [V] * N)

        for n, (vv, ff) in enumerate(zip(mesh.verts_list(), mesh.faces_list())):
            self.assertClose(ff, faces[n][: num_faces[n]])
            self.assertClose(vv, verts[n])

        new_faces = [ff.clone() for ff in faces]
        v = torch.randint(3, high=V, size=(1,), dtype=torch.int32, device=device)[0]
        f = torch.randint(F - 10, size=(1,), dtype=torch.int32, device=device)[0]
        this_faces = torch.full((F, 3), -1, dtype=torch.int64, device=device)
        this_faces[10 : f + 10, :] = torch.randint(
            v, size=(f, 3), dtype=torch.int64, device=device
        )
        new_faces[3] = this_faces

        with self.assertRaisesRegex(ValueError, "Padding of faces"):
            Meshes(verts=torch.stack(verts), faces=torch.stack(new_faces))

    def test_clone(self):
        N = 5
        mesh = init_mesh(N, 10, 100)
        for force in [0, 1]:
            if force:
                # force mesh to have computed attributes
                mesh.verts_packed()
                mesh.edges_packed()
                mesh.verts_padded()

            new_mesh = mesh.clone()

            # Modify tensors in both meshes.
            new_mesh._verts_list[0] = new_mesh._verts_list[0] * 5

            # Check cloned and original Meshes objects do not share tensors.
            self.assertFalse(
                torch.allclose(new_mesh._verts_list[0], mesh._verts_list[0])
            )
            self.assertSeparate(new_mesh.verts_packed(), mesh.verts_packed())
            self.assertSeparate(new_mesh.verts_padded(), mesh.verts_padded())
            self.assertSeparate(new_mesh.faces_packed(), mesh.faces_packed())
            self.assertSeparate(new_mesh.faces_padded(), mesh.faces_padded())
            self.assertSeparate(new_mesh.edges_packed(), mesh.edges_packed())

    def test_detach(self):
        N = 5
        mesh = init_mesh(N, 10, 100, requires_grad=True)
        for force in [0, 1]:
            if force:
                # force mesh to have computed attributes
                mesh.verts_packed()
                mesh.edges_packed()
                mesh.verts_padded()

            new_mesh = mesh.detach()

            self.assertFalse(new_mesh.verts_packed().requires_grad)
            self.assertClose(new_mesh.verts_packed(), mesh.verts_packed())
            self.assertFalse(new_mesh.verts_padded().requires_grad)
            self.assertClose(new_mesh.verts_padded(), mesh.verts_padded())
            for v, newv in zip(mesh.verts_list(), new_mesh.verts_list()):
                self.assertFalse(newv.requires_grad)
                self.assertClose(newv, v)

    def test_offset_verts(self):
        def naive_offset_verts(mesh, vert_offsets_packed):
            # new Meshes class
            new_verts_packed = mesh.verts_packed() + vert_offsets_packed
            new_verts_list = list(
                new_verts_packed.split(mesh.num_verts_per_mesh().tolist(), 0)
            )
            new_faces_list = [f.clone() for f in mesh.faces_list()]
            return Meshes(verts=new_verts_list, faces=new_faces_list)

        N = 5
        mesh = init_mesh(N, 30, 100, lists_to_tensors=True)
        all_v = mesh.verts_packed().size(0)
        verts_per_mesh = mesh.num_verts_per_mesh()
        for force, deform_shape in itertools.product([False, True], [(all_v, 3), 3]):
            if force:
                # force mesh to have computed attributes
                mesh._compute_packed(refresh=True)
                mesh._compute_padded()
                mesh._compute_edges_packed()
                mesh.verts_padded_to_packed_idx()
                mesh._compute_face_areas_normals(refresh=True)
                mesh._compute_vertex_normals(refresh=True)

            deform = torch.rand(deform_shape, dtype=torch.float32, device=mesh.device)
            # new meshes class to hold the deformed mesh
            new_mesh_naive = naive_offset_verts(mesh, deform)

            new_mesh = mesh.offset_verts(deform)

            # check verts_list & faces_list
            verts_cumsum = torch.cumsum(verts_per_mesh, 0).tolist()
            verts_cumsum.insert(0, 0)
            for i in range(N):
                item_offset = (
                    deform
                    if deform.ndim == 1
                    else deform[verts_cumsum[i] : verts_cumsum[i + 1]]
                )
                self.assertClose(
                    new_mesh.verts_list()[i],
                    mesh.verts_list()[i] + item_offset,
                )
                self.assertClose(
                    new_mesh.verts_list()[i], new_mesh_naive.verts_list()[i]
                )
                self.assertClose(mesh.faces_list()[i], new_mesh_naive.faces_list()[i])
                self.assertClose(
                    new_mesh.faces_list()[i], new_mesh_naive.faces_list()[i]
                )

                # check faces and vertex normals
                self.assertClose(
                    new_mesh.verts_normals_list()[i],
                    new_mesh_naive.verts_normals_list()[i],
                    atol=1e-6,
                )
                self.assertClose(
                    new_mesh.faces_normals_list()[i],
                    new_mesh_naive.faces_normals_list()[i],
                    atol=1e-6,
                )

            # check padded & packed
            self.assertClose(new_mesh.faces_padded(), new_mesh_naive.faces_padded())
            self.assertClose(new_mesh.verts_padded(), new_mesh_naive.verts_padded())
            self.assertClose(new_mesh.faces_packed(), new_mesh_naive.faces_packed())
            self.assertClose(new_mesh.verts_packed(), new_mesh_naive.verts_packed())
            self.assertClose(new_mesh.edges_packed(), new_mesh_naive.edges_packed())
            self.assertClose(
                new_mesh.verts_packed_to_mesh_idx(),
                new_mesh_naive.verts_packed_to_mesh_idx(),
            )
            self.assertClose(
                new_mesh.mesh_to_verts_packed_first_idx(),
                new_mesh_naive.mesh_to_verts_packed_first_idx(),
            )
            self.assertClose(
                new_mesh.num_verts_per_mesh(), new_mesh_naive.num_verts_per_mesh()
            )
            self.assertClose(
                new_mesh.faces_packed_to_mesh_idx(),
                new_mesh_naive.faces_packed_to_mesh_idx(),
            )
            self.assertClose(
                new_mesh.mesh_to_faces_packed_first_idx(),
                new_mesh_naive.mesh_to_faces_packed_first_idx(),
            )
            self.assertClose(
                new_mesh.num_faces_per_mesh(), new_mesh_naive.num_faces_per_mesh()
            )
            self.assertClose(
                new_mesh.edges_packed_to_mesh_idx(),
                new_mesh_naive.edges_packed_to_mesh_idx(),
            )
            self.assertClose(
                new_mesh.verts_padded_to_packed_idx(),
                new_mesh_naive.verts_padded_to_packed_idx(),
            )
            self.assertTrue(all(new_mesh.valid == new_mesh_naive.valid))
            self.assertTrue(new_mesh.equisized == new_mesh_naive.equisized)

            # check face areas, normals and vertex normals
            self.assertClose(
                new_mesh.verts_normals_packed(),
                new_mesh_naive.verts_normals_packed(),
                atol=1e-6,
            )
            self.assertClose(
                new_mesh.verts_normals_padded(),
                new_mesh_naive.verts_normals_padded(),
                atol=1e-6,
            )
            self.assertClose(
                new_mesh.faces_normals_packed(),
                new_mesh_naive.faces_normals_packed(),
                atol=1e-6,
            )
            self.assertClose(
                new_mesh.faces_normals_padded(),
                new_mesh_naive.faces_normals_padded(),
                atol=1e-6,
            )
            self.assertClose(
                new_mesh.faces_areas_packed(), new_mesh_naive.faces_areas_packed()
            )
            self.assertClose(
                new_mesh.mesh_to_edges_packed_first_idx(),
                new_mesh_naive.mesh_to_edges_packed_first_idx(),
            )

    def test_scale_verts(self):
        def naive_scale_verts(mesh, scale):
            if not torch.is_tensor(scale):
                scale = torch.ones(len(mesh)).mul_(scale)
            # new Meshes class
            new_verts_list = [
                scale[i] * v.clone() for (i, v) in enumerate(mesh.verts_list())
            ]
            new_faces_list = [f.clone() for f in mesh.faces_list()]
            return Meshes(verts=new_verts_list, faces=new_faces_list)

        N = 5
        for test in ["tensor", "scalar"]:
            for force in (False, True):
                mesh = init_mesh(N, 10, 100, lists_to_tensors=True)
                if force:
                    # force mesh to have computed attributes
                    mesh.verts_packed()
                    mesh.edges_packed()
                    mesh.verts_padded()
                    mesh._compute_face_areas_normals(refresh=True)
                    mesh._compute_vertex_normals(refresh=True)

                if test == "tensor":
                    scales = torch.rand(N)
                elif test == "scalar":
                    scales = torch.rand(1)[0].item()
                new_mesh_naive = naive_scale_verts(mesh, scales)
                new_mesh = mesh.scale_verts(scales)
                for i in range(N):
                    if test == "tensor":
                        self.assertClose(
                            scales[i] * mesh.verts_list()[i], new_mesh.verts_list()[i]
                        )
                    else:
                        self.assertClose(
                            scales * mesh.verts_list()[i], new_mesh.verts_list()[i]
                        )
                    self.assertClose(
                        new_mesh.verts_list()[i], new_mesh_naive.verts_list()[i]
                    )
                    self.assertClose(
                        mesh.faces_list()[i], new_mesh_naive.faces_list()[i]
                    )
                    self.assertClose(
                        new_mesh.faces_list()[i], new_mesh_naive.faces_list()[i]
                    )
                    # check face and vertex normals
                    self.assertClose(
                        new_mesh.verts_normals_list()[i],
                        new_mesh_naive.verts_normals_list()[i],
                    )
                    self.assertClose(
                        new_mesh.faces_normals_list()[i],
                        new_mesh_naive.faces_normals_list()[i],
                    )

                # check padded & packed
                self.assertClose(new_mesh.faces_padded(), new_mesh_naive.faces_padded())
                self.assertClose(new_mesh.verts_padded(), new_mesh_naive.verts_padded())
                self.assertClose(new_mesh.faces_packed(), new_mesh_naive.faces_packed())
                self.assertClose(new_mesh.verts_packed(), new_mesh_naive.verts_packed())
                self.assertClose(new_mesh.edges_packed(), new_mesh_naive.edges_packed())
                self.assertClose(
                    new_mesh.verts_packed_to_mesh_idx(),
                    new_mesh_naive.verts_packed_to_mesh_idx(),
                )
                self.assertClose(
                    new_mesh.mesh_to_verts_packed_first_idx(),
                    new_mesh_naive.mesh_to_verts_packed_first_idx(),
                )
                self.assertClose(
                    new_mesh.num_verts_per_mesh(), new_mesh_naive.num_verts_per_mesh()
                )
                self.assertClose(
                    new_mesh.faces_packed_to_mesh_idx(),
                    new_mesh_naive.faces_packed_to_mesh_idx(),
                )
                self.assertClose(
                    new_mesh.mesh_to_faces_packed_first_idx(),
                    new_mesh_naive.mesh_to_faces_packed_first_idx(),
                )
                self.assertClose(
                    new_mesh.num_faces_per_mesh(), new_mesh_naive.num_faces_per_mesh()
                )
                self.assertClose(
                    new_mesh.edges_packed_to_mesh_idx(),
                    new_mesh_naive.edges_packed_to_mesh_idx(),
                )
                self.assertClose(
                    new_mesh.verts_padded_to_packed_idx(),
                    new_mesh_naive.verts_padded_to_packed_idx(),
                )
                self.assertTrue(all(new_mesh.valid == new_mesh_naive.valid))
                self.assertTrue(new_mesh.equisized == new_mesh_naive.equisized)

                # check face areas, normals and vertex normals
                self.assertClose(
                    new_mesh.verts_normals_packed(),
                    new_mesh_naive.verts_normals_packed(),
                )
                self.assertClose(
                    new_mesh.verts_normals_padded(),
                    new_mesh_naive.verts_normals_padded(),
                )
                self.assertClose(
                    new_mesh.faces_normals_packed(),
                    new_mesh_naive.faces_normals_packed(),
                )
                self.assertClose(
                    new_mesh.faces_normals_padded(),
                    new_mesh_naive.faces_normals_padded(),
                )
                self.assertClose(
                    new_mesh.faces_areas_packed(), new_mesh_naive.faces_areas_packed()
                )
                self.assertClose(
                    new_mesh.mesh_to_edges_packed_first_idx(),
                    new_mesh_naive.mesh_to_edges_packed_first_idx(),
                )

    def test_extend_list(self):
        N = 10
        mesh = init_mesh(5, 10, 100)
        for force in [0, 1]:
            if force:
                # force some computes to happen
                mesh._compute_packed(refresh=True)
                mesh._compute_padded()
                mesh._compute_edges_packed()
                mesh.verts_padded_to_packed_idx()
            new_mesh = mesh.extend(N)
            self.assertEqual(len(mesh) * 10, len(new_mesh))
            for i in range(len(mesh)):
                for n in range(N):
                    self.assertClose(
                        mesh.verts_list()[i], new_mesh.verts_list()[i * N + n]
                    )
                    self.assertClose(
                        mesh.faces_list()[i], new_mesh.faces_list()[i * N + n]
                    )
                    self.assertTrue(mesh.valid[i] == new_mesh.valid[i * N + n])
            self.assertAllSeparate(
                mesh.verts_list()
                + new_mesh.verts_list()
                + mesh.faces_list()
                + new_mesh.faces_list()
            )
            self.assertTrue(new_mesh._verts_packed is None)
            self.assertTrue(new_mesh._faces_packed is None)
            self.assertTrue(new_mesh._verts_padded is None)
            self.assertTrue(new_mesh._faces_padded is None)
            self.assertTrue(new_mesh._edges_packed is None)

        with self.assertRaises(ValueError):
            mesh.extend(N=-1)

    def test_to(self):
        mesh = init_mesh(5, 10, 100)

        cpu_device = torch.device("cpu")

        converted_mesh = mesh.to("cpu")
        self.assertEqual(cpu_device, converted_mesh.device)
        self.assertEqual(cpu_device, mesh.device)
        self.assertIs(mesh, converted_mesh)

        converted_mesh = mesh.to(cpu_device)
        self.assertEqual(cpu_device, converted_mesh.device)
        self.assertEqual(cpu_device, mesh.device)
        self.assertIs(mesh, converted_mesh)

        cuda_device = torch.device("cuda:0")

        converted_mesh = mesh.to("cuda:0")
        self.assertEqual(cuda_device, converted_mesh.device)
        self.assertEqual(cpu_device, mesh.device)
        self.assertIsNot(mesh, converted_mesh)

        converted_mesh = mesh.to(cuda_device)
        self.assertEqual(cuda_device, converted_mesh.device)
        self.assertEqual(cpu_device, mesh.device)
        self.assertIsNot(mesh, converted_mesh)

    def test_split_mesh(self):
        mesh = init_mesh(5, 10, 100)
        split_sizes = [2, 3]
        split_meshes = mesh.split(split_sizes)
        self.assertTrue(len(split_meshes[0]) == 2)
        self.assertTrue(
            split_meshes[0].verts_list()
            == [mesh.get_mesh_verts_faces(0)[0], mesh.get_mesh_verts_faces(1)[0]]
        )
        self.assertTrue(len(split_meshes[1]) == 3)
        self.assertTrue(
            split_meshes[1].verts_list()
            == [
                mesh.get_mesh_verts_faces(2)[0],
                mesh.get_mesh_verts_faces(3)[0],
                mesh.get_mesh_verts_faces(4)[0],
            ]
        )

        split_sizes = [2, 0.3]
        with self.assertRaises(ValueError):
            mesh.split(split_sizes)

    def test_update_padded(self):
        # Define the test mesh object either as a list or tensor of faces/verts.
        N = 10
        for lists_to_tensors in (False, True):
            for force in (True, False):
                mesh = init_mesh(N, 100, 300, lists_to_tensors=lists_to_tensors)
                num_verts_per_mesh = mesh.num_verts_per_mesh()
                if force:
                    # force mesh to have computed attributes
                    mesh.verts_packed()
                    mesh.edges_packed()
                    mesh.laplacian_packed()
                    mesh.faces_areas_packed()

                new_verts = torch.rand((mesh._N, mesh._V, 3), device=mesh.device)
                new_verts_list = [
                    new_verts[i, : num_verts_per_mesh[i]] for i in range(N)
                ]
                new_mesh = mesh.update_padded(new_verts)

                # check the attributes assigned at construction time
                self.assertEqual(new_mesh._N, mesh._N)
                self.assertEqual(new_mesh._F, mesh._F)
                self.assertEqual(new_mesh._V, mesh._V)
                self.assertEqual(new_mesh.equisized, mesh.equisized)
                self.assertTrue(all(new_mesh.valid == mesh.valid))
                self.assertNotSeparate(
                    new_mesh.num_verts_per_mesh(), mesh.num_verts_per_mesh()
                )
                self.assertClose(
                    new_mesh.num_verts_per_mesh(), mesh.num_verts_per_mesh()
                )
                self.assertNotSeparate(
                    new_mesh.num_faces_per_mesh(), mesh.num_faces_per_mesh()
                )
                self.assertClose(
                    new_mesh.num_faces_per_mesh(), mesh.num_faces_per_mesh()
                )

                # check that the following attributes are not assigned
                self.assertIsNone(new_mesh._verts_list)
                self.assertIsNone(new_mesh._faces_areas_packed)
                self.assertIsNone(new_mesh._faces_normals_packed)
                self.assertIsNone(new_mesh._verts_normals_packed)

                check_tensors = [
                    "_faces_packed",
                    "_verts_packed_to_mesh_idx",
                    "_faces_packed_to_mesh_idx",
                    "_mesh_to_verts_packed_first_idx",
                    "_mesh_to_faces_packed_first_idx",
                    "_edges_packed",
                    "_edges_packed_to_mesh_idx",
                    "_mesh_to_edges_packed_first_idx",
                    "_faces_packed_to_edges_packed",
                    "_num_edges_per_mesh",
                ]
                for k in check_tensors:
                    v = getattr(new_mesh, k)
                    if not force:
                        self.assertIsNone(v)
                    else:
                        v_old = getattr(mesh, k)
                        self.assertNotSeparate(v, v_old)
                        self.assertClose(v, v_old)

                # check verts/faces padded
                self.assertClose(new_mesh.verts_padded(), new_verts)
                self.assertNotSeparate(new_mesh.verts_padded(), new_verts)
                self.assertClose(new_mesh.faces_padded(), mesh.faces_padded())
                self.assertNotSeparate(new_mesh.faces_padded(), mesh.faces_padded())
                # check verts/faces list
                for i in range(N):
                    self.assertNotSeparate(
                        new_mesh.faces_list()[i], mesh.faces_list()[i]
                    )
                    self.assertClose(new_mesh.faces_list()[i], mesh.faces_list()[i])
                    self.assertSeparate(new_mesh.verts_list()[i], mesh.verts_list()[i])
                    self.assertClose(new_mesh.verts_list()[i], new_verts_list[i])
                # check verts/faces packed
                self.assertClose(new_mesh.verts_packed(), torch.cat(new_verts_list))
                self.assertSeparate(new_mesh.verts_packed(), mesh.verts_packed())
                self.assertClose(new_mesh.faces_packed(), mesh.faces_packed())
                # check pad_to_packed
                self.assertClose(
                    new_mesh.verts_padded_to_packed_idx(),
                    mesh.verts_padded_to_packed_idx(),
                )
                # check edges
                self.assertClose(new_mesh.edges_packed(), mesh.edges_packed())

    def test_get_mesh_verts_faces(self):
        device = torch.device("cuda:0")
        verts_list = []
        faces_list = []
        verts_faces = [(10, 100), (20, 200)]
        for (V, F) in verts_faces:
            verts = torch.rand((V, 3), dtype=torch.float32, device=device)
            faces = torch.randint(V, size=(F, 3), dtype=torch.int64, device=device)
            verts_list.append(verts)
            faces_list.append(faces)

        mesh = Meshes(verts=verts_list, faces=faces_list)

        for i, (V, F) in enumerate(verts_faces):
            verts, faces = mesh.get_mesh_verts_faces(i)
            self.assertTrue(len(verts) == V)
            self.assertClose(verts, verts_list[i])
            self.assertTrue(len(faces) == F)
            self.assertClose(faces, faces_list[i])

        with self.assertRaises(ValueError):
            mesh.get_mesh_verts_faces(5)
        with self.assertRaises(ValueError):
            mesh.get_mesh_verts_faces(0.2)

    def test_get_bounding_boxes(self):
        device = torch.device("cuda:0")
        verts_list = []
        faces_list = []
        for (V, F) in [(10, 100)]:
            verts = torch.rand((V, 3), dtype=torch.float32, device=device)
            faces = torch.randint(V, size=(F, 3), dtype=torch.int64, device=device)
            verts_list.append(verts)
            faces_list.append(faces)

        mins = torch.min(verts, dim=0)[0]
        maxs = torch.max(verts, dim=0)[0]
        bboxes_gt = torch.stack([mins, maxs], dim=1).unsqueeze(0)
        mesh = Meshes(verts=verts_list, faces=faces_list)
        bboxes = mesh.get_bounding_boxes()
        self.assertClose(bboxes_gt, bboxes)

    def test_padded_to_packed_idx(self):
        device = torch.device("cuda:0")
        verts_list = []
        faces_list = []
        verts_faces = [(10, 100), (20, 200), (30, 300)]
        for (V, F) in verts_faces:
            verts = torch.rand((V, 3), dtype=torch.float32, device=device)
            faces = torch.randint(V, size=(F, 3), dtype=torch.int64, device=device)
            verts_list.append(verts)
            faces_list.append(faces)

        mesh = Meshes(verts=verts_list, faces=faces_list)
        verts_padded_to_packed_idx = mesh.verts_padded_to_packed_idx()
        verts_packed = mesh.verts_packed()
        verts_padded = mesh.verts_padded()
        verts_padded_flat = verts_padded.view(-1, 3)

        self.assertClose(verts_padded_flat[verts_padded_to_packed_idx], verts_packed)

        idx = verts_padded_to_packed_idx.view(-1, 1).expand(-1, 3)
        self.assertClose(verts_padded_flat.gather(0, idx), verts_packed)

    def test_getitem(self):
        device = torch.device("cuda:0")
        verts_list = []
        faces_list = []
        verts_faces = [(10, 100), (20, 200), (30, 300)]
        for (V, F) in verts_faces:
            verts = torch.rand((V, 3), dtype=torch.float32, device=device)
            faces = torch.randint(V, size=(F, 3), dtype=torch.int64, device=device)
            verts_list.append(verts)
            faces_list.append(faces)

        mesh = Meshes(verts=verts_list, faces=faces_list)

        def check_equal(selected, indices):
            for selectedIdx, index in enumerate(indices):
                self.assertClose(
                    selected.verts_list()[selectedIdx], mesh.verts_list()[index]
                )
                self.assertClose(
                    selected.faces_list()[selectedIdx], mesh.faces_list()[index]
                )

        # int index
        index = 1
        mesh_selected = mesh[index]
        self.assertTrue(len(mesh_selected) == 1)
        check_equal(mesh_selected, [index])

        # list index
        index = [1, 2]
        mesh_selected = mesh[index]
        self.assertTrue(len(mesh_selected) == len(index))
        check_equal(mesh_selected, index)

        # slice index
        index = slice(0, 2, 1)
        mesh_selected = mesh[index]
        check_equal(mesh_selected, [0, 1])

        # bool tensor
        index = torch.tensor([1, 0, 1], dtype=torch.bool, device=device)
        mesh_selected = mesh[index]
        self.assertTrue(len(mesh_selected) == index.sum())
        check_equal(mesh_selected, [0, 2])

        # int tensor
        index = torch.tensor([1, 2], dtype=torch.int64, device=device)
        mesh_selected = mesh[index]
        self.assertTrue(len(mesh_selected) == index.numel())
        check_equal(mesh_selected, index.tolist())

        # invalid index
        index = torch.tensor([1, 0, 1], dtype=torch.float32, device=device)
        with self.assertRaises(IndexError):
            mesh_selected = mesh[index]
        index = 1.2
        with self.assertRaises(IndexError):
            mesh_selected = mesh[index]

    def test_compute_faces_areas(self):
        verts = torch.tensor(
            [
                [0.0, 0.0, 0.0],
                [0.5, 0.0, 0.0],
                [0.5, 0.5, 0.0],
                [0.5, 0.0, 0.0],
                [0.25, 0.8, 0.0],
            ],
            dtype=torch.float32,
        )
        faces = torch.tensor([[0, 1, 2], [0, 3, 4]], dtype=torch.int64)
        mesh = Meshes(verts=[verts], faces=[faces])

        face_areas = mesh.faces_areas_packed()
        expected_areas = torch.tensor([0.125, 0.2])
        self.assertClose(face_areas, expected_areas)

    def test_compute_normals(self):

        # Simple case with one mesh where normals point in either +/- ijk
        verts = torch.tensor(
            [
                [0.1, 0.3, 0.0],
                [0.5, 0.2, 0.0],
                [0.6, 0.8, 0.0],
                [0.0, 0.3, 0.2],
                [0.0, 0.2, 0.5],
                [0.0, 0.8, 0.7],
                [0.5, 0.0, 0.2],
                [0.6, 0.0, 0.5],
                [0.8, 0.0, 0.7],
                [0.0, 0.0, 0.0],
                [0.0, 0.0, 0.0],
                [0.0, 0.0, 0.0],
            ],
            dtype=torch.float32,
        )
        faces = torch.tensor(
            [[0, 1, 2], [3, 4, 5], [6, 7, 8], [9, 10, 11]], dtype=torch.int64
        )
        mesh = Meshes(verts=[verts], faces=[faces])
        self.assertFalse(mesh.has_verts_normals())
        verts_normals_expected = torch.tensor(
            [
                [0.0, 0.0, 1.0],
                [0.0, 0.0, 1.0],
                [0.0, 0.0, 1.0],
                [-1.0, 0.0, 0.0],
                [-1.0, 0.0, 0.0],
                [-1.0, 0.0, 0.0],
                [0.0, 1.0, 0.0],
                [0.0, 1.0, 0.0],
                [0.0, 1.0, 0.0],
                [0.0, 0.0, 0.0],
                [0.0, 0.0, 0.0],
                [0.0, 0.0, 0.0],
            ]
        )
        faces_normals_expected = verts_normals_expected[[0, 3, 6, 9], :]

        self.assertTrue(
            torch.allclose(mesh.verts_normals_list()[0], verts_normals_expected)
        )
        self.assertTrue(mesh.has_verts_normals())
        self.assertTrue(
            torch.allclose(mesh.faces_normals_list()[0], faces_normals_expected)
        )
        self.assertTrue(
            torch.allclose(mesh.verts_normals_packed(), verts_normals_expected)
        )
        self.assertTrue(
            torch.allclose(mesh.faces_normals_packed(), faces_normals_expected)
        )

        # Multiple meshes in the batch with equal sized meshes
        meshes_extended = mesh.extend(3)
        for m in meshes_extended.verts_normals_list():
            self.assertClose(m, verts_normals_expected)
        for f in meshes_extended.faces_normals_list():
            self.assertClose(f, faces_normals_expected)

        # Multiple meshes in the batch with different sized meshes
        # Check padded and packed normals are the correct sizes.
        verts2 = torch.tensor(
            [
                [0.1, 0.3, 0.0],
                [0.5, 0.2, 0.0],
                [0.6, 0.8, 0.0],
                [0.0, 0.3, 0.2],
                [0.0, 0.2, 0.5],
                [0.0, 0.8, 0.7],
            ],
            dtype=torch.float32,
        )
        faces2 = torch.tensor([[0, 1, 2], [3, 4, 5]], dtype=torch.int64)
        verts_list = [verts, verts2]
        faces_list = [faces, faces2]
        meshes = Meshes(verts=verts_list, faces=faces_list)
        verts_normals_padded = meshes.verts_normals_padded()
        faces_normals_padded = meshes.faces_normals_padded()

        for n in range(len(meshes)):
            v = verts_list[n].shape[0]
            f = faces_list[n].shape[0]
            if verts_normals_padded.shape[1] > v:
                self.assertTrue(verts_normals_padded[n, v:, :].eq(0).all())
                self.assertTrue(
                    torch.allclose(
                        verts_normals_padded[n, :v, :].view(-1, 3),
                        verts_normals_expected[:v, :],
                    )
                )
            if faces_normals_padded.shape[1] > f:
                self.assertTrue(faces_normals_padded[n, f:, :].eq(0).all())
                self.assertTrue(
                    torch.allclose(
                        faces_normals_padded[n, :f, :].view(-1, 3),
                        faces_normals_expected[:f, :],
                    )
                )

        verts_normals_packed = meshes.verts_normals_packed()
        faces_normals_packed = meshes.faces_normals_packed()
        self.assertTrue(
            list(verts_normals_packed.shape) == [verts.shape[0] + verts2.shape[0], 3]
        )
        self.assertTrue(
            list(faces_normals_packed.shape) == [faces.shape[0] + faces2.shape[0], 3]
        )

        # Single mesh where two faces share one vertex so the normal is
        # the weighted sum of the two face normals.
        verts = torch.tensor(
            [
                [0.1, 0.3, 0.0],
                [0.5, 0.2, 0.0],
                [0.0, 0.3, 0.2],  # vertex is shared between two faces
                [0.0, 0.2, 0.5],
                [0.0, 0.8, 0.7],
            ],
            dtype=torch.float32,
        )
        faces = torch.tensor([[0, 1, 2], [2, 3, 4]], dtype=torch.int64)
        mesh = Meshes(verts=[verts], faces=[faces])

        verts_normals_expected = torch.tensor(
            [
                [-0.2408, -0.9631, -0.1204],
                [-0.2408, -0.9631, -0.1204],
                [-0.9389, -0.3414, -0.0427],
                [-1.0000, 0.0000, 0.0000],
                [-1.0000, 0.0000, 0.0000],
            ]
        )
        faces_normals_expected = torch.tensor(
            [[-0.2408, -0.9631, -0.1204], [-1.0000, 0.0000, 0.0000]]
        )
        self.assertTrue(
            torch.allclose(
                mesh.verts_normals_list()[0], verts_normals_expected, atol=4e-5
            )
        )
        self.assertTrue(
            torch.allclose(
                mesh.faces_normals_list()[0], faces_normals_expected, atol=4e-5
            )
        )

        # Check empty mesh has empty normals
        meshes = Meshes(verts=[], faces=[])
        self.assertEqual(meshes.verts_normals_packed().shape[0], 0)
        self.assertEqual(meshes.verts_normals_padded().shape[0], 0)
        self.assertEqual(meshes.verts_normals_list(), [])
        self.assertEqual(meshes.faces_normals_packed().shape[0], 0)
        self.assertEqual(meshes.faces_normals_padded().shape[0], 0)
        self.assertEqual(meshes.faces_normals_list(), [])

    def test_assigned_normals(self):
        verts = torch.rand(2, 6, 3)
        faces = torch.randint(6, size=(2, 4, 3))
        no_normals = Meshes(verts=verts, faces=faces)
        self.assertFalse(no_normals.has_verts_normals())

        for verts_normals in [list(verts.unbind(0)), verts]:
            yes_normals = Meshes(
                verts=verts.clone(), faces=faces, verts_normals=verts_normals
            )
            self.assertTrue(yes_normals.has_verts_normals())
            self.assertClose(yes_normals.verts_normals_padded(), verts)
            yes_normals.offset_verts_(torch.FloatTensor([1, 2, 3]))
            self.assertClose(yes_normals.verts_normals_padded(), verts)
            yes_normals.offset_verts_(torch.FloatTensor([1, 2, 3]).expand(12, 3))
            self.assertFalse(torch.allclose(yes_normals.verts_normals_padded(), verts))

    def test_compute_faces_areas_cpu_cuda(self):
        num_meshes = 10
        max_v = 100
        max_f = 300
        mesh_cpu = init_mesh(num_meshes, max_v, max_f, device="cpu")
        device = torch.device("cuda:0")
        mesh_cuda = mesh_cpu.to(device)

        face_areas_cpu = mesh_cpu.faces_areas_packed()
        face_normals_cpu = mesh_cpu.faces_normals_packed()
        face_areas_cuda = mesh_cuda.faces_areas_packed()
        face_normals_cuda = mesh_cuda.faces_normals_packed()
        self.assertClose(face_areas_cpu, face_areas_cuda.cpu(), atol=1e-6)
        # because of the normalization of the normals with arbitrarily small values,
        # normals can become unstable. Thus only compare normals, for faces
        # with areas > eps=1e-6
        nonzero = face_areas_cpu > 1e-6
        self.assertClose(
            face_normals_cpu[nonzero], face_normals_cuda.cpu()[nonzero], atol=1e-6
        )

    def test_equality(self):
        meshes1 = init_mesh(num_meshes=2)
        meshes2 = init_mesh(num_meshes=2)
        meshes3 = init_mesh(num_meshes=3)
        empty_mesh = Meshes([], [])
        self.assertTrue(mesh_structures_equal(empty_mesh, Meshes([], [])))
        self.assertTrue(mesh_structures_equal(meshes1, meshes1))
        self.assertTrue(mesh_structures_equal(meshes1, meshes1.clone()))
        self.assertFalse(mesh_structures_equal(empty_mesh, meshes1))
        self.assertFalse(mesh_structures_equal(meshes1, meshes2))
        self.assertFalse(mesh_structures_equal(meshes1, meshes3))

    def test_to_sorted(self):
        mesh = init_simple_mesh()
        sorted_mesh = to_sorted(mesh)

        expected_verts = [
            torch.tensor(
                [[0.1, 0.3, 0.5], [0.5, 0.2, 0.1], [0.6, 0.8, 0.7]],
                dtype=torch.float32,
            ),
            torch.tensor(
                # Vertex permutation: 0->0, 1->3, 2->2, 3->1
                [[0.1, 0.3, 0.3], [0.1, 0.5, 0.3], [0.2, 0.3, 0.4], [0.6, 0.7, 0.8]],
                dtype=torch.float32,
            ),
            torch.tensor(
                # Vertex permutation: 0->2, 1->1, 2->4, 3->0, 4->3
                [
                    [0.2, 0.3, 0.4],
                    [0.2, 0.4, 0.8],
                    [0.7, 0.3, 0.6],
                    [0.9, 0.3, 0.8],
                    [0.9, 0.5, 0.2],
                ],
                dtype=torch.float32,
            ),
        ]

        expected_faces = [
            torch.tensor([[0, 1, 2]], dtype=torch.int64),
            torch.tensor([[0, 3, 2], [3, 2, 1]], dtype=torch.int64),
            torch.tensor(
                [
                    [1, 4, 2],
                    [2, 1, 0],
                    [4, 0, 1],
                    [3, 0, 4],
                    [3, 2, 1],
                    [3, 0, 1],
                    [3, 4, 1],
                ],
                dtype=torch.int64,
            ),
        ]

        self.assertFalse(mesh_structures_equal(mesh, sorted_mesh))
        self.assertTrue(
            mesh_structures_equal(
                Meshes(verts=expected_verts, faces=expected_faces), sorted_mesh
            )
        )

    @staticmethod
    def compute_packed_with_init(
        num_meshes: int = 10, max_v: int = 100, max_f: int = 300, device: str = "cpu"
    ):
        mesh = init_mesh(num_meshes, max_v, max_f, device=device)
        torch.cuda.synchronize()

        def compute_packed():
            mesh._compute_packed(refresh=True)
            torch.cuda.synchronize()

        return compute_packed

    @staticmethod
    def compute_padded_with_init(
        num_meshes: int = 10, max_v: int = 100, max_f: int = 300, device: str = "cpu"
    ):
        mesh = init_mesh(num_meshes, max_v, max_f, device=device)
        torch.cuda.synchronize()

        def compute_padded():
            mesh._compute_padded(refresh=True)
            torch.cuda.synchronize()

        return compute_padded