sample_points_from_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.


"""
This module implements utility functions for sampling points from
batches of meshes.
"""
import sys
from typing import Tuple, Union

import torch
from pytorch3d.ops.mesh_face_areas_normals import mesh_face_areas_normals
from pytorch3d.ops.packed_to_padded import packed_to_padded
from pytorch3d.renderer.mesh.rasterizer import Fragments as MeshFragments
from pytorch3d.structures import Meshes


def sample_points_from_meshes(
    meshes,
    num_samples: int = 10000,
    return_normals: bool = False,
    return_textures: bool = False,
    return_mappers: bool = False,
) -> Union[
    torch.Tensor,
    Tuple[torch.Tensor, torch.Tensor],
    Tuple[torch.Tensor, torch.Tensor, torch.Tensor],
]:
    """
    Convert a batch of meshes to a batch of pointclouds by uniformly sampling
    points on the surface of the mesh with probability proportional to the
    face area.

    Args:
        meshes: A Meshes object with a batch of N meshes.
        num_samples: Integer giving the number of point samples per mesh.
        return_normals: If True, return normals for the sampled points.
        return_textures: If True, return textures for the sampled points.
        return_mappers: If True, return a mapping of each point to its origin face.
    Returns:
        4-element tuple containing

        - **samples**: FloatTensor of shape (N, num_samples, 3) giving the
          coordinates of sampled points for each mesh in the batch. For empty
          meshes the corresponding row in the samples array will be filled with 0.
        - **normals**: FloatTensor of shape (N, num_samples, 3) giving a normal vector
          to each sampled point. Only returned if return_normals is True.
          For empty meshes the corresponding row in the normals array will
          be filled with 0.
        - **textures**: FloatTensor of shape (N, num_samples, C) giving a C-dimensional
          texture vector to each sampled point. Only returned if return_textures is True.
          For empty meshes the corresponding row in the textures array will
          be filled with 0.
        - **mappers**: IntTensor of shape (N, num_samples) providing a point to face
          mapping for each point's origin face in the sample.

        Note that in a future releases, we will replace the 4-element tuple output
        with a `Pointclouds` datastructure, as follows

        .. code-block:: python

            Pointclouds(samples, normals=normals, features=textures)
    """
    if meshes.isempty():
        raise ValueError("Meshes are empty.")

    # initialize all return values
    samples, normals, textures, mappers = None, None, None, None

    verts = meshes.verts_packed()
    if not torch.isfinite(verts).all():
        raise ValueError("Meshes contain nan or inf.")

    if return_textures and meshes.textures is None:
        raise ValueError("Meshes do not contain textures.")

    faces = meshes.faces_packed()
    mesh_to_face = meshes.mesh_to_faces_packed_first_idx()
    num_valid_meshes = torch.sum(meshes.valid)  # Non empty meshes.

    # Only compute samples for non empty meshes
    with torch.no_grad():
        areas, _ = mesh_face_areas_normals(verts, faces)  # Face areas can be zero.
        max_faces = meshes.num_faces_per_mesh().max().item()
        areas_padded = packed_to_padded(
            areas, mesh_to_face[meshes.valid], max_faces
        )  # (N, F)

        # TODO (gkioxari) Confirm multinomial bug is not present with real data.
        sample_face_idxs = areas_padded.multinomial(
            num_samples, replacement=True
        )  # (N, num_samples)

        if return_mappers:
            # for each mesh, a mapping of each point to its origin face by the face index
            mappers = sample_face_idxs.clone()

        sample_face_idxs += mesh_to_face[meshes.valid].view(num_valid_meshes, 1)

    (samples, (v0, v1, v2), (w0, w1, w2)) = _sample_points(
        meshes,
        num_samples,
        sample_face_idxs,
        verts,
        faces,
    )

    if return_normals:
        normals = _sample_normals(meshes, num_samples, sample_face_idxs, v0, v1, v2)

    if return_textures:
        textures = _sample_textures(meshes, num_samples, sample_face_idxs, w0, w1, w2)

    # return
    # TODO(gkioxari) consider returning a Pointclouds instance [breaking]
    if return_mappers:
        # return a 4-element tuple
        return samples, normals, textures, mappers
    if return_normals and return_textures:
        # pyre-fixme[61]: `normals` may not be initialized here.
        # pyre-fixme[61]: `textures` may not be initialized here.
        return samples, normals, textures
    if return_normals:  # return_textures is False
        # pyre-fixme[61]: `normals` may not be initialized here.
        return samples, normals
    if return_textures:  # return_normals is False
        # pyre-fixme[61]: `textures` may not be initialized here.
        return samples, textures
    return samples


def _rand_barycentric_coords(
    size1, size2, dtype: torch.dtype, device: torch.device
) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
    """
    Helper function to generate random barycentric coordinates which are uniformly
    distributed over a triangle.

    Args:
        size1, size2: The number of coordinates generated will be size1*size2.
                      Output tensors will each be of shape (size1, size2).
        dtype: Datatype to generate.
        device: A torch.device object on which the outputs will be allocated.

    Returns:
        w0, w1, w2: Tensors of shape (size1, size2) giving random barycentric
            coordinates
    """
    uv = torch.rand(2, size1, size2, dtype=dtype, device=device)
    u, v = uv[0], uv[1]
    u_sqrt = u.sqrt()
    w0 = 1.0 - u_sqrt
    w1 = u_sqrt * (1.0 - v)
    w2 = u_sqrt * v
    return w0, w1, w2


def _sample_points(
    meshes: Meshes,
    num_samples: int,
    sample_face_idxs: torch.Tensor,
    verts: torch.Tensor,
    faces: torch.Tensor,
) -> Tuple[
    torch.Tensor,
    Tuple[torch.Tensor, torch.Tensor, torch.Tensor],
    Tuple[torch.Tensor, torch.Tensor, torch.Tensor],
]:
    """This is a helper function that re-packages the core sampling function for points.
    Args:
        meshes: A Meshes object to sample points from.
        num_samples: Integer number of samples to generate per mesh.
        num_valid_meshes: Integer value, typically the value equal to torch.sum(meshes.valid).
        sample_face_idxs: An array of face indices to sample from Meshes.
        verts: torch.Tensor of verts, typically meshes.verts_packed().
        faces: torch.Tensor of faces, typically meshes.faces_packed().

    Returns:
        A 3-Tuple of sampled points array, face_verts arrays as a 3-Tuple, and
        barycentric coordinate arrays as a 3-Tuple.

    """
    # Initialize samples tensor with fill value 0 for empty meshes.
    samples = _empty_sample(len(meshes), num_samples, verts.device, verts.dtype)

    # Get the vertex coordinates of the sampled faces.
    face_verts = verts[faces]
    v0, v1, v2 = face_verts[:, 0], face_verts[:, 1], face_verts[:, 2]

    # Randomly generate barycentric coords.
    w0, w1, w2 = _rand_barycentric_coords(
        torch.sum(meshes.valid), num_samples, verts.dtype, verts.device
    )

    # Use the barycentric coords to get a point on each sampled face.
    a = v0[sample_face_idxs]  # (N, num_samples, 3)
    b = v1[sample_face_idxs]
    c = v2[sample_face_idxs]
    samples[meshes.valid] = w0[:, :, None] * a + w1[:, :, None] * b + w2[:, :, None] * c
    return samples, (v0, v1, v2), (w0, w1, w2)


def _sample_normals(
    meshes: Meshes,
    num_samples: int,
    sample_face_idxs: torch.Tensor,
    v0: torch.Tensor,
    v1: torch.Tensor,
    v2: torch.Tensor,
) -> torch.Tensor:
    """This is a helper function that implements the core sampling function for point normals.

    Args:
        meshes: A Meshes object to sample points from.
        num_samples: Integer number of samples to generate per mesh.
        sample_face_idxs: An array of face indices to sample from Meshes.
        v0, v1, v2: torch.Tensors of face_verts.

    Returns:
        a torch.Tensor of normals
    """
    # Initialize normals tensor with fill value 0 for empty meshes.
    # Normals for the sampled points are face normals computed from
    # the vertices of the face in which the sampled point lies.
    normals = torch.zeros(
        (len(meshes), num_samples, 3), device=meshes.device, dtype=v0.dtype
    )
    vert_normals = (v1 - v0).cross(v2 - v1, dim=1)
    vert_normals = vert_normals / vert_normals.norm(dim=1, p=2, keepdim=True).clamp(
        min=sys.float_info.epsilon
    )
    vert_normals = vert_normals[sample_face_idxs]
    normals[meshes.valid] = vert_normals
    return normals


def _sample_textures(
    meshes: Meshes,
    num_samples: int,
    sample_face_idxs: torch.Tensor,
    w0: torch.Tensor,
    w1: torch.Tensor,
    w2: torch.Tensor,
) -> torch.Tensor:
    """This is a helper function that implements the core sampling function for point textures.

    Args:
        meshes: A Meshes object from which to sample textures.
        num_samples: Integer value for number of texture samples.
        sample_face_idxs: An array of face indices to sample from Meshes.
        w0, w1, w2: Tensors giving random barycentric coordinates from _sample_points.

    Returns:
        A torch.Tensor of sampled textures for Meshes.
    """
    # fragment data are of shape NxHxWxK. Here H=S, W=1 & K=1.
    pix_to_face = sample_face_idxs.view(len(meshes), num_samples, 1, 1)  # NxSx1x1
    bary = torch.stack((w0, w1, w2), dim=2).unsqueeze(2).unsqueeze(2)  # NxSx1x1x3
    # zbuf and dists are not used in `sample_textures` so we initialize them with dummy
    dummy = torch.zeros(
        (len(meshes), num_samples, 1, 1), device=meshes.device, dtype=bary.dtype
    )  # NxSx1x1
    fragments = MeshFragments(
        pix_to_face=pix_to_face, zbuf=dummy, bary_coords=bary, dists=dummy
    )
    textures = meshes.sample_textures(fragments)  # NxSx1x1xC
    textures = textures[:, :, 0, 0, :]  # NxSxC
    return textures


def _empty_sample(
    num_meshes: int, num_samples: int, device: torch.device, dtype: torch.dtype = None
) -> torch.Tensor:
    """This is a helper function that returns an empty (zeros) tensor to initialize a point sample.

    Args:
        num_meshes: Integer value for dim 0 of the array.
        num_samples: Integer value for dim 1 of the array.
        device: torch.device
        dtype: Optionally specify the torch.dtype to force a specific type.

    Returns:
        A torch.zeros Tensor in the shape of (num_meshes x num_samples x 3)
    """
    if dtype is not None:
        return torch.zeros((num_meshes, num_samples, 3), device=device, dtype=dtype)
    else:
        return torch.zeros((num_meshes, num_samples, 3), device=device)