Initial commit

fbshipit-source-id: afc575e8e7d8e2796a3f77d8b1c6c4fcb999558d

.flake8

+[flake8]
+select = B,C,E,F,P,W,B9
+max-line-length = 100
+### DEFAULT IGNORES FOR 4-space INDENTED PROJECTS ###
+# Main Explanation Docs: https://lintlyci.github.io/Flake8Rules/
+#
+# E127, E128 are hard to silence in certain nested formatting situations.
+# E203 doesn't work for slicing
+# E265, E266 talk about comment formatting which is too opinionated.
+# E402 warns on imports coming after statements. There are important use cases
+# like demandimport (https://fburl.com/demandimport) that require statements
+# before imports.
+# E501 is not flexible enough, we're using B950 instead.
+# E722 is a duplicate of B001.
+# F811 looks for duplicate imports + noise for overload typing
+# P207 is a duplicate of B003.
+# P208 is a duplicate of C403.
+# W503 talks about operator formatting which is too opinionated.
+ignore = E127, E128, E203, E265, E266, E402, E501, E722, F811, P207, P208, W503
+### DEFAULT IGNORES FOR 2-space INDENTED PROJECTS (uncomment) ###
+# ignore = E111, E114, E121, E127, E128, E265, E266, E402, E501, P207, P208, W503
+exclude =
+  .git,
+  .hg,
+  __pycache__,
+  _bin/*,
+  _build/*,
+  _ig_fbcode_wheel/*,
+  buck-out/*,
+  third-party-buck/*,
+  third-party2/*
+
+# Calculate max-complexity by changing the value below to 1, then surveying fbcode
+# to see the distribution of complexity:
+#   find ./[a-z0-9]* -name 'buck-*' -prune -o -name 'third*party*' -prune -o \
+#     -name '*.py' -print |\
+#   parallel flake8 --config ./.flake8 |\
+#   perl -ne 'if (/C901/) { s/.*\((\d+)\)/$1/; print; }' | stats
+# NOTE: This will take a while to run (near an hour IME) so you probably want a
+# second working dir to run it in.
+# Pick a reasonable point from there (e.g. p95 or "95%")
+# As of 2016-05-18 the rough distribution is:
+#
+# count:    134807
+# min:      2
+# max:      206
+# avg:      4.361
+# median:   3
+# sum:      587882
+# stddev:   4.317
+# variance: 18.635
+#
+# percentiles:
+#     75%: 5
+#     90%: 8
+#     95%: 11
+#     99%: 20
+#   99.9%: 48
+#  99.99%: 107
+# 99.999%: 160
+max-complexity = 12

CODE_OF_CONDUCT.md

+# Code of Conduct
+
+## Our Pledge
+
+In the interest of fostering an open and welcoming environment, we as
+contributors and maintainers pledge to make participation in our project and
+our community a harassment-free experience for everyone, regardless of age, body
+size, disability, ethnicity, sex characteristics, gender identity and expression,
+level of experience, education, socio-economic status, nationality, personal
+appearance, race, religion, or sexual identity and orientation.
+
+## Our Standards
+
+Examples of behavior that contributes to creating a positive environment
+include:
+
+* Using welcoming and inclusive language
+* Being respectful of differing viewpoints and experiences
+* Gracefully accepting constructive criticism
+* Focusing on what is best for the community
+* Showing empathy towards other community members
+
+Examples of unacceptable behavior by participants include:
+
+* The use of sexualized language or imagery and unwelcome sexual attention or
+advances
+* Trolling, insulting/derogatory comments, and personal or political attacks
+* Public or private harassment
+* Publishing others' private information, such as a physical or electronic
+address, without explicit permission
+* Other conduct which could reasonably be considered inappropriate in a
+professional setting
+
+## Our Responsibilities
+
+Project maintainers are responsible for clarifying the standards of acceptable
+behavior and are expected to take appropriate and fair corrective action in
+response to any instances of unacceptable behavior.
+
+Project maintainers have the right and responsibility to remove, edit, or
+reject comments, commits, code, wiki edits, issues, and other contributions
+that are not aligned to this Code of Conduct, or to ban temporarily or
+permanently any contributor for other behaviors that they deem inappropriate,
+threatening, offensive, or harmful.
+
+## Scope
+
+This Code of Conduct applies within all project spaces, and it also applies when
+an individual is representing the project or its community in public spaces.
+Examples of representing a project or community include using an official
+project e-mail address, posting via an official social media account, or acting
+as an appointed representative at an online or offline event. Representation of
+a project may be further defined and clarified by project maintainers.
+
+This Code of Conduct also applies outside the project spaces when there is a
+reasonable belief that an individual's behavior may have a negative impact on
+the project or its community.
+
+## Enforcement
+
+Instances of abusive, harassing, or otherwise unacceptable behavior may be
+reported by contacting the project team at <opensource-conduct@meta.com>. All
+complaints will be reviewed and investigated and will result in a response that
+is deemed necessary and appropriate to the circumstances. The project team is
+obligated to maintain confidentiality with regard to the reporter of an incident.
+Further details of specific enforcement policies may be posted separately.
+
+Project maintainers who do not follow or enforce the Code of Conduct in good
+faith may face temporary or permanent repercussions as determined by other
+members of the project's leadership.
+
+## Attribution
+
+This Code of Conduct is adapted from the [Contributor Covenant][homepage], version 1.4,
+available at https://www.contributor-covenant.org/version/1/4/code-of-conduct.html
+
+[homepage]: https://www.contributor-covenant.org
+
+For answers to common questions about this code of conduct, see
+https://www.contributor-covenant.org/faq

CONTRIBUTING.md

+# Contributing to Meta Open Source Projects
+
+We want to make contributing to this project as easy and transparent as
+possible.
+
+## Pull Requests
+We actively welcome your pull requests.
+
+Note: pull requests are not imported into the GitHub directory in the usual way. There is an internal Meta repository that is the "source of truth" for the project. The GitHub repository is generated *from* the internal Meta repository. So we don't merge GitHub PRs directly to the GitHub repository -- they must first be imported into internal Meta repository. When Meta employees look at the GitHub PR, there is a special button visible only to them that executes that import. The changes are then automatically reflected from the internal Meta repository back to GitHub. This is why you won't see your PR having being directly merged, but you still see your changes in the repository once it reflects the imported changes.
+
+1. Fork the repo and create your branch from `main`.
+2. If you've added code that should be tested, add tests.
+3. If you've changed APIs, update the documentation.
+4. Ensure the test suite passes.
+5. Make sure your code lints.
+6. If you haven't already, complete the Contributor License Agreement ("CLA").
+
+## Contributor License Agreement ("CLA")
+In order to accept your pull request, we need you to submit a CLA. You only need
+to do this once to work on any of Meta's open source projects.
+
+Complete your CLA here: <https://code.facebook.com/cla>
+
+## Issues
+We use GitHub issues to track public bugs. Please ensure your description is
+clear and has sufficient instructions to be able to reproduce the issue.
+
+Meta has a [bounty program](https://www.facebook.com/whitehat/) for the safe
+disclosure of security bugs. In those cases, please go through the process
+outlined on that page and do not file a public issue.
+
+## License
+By contributing to this project, you agree that your contributions will be licensed
+under the LICENSE file in the root directory of this source tree.

LICENSE

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README.md

+# DRTK - Differentiable Rendering Toolkit
+
+This package is a PyTorch library that provides functionality for differentiable rasterization.
+
+It consists of five main components
+
+* **transform**
+* **rasterize**
+* **render**
+* **interpolate**
+* **edge_grad**
+
+There are also optional components such as **msi** and **mipmap_grid_sampler**. New components may be added in the future.
+
+Typical flow looks like this:
+
+**transform** -> **rasterize** -> **render** -> **interpolate** -> **CUSTOM SHADING** -> **edge_grad**
+
+where:
+- **transform**: projects the vertex positions from camera space to image space
+- **rasterize**: performs rasterization, where pixels in the output image are associated with triangles
+- **render**: computes depth and baricentric image
+- **interpolate**: interpolates arbitrary vertex attributes
+- **CUSTOM SHADING**: user implemented shading.
+- **edge_grad**: special module that computes gradients for the **rasterize** step which is not differentiable on its own. For details please see [**Rasterized Edge Gradients: Handling Discontinuities Differentiably**](https://arxiv.org/abs/2405.02508)
+
+## Hellow Triangle
+The "Hellow Triangle" with DRTK would look like this:
+```python
+import drtk
+import torch as th
+from torchvision.utils import save_image  # to save images
+
+# create vertex buffer of shape [1 x n_vertices x 3], here for triangle `n_vertices` == 3
+v = th.as_tensor([[[0, 511, 1], [255, 0, 1], [511, 511, 1]]]).float().cuda()
+
+# create index buffer
+vi = th.as_tensor([[0, 1, 2]]).int().cuda()
+
+# rasterize
+index_img = drtk.rasterize(v, vi, height=512, width=512)
+
+# compute baricentrics
+_, bary = drtk.render(v, vi, index_img)
+
+# we won't do shading, we'll just save the baricentrics and filter out the empty region
+# which is marked with `-1` in `index_img`
+img = bary * (index_img != -1)
+
+save_image(img, "render.png")
+```
+
+![hellow triangle](doc/hellow_triangle.png)
+
+## Dependencies
+* PyTorch >= 2.1.0
+
+## Building
+
+To build a wheel and install it:
+```
+pip install wheel
+python setup.py  bdist_wheel
+pip install dist/drtk-<wheel_name>.whl
+```
+
+To build inplace, which is useful for package development:
+```
+python setup.py build_ext --inplace -j 1
+```
+
+## Contributing
+
+See the [CONTRIBUTING](CONTRIBUTING.md) file for how to help out.
+
+## License
+DRTK is CC-BY-NC 4.0 licensed, as found in the LICENSE file.
+
+## Citation
+```
+@article{pidhorskyi2024rasterized,
+  title={Rasterized Edge Gradients: Handling Discontinuities Differentiably},
+  author={Pidhorskyi, Stanislav and Simon, Tomas and Schwartz, Gabriel and Wen, He and Sheikh, Yaser and Saragih, Jason},
+  journal={arXiv preprint arXiv:2405.02508},
+  year={2024}
+}
+```

drtk/__init__.py

+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+from . import utils  # noqa  # noqa
+from .edge_grad_estimator import edge_grad_estimator, edge_grad_estimator_ref  # noqa
+from .interpolate import interpolate, interpolate_ref  # noqa
+from .mipmap_grid_sample import mipmap_grid_sample, mipmap_grid_sample_ref  # noqa
+from .msi import msi  # noqa
+from .rasterize import rasterize  # noqa
+from .render import render, render_ref  # noqa
+from .transform import transform  # noqa
+
+__version__ = "0.1.0"  # noqa

drtk/edge_grad_estimator.py

+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+from typing import Callable, Optional, Tuple
+
+import torch as th
+import torch.nn.functional as thf
+from drtk import edge_grad_ext
+from drtk.interpolate import interpolate
+from drtk.utils import index
+
+
+th.ops.load_library(edge_grad_ext.__file__)
+
+
+def edge_grad_estimator(
+    v_pix: th.Tensor,
+    vi: th.Tensor,
+    bary_img: th.Tensor,
+    img: th.Tensor,
+    index_img: th.Tensor,
+    v_pix_img_hook: Optional[Callable[[th.Tensor], None]] = None,
+) -> th.Tensor:
+    """
+    Args:
+        v_pix: Pixel-space vertex coordinates with preserved camera-space Z-values.
+            N x V x 3
+
+        vi: face vertex index list tensor
+            V x 3
+
+        bary_img: 3D barycentric coordinate image tensor
+            N x 3 x H x W
+
+        img: The rendered image
+            N x C x H x W
+
+        index_img: index image tensor
+            N x H x W
+
+        v_pix_img_hook: a backward hook that will be registered to v_pix_img. Useful for examining
+            generated image space. Default None
+
+    Returns:
+        returns the img argument unchanged. Optionally also returns computed
+        v_pix_img. Your loss should use the returned img, even though it is
+        unchanged.
+
+    Note:
+        It is important to not spatially modify the rasterized image before passing it to edge_grad_estimator.
+        Any operation as long as it is differentiable is ok after the edge_grad_estimator.
+
+        Examples of opeartions that can be done before edge_grad_estimator:
+            - Pixel-wise MLP
+            - Color mapping
+            - Color correction, gamma correction
+        If the operation is significantly non-linear, then it is recommended to do it before
+        edge_grad_estimator. All sorts of clipping and clamping (e.g. `x.clamp(min=0.0, max=1.0)`), must be
+        done before edge_grad_estimator.
+
+        Examples of operations that are not allowed before edge_grad_estimator:
+            - Gaussian blur
+            - Warping, deformation
+            - Masking, cropping, making holes.
+
+    Usage::
+
+        from drtk.renderlayer import edge_grad_estimator
+
+        ...
+
+        out = renderlayer(v, tex, campos, camrot, focal, princpt,
+                 output_filters=["index_img", "render", "mask", "bary_img", "v_pix"])
+
+        img = out["render"] * out["mask"]
+
+        img = edge_grad_estimator(
+            v_pix=out["v_pix"],
+            vi=rl.vi,
+            bary_img=out["bary_img"],
+            img=img,
+            index_img=out["index_img"]
+        )
+
+        optim.zero_grad()
+        image_loss = loss_func(img, img_gt)
+        image_loss.backward()
+        optim.step()
+    """
+
+    # Could use v_pix_img output from DRTK, but bary_img needs to be detached.
+    v_pix_img = interpolate(v_pix, vi, index_img, bary_img.detach())
+
+    img = th.ops.edge_grad_ext.edge_grad_estimator(v_pix, v_pix_img, vi, img, index_img)
+
+    if v_pix_img_hook is not None:
+        v_pix_img.register_hook(v_pix_img_hook)
+    return img
+
+
+def edge_grad_estimator_ref(
+    v_pix: th.Tensor,
+    vi: th.Tensor,
+    bary_img: th.Tensor,
+    img: th.Tensor,
+    index_img: th.Tensor,
+    v_pix_img_hook: Optional[Callable[[th.Tensor], None]] = None,
+) -> th.Tensor:
+    """
+    Python reference implementation for
+    :func:`drtk.edge_grad_estimator.edge_grad_estimator`.
+    """
+
+    # could use v_pix_img output from DRTK, but bary_img needs to be detached.
+    v_pix_img = interpolate(v_pix, vi, index_img, bary_img.detach())
+    # pyre-fixme[16]: `EdgeGradEstimatorFunction` has no attribute `apply`.
+    img = EdgeGradEstimatorFunction.apply(v_pix, v_pix_img, vi, img, index_img)
+
+    if v_pix_img_hook is not None:
+        v_pix_img.register_hook(v_pix_img_hook)
+    return img
+
+
+class EdgeGradEstimatorFunction(th.autograd.Function):
+    @staticmethod
+    @th.cuda.amp.custom_fwd(cast_inputs=th.float32)
+    # pyre-fixme[14]: `forward` overrides method defined in `Function` inconsistently.
+    def forward(
+        ctx,
+        v_pix: th.Tensor,
+        v_pix_img: th.Tensor,
+        vi: th.Tensor,
+        img: th.Tensor,
+        index_img: th.Tensor,
+    ) -> th.Tensor:
+        ctx.save_for_backward(v_pix, img, index_img, vi)
+        return img
+
+    @staticmethod
+    @th.cuda.amp.custom_bwd
+    # pyre-fixme[14]: `backward` overrides method defined in `Function` inconsistently.
+    def backward(ctx, grad_output: th.Tensor) -> Tuple[
+        Optional[th.Tensor],
+        Optional[th.Tensor],
+        Optional[th.Tensor],
+        Optional[th.Tensor],
+        Optional[th.Tensor],
+    ]:
+        # early exit in case geometry is not optimized.
+        if not ctx.needs_input_grad[1]:
+            return None, None, None, grad_output, None
+
+        v_pix, img, index_img, vi = ctx.saved_tensors
+
+        x_grad = img[:, :, :, 1:] - img[:, :, :, :-1]
+        y_grad = img[:, :, 1:, :] - img[:, :, :-1, :]
+
+        l_index = index_img[:, None, :, :-1]
+        r_index = index_img[:, None, :, 1:]
+        t_index = index_img[:, None, :-1, :]
+        b_index = index_img[:, None, 1:, :]
+
+        x_mask = r_index != l_index
+        y_mask = b_index != t_index
+
+        x_both_triangles = (r_index != -1) & (l_index != -1)
+        y_both_triangles = (b_index != -1) & (t_index != -1)
+
+        iimg_clamped = index_img.clamp(min=0).long()
+
+        # compute barycentric coordinates
+        b = v_pix.shape[0]
+        vi_img = index(vi, iimg_clamped, 0).long()
+        p0 = th.cat(
+            [index(v_pix[i], vi_img[i, ..., 0].data, 0)[None, ...] for i in range(b)],
+            dim=0,
+        )
+        p1 = th.cat(
+            [index(v_pix[i], vi_img[i, ..., 1].data, 0)[None, ...] for i in range(b)],
+            dim=0,
+        )
+        p2 = th.cat(
+            [index(v_pix[i], vi_img[i, ..., 2].data, 0)[None, ...] for i in range(b)],
+            dim=0,
+        )
+
+        v10 = p1 - p0
+        v02 = p0 - p2
+        n = th.cross(v02, v10)
+
+        px, py = th.meshgrid(
+            th.arange(img.shape[-2], device=v_pix.device),
+            th.arange(img.shape[-1], device=v_pix.device),
+        )
+
+        def epsclamp(x: th.Tensor) -> th.Tensor:
+            return th.where(x < 0, x.clamp(max=-1e-8), x.clamp(min=1e-8))
+
+        # pyre-fixme[53]: Captured variable `n` is not annotated.
+        # pyre-fixme[53]: Captured variable `p0` is not annotated.
+        # pyre-fixme[53]: Captured variable `px` is not annotated.
+        # pyre-fixme[53]: Captured variable `py` is not annotated.
+        # pyre-fixme[53]: Captured variable `v02` is not annotated.
+        # pyre-fixme[53]: Captured variable `v10` is not annotated.
+        def check_if_point_inside_triangle(offset_x: int, offset_y: int) -> th.Tensor:
+            _px = px + offset_x
+            _py = py + offset_y
+
+            vp0p = th.stack([p0[..., 0] - _px, p0[..., 1] - _py], dim=-1) / epsclamp(
+                n[..., 2:3]
+            )
+
+            bary_1 = v02[..., 0] * -vp0p[..., 1] + v02[..., 1] * vp0p[..., 0]
+            bary_2 = v10[..., 0] * -vp0p[..., 1] + v10[..., 1] * vp0p[..., 0]
+
+            return ((bary_1 > 0) & (bary_2 > 0) & ((bary_1 + bary_2) < 1))[:, None]
+
+        left_pnt_inside_right_triangle = (
+            check_if_point_inside_triangle(-1, 0)[..., :, 1:]
+            & x_mask
+            & x_both_triangles
+        )
+        right_pnt_inside_left_triangle = (
+            check_if_point_inside_triangle(1, 0)[..., :, :-1]
+            & x_mask
+            & x_both_triangles
+        )
+        down_pnt_inside_up_triangle = (
+            check_if_point_inside_triangle(0, 1)[..., :-1, :]
+            & y_mask
+            & y_both_triangles
+        )
+        up_pnt_inside_down_triangle = (
+            check_if_point_inside_triangle(0, -1)[..., 1:, :]
+            & y_mask
+            & y_both_triangles
+        )
+
+        horizontal_intersection = (
+            right_pnt_inside_left_triangle & left_pnt_inside_right_triangle
+        )
+        vertical_intersection = (
+            down_pnt_inside_up_triangle & up_pnt_inside_down_triangle
+        )
+
+        left_hangs_over_right = left_pnt_inside_right_triangle & (
+            ~right_pnt_inside_left_triangle
+        )
+        right_hangs_over_left = right_pnt_inside_left_triangle & (
+            ~left_pnt_inside_right_triangle
+        )
+
+        up_hangs_over_down = up_pnt_inside_down_triangle & (
+            ~down_pnt_inside_up_triangle
+        )
+        down_hangs_over_up = down_pnt_inside_up_triangle & (
+            ~up_pnt_inside_down_triangle
+        )
+
+        x_grad *= x_mask
+        y_grad *= y_mask
+
+        grad_output_x = 0.5 * (grad_output[:, :, :, 1:] + grad_output[:, :, :, :-1])
+        grad_output_y = 0.5 * (grad_output[:, :, 1:, :] + grad_output[:, :, :-1, :])
+
+        x_grad = (x_grad * grad_output_x).sum(dim=1)
+        y_grad = (y_grad * grad_output_y).sum(dim=1)
+
+        x_grad_no_int = x_grad * (~horizontal_intersection[:, 0])
+        y_grad_no_int = y_grad * (~vertical_intersection[:, 0])
+
+        x_grad_spread = th.zeros(
+            *x_grad_no_int.shape[:1],
+            x_grad_no_int.shape[1],
+            y_grad_no_int.shape[2],
+            dtype=x_grad_no_int.dtype,
+            device=x_grad_no_int.device,
+        )
+        x_grad_spread[:, :, :-1] = x_grad_no_int * (~right_hangs_over_left[:, 0])
+        x_grad_spread[:, :, 1:] += x_grad_no_int * (~left_hangs_over_right[:, 0])
+
+        y_grad_spread = th.zeros_like(x_grad_spread)
+        y_grad_spread[:, :-1, :] = y_grad_no_int * (~down_hangs_over_up[:, 0])
+        y_grad_spread[:, 1:, :] += y_grad_no_int * (~up_hangs_over_down[:, 0])
+
+        # Intersections. Compute border sliding gradients
+        #################################################
+        z_grad_spread = th.zeros_like(x_grad_spread)
+        x_grad_int = x_grad * horizontal_intersection[:, 0]
+        y_grad_int = y_grad * vertical_intersection[:, 0]
+
+        n = thf.normalize(n, dim=-1)
+        n = n.permute(0, 3, 1, 2)
+
+        n_left = n[..., :, :-1]
+        n_right = n[..., :, 1:]
+        n_up = n[..., :-1, :]
+        n_down = n[..., 1:, :]
+
+        def get_dp_db(v_varying: th.Tensor, v_fixed: th.Tensor) -> th.Tensor:
+            """
+            Computes derivative of the point position with respect to edge displacement
+            See drtk/src/edge_grad/edge_grad_kernel.cu
+            Please refer to the paper "Rasterized Edge Gradients: Handling Discontinuities Differentiably"
+            for details.
+            """
+
+            v_varying = thf.normalize(v_varying, dim=1)
+            v_fixed = thf.normalize(v_fixed, dim=1)
+            b = th.stack([-v_fixed[:, 1], v_fixed[:, 0]], dim=1)
+            b_dot_varying = (b * v_varying).sum(dim=1, keepdim=True)
+            return b[:, 0:1] / epsclamp(b_dot_varying) * v_varying
+
+        # We compute partial derivatives by fixing one triangle and moving the
+        # other, and then vice versa.
+
+        # Left triangle moves, right fixed
+        dp_dbx = get_dp_db(n_left[:, [0, 2]], -n_right[:, [0, 2]])
+        x_grad_spread[:, :, :-1] += x_grad_int * dp_dbx[:, 0]
+        z_grad_spread[:, :, :-1] += x_grad_int * dp_dbx[:, 1]
+
+        # Left triangle fixed, right moves
+        dp_dbx = get_dp_db(n_right[:, [0, 2]], n_left[:, [0, 2]])
+        x_grad_spread[:, :, 1:] += x_grad_int * dp_dbx[:, 0]
+        z_grad_spread[:, :, 1:] += x_grad_int * dp_dbx[:, 1]
+
+        # Upper triangle moves, lower fixed
+        dp_dby = get_dp_db(n_up[:, [1, 2]], -n_down[:, [1, 2]])
+        y_grad_spread[:, :-1, :] += y_grad_int * dp_dby[:, 0]
+        z_grad_spread[:, :-1, :] += y_grad_int * dp_dby[:, 1]
+
+        # Lower triangle moves, upper fixed
+        dp_dby = get_dp_db(n_down[:, [1, 2]], n_up[:, [1, 2]])
+        y_grad_spread[:, 1:, :] += y_grad_int * dp_dby[:, 0]
+        z_grad_spread[:, 1:, :] += y_grad_int * dp_dby[:, 1]
+
+        m = index_img == -1
+        x_grad_spread[m] = 0.0
+        y_grad_spread[m] = 0.0
+
+        grad_v_pix = -th.stack([x_grad_spread, y_grad_spread, z_grad_spread], dim=3)
+
+        return None, grad_v_pix, None, grad_output, None

drtk/edge_grad_ext.pyi

+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+from torch import Tensor
+
+def edge_grad_estimator(
+    v_pix: Tensor,
+    v_pix_img: Tensor,
+    vi: Tensor,
+    img: Tensor,
+    index_img: Tensor,
+) -> Tensor: ...

drtk/interpolate.py

+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+import torch as th
+from drtk import interpolate_ext
+
+th.ops.load_library(interpolate_ext.__file__)
+
+
+def interpolate(
+    vert_attributes: th.Tensor,
+    vi: th.Tensor,
+    index_img: th.Tensor,
+    bary_img: th.Tensor,
+) -> th.Tensor:
+    """
+    Performs a linear interpolation of the vertex attributes given the barycentric coordinates
+    Args:
+        vert_attributes (th.Tensor):  vertex attribute tensor
+            N x V x C
+        vi (th.Tensor): face vertex index list tensor
+            V x 3
+        index_img (th.Tensor): index image tensor
+            N x H x W
+        bary_img (th.Tensor): 3D barycentric coordinate image tensor
+            N x 3 x H x W
+    Returns:
+        A tensor with interpolated vertex attributes with a shape [N, C, H, W]
+    Note:
+        1. The default of `channels_last` is set to true to make this function backward compatible.
+        Please consider using the argument `channels_last` instead of permuting the result afterward.
+        2. By default, the output is not contiguous. Make sure you cal .contiguous() if that is a requirement.
+    """
+    return th.ops.interpolate_ext.interpolate(vert_attributes, vi, index_img, bary_img)
+
+
+def interpolate_ref(
+    vert_attributes: th.Tensor,
+    vi: th.Tensor,
+    index_img: th.Tensor,
+    bary_img: th.Tensor,
+) -> th.Tensor:
+    """
+    A reference implementation for `interpolate`. See the doc string from `interpolate`
+    """
+
+    # Run reference implementation in double precision to get as good reference as possible
+    orig_dtype = vert_attributes.dtype
+    vert_attributes = vert_attributes.double()
+    bary_img = bary_img.double()
+    b = vert_attributes.shape[0]
+    iimg_clamped = index_img.clamp(min=0).long()
+    vi_img = vi[iimg_clamped].long()
+
+    v_img = th.gather(
+        vert_attributes,
+        1,
+        vi_img.view(b, -1, 1).expand(-1, -1, vert_attributes.shape[-1]),
+    )
+    v_img = (
+        v_img.view(*vi_img.shape[:3], 3, vert_attributes.shape[-1])
+        .permute(0, 3, 1, 2, 4)
+        .contiguous()
+    )
+    v_img = (v_img * bary_img[..., None]).sum(dim=1)
+
+    # Do the sweep of value in the range -1..1 for the `index_img == -1` region, like
+    # in is done in the CUDA kernel.
+    undefined_region = th.stack(
+        [
+            (
+                th.arange(0, index_img.shape[-1], device=vert_attributes.device)[
+                    None, ...
+                ]
+                .repeat(index_img.shape[-2], 1)
+                .double()
+                * 2.0
+                + 1.0
+            )
+            / index_img.shape[-1]
+            - 1.0,
+            (
+                th.arange(0, index_img.shape[-2], device=vert_attributes.device)[
+                    ..., None
+                ]
+                .repeat(1, index_img.shape[-1])
+                .double()
+                * 2.0
+                + 1.0
+            )
+            / index_img.shape[-2]
+            - 1.0,
+        ],
+        dim=2,
+    )
+    undefined_region = th.tile(
+        undefined_region[None], dims=[1, 1, 1, (vert_attributes.shape[-1] + 1) // 2]
+    )[:, :, :, : vert_attributes.shape[-1]]
+    v_img[index_img == -1] = undefined_region.expand(index_img.shape[0], -1, -1, -1)[
+        index_img == -1, :
+    ]
+
+    return v_img.permute(0, 3, 1, 2).to(orig_dtype)

drtk/interpolate_ext.pyi

+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+from torch import Tensor
+
+def interpolate(
+    vert_attributes: Tensor,
+    vi: Tensor,
+    index_img: Tensor,
+    bary_img: Tensor,
+) -> Tensor: ...

drtk/mipmap_grid_sample.py

+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+from typing import List, Optional, Tuple
+
+import torch as th
+import torch.nn.functional as thf
+from drtk import mipmap_grid_sampler_ext
+
+th.ops.load_library(mipmap_grid_sampler_ext.__file__)
+
+
+def mipmap_grid_sample(
+    input: List[th.Tensor],
+    grid: th.Tensor,
+    vt_dxdy_img: th.Tensor,
+    max_aniso: int,
+    mode: str = "bilinear",
+    padding_mode: str = "zeros",
+    align_corners: Optional[bool] = None,
+    force_max_aniso: Optional[bool] = False,
+    clip_grad: Optional[bool] = False,
+) -> th.Tensor:
+    """
+    Similar to torch.nn.functional.grid_sample, but supports mipmapping and anisotropic filtering which mimics
+    graphics hardware behaviour.
+    Currently, only spatial (4-D) inputs are supported.
+    No nearest filtering.
+
+    Args:
+        input (List[th.Tensor]): A list of tensors which represents a mipmap pyramid of a texture. List should
+            contain highest resolution texture at index 0.
+            All subsequent elements of the list should contain miplayers that are twice smaller, but is not a
+            hard requirement. Also there is no hard requirement for all mip levels to be present.
+            List of tensors of shape [N x C x H_in x W_in], [N x C x H_in / 2 x W_in / 2] ... [N x C x 1 x 1]
+
+        grid (th.Tensor): uv coordinates field according to which the inputs are sampled.
+            N x H_out x W_out x 2
+
+        vt_dxdy_img (th.Tensor): Jacobian of uv coordinates field with respect to pixel position.
+            N x H_out x W_out x 2 x 2
+
+        max_aniso (int): Maximum number of samples for anisotropic filtering.
+
+        mode (str): Interpolation mode to calculate output values. Same as grid_sample, but without 'nearest'.
+            'bilinear' | 'bicubic'. Default: 'bilinear'
+
+        padding_mode (str): padding mode for outside grid values
+            'zeros' | 'border' | 'reflection'. Default: 'zeros'
+
+        align_corners (bool, optional): Same as in grid_sample. Default: False.
+
+        force_max_aniso (bool, optional): Contols number of samples for anisotropic filtering.
+            When it is False, the extension will work similarly to the graphics hardware implementation,
+            e.i. it does only needed number of samples, which could be anything from 1 to max_aniso depending
+            on the ratio of max and min uv gradient. When force_max_aniso is True, the extension always
+            produces max_aniso number of samples. However this mode is only intended for
+            debugging/tesing/comparing with reference implementation and it is not intended for the real
+            usage. Default: False.
+
+        clip_grad (bool, optional): Controls behaviour when mipmap layer is missing.
+            This mipmap implementation allows using not full mipmap pyramid, e.g. you can have only 2, 3 or 4
+            layers for a texture of size 1024 instead of all 10. Hardware require all of the layers of the
+            pyramid to be present. Such relaxed requirement leads to ambiguity when it needs to sample from
+            the missing layer. The flag clip_grad only impacts the cases when needed layers from the mipmap
+            pyramid are missing. In this scenario:
+                - when False: it will sample from the last available layer. This will lead to aliasing and
+                  sparsely placed taps. The downside is that it may sample from arbitrary far regions of
+                  the texture.
+                - when True: it will sample from the last available layer, but it will adjust the step size
+                  to match the sampling rate of the available layer. This will lead to aliasing but densely
+                  placed taps. Which in turn forbids it to sample from arbitrary far regions of the texture.
+
+    Returns:
+        output (Tensor): Result of sampling from inputs given the grid.
+            N x C x H_out x W_out
+    """
+
+    if mode != "bilinear" and mode != "bicubic":
+        raise ValueError(
+            "mipmap_grid_sample(): only 'bilinear' and 'bicubic' modes are supported "
+            "but got: '{}'".format(mode)
+        )
+    if (
+        padding_mode != "zeros"
+        and padding_mode != "border"
+        and padding_mode != "reflection"
+    ):
+        raise ValueError(
+            "mipmap_grid_sample(): expected padding_mode "
+            "to be 'zeros', 'border', or 'reflection', "
+            "but got: '{}'".format(padding_mode)
+        )
+    if mode == "bilinear":
+        mode_enum = 0
+    elif mode == "nearest":  # not supported
+        mode_enum = 1
+    else:  # mode == 'bicubic'
+        mode_enum = 2
+
+    if padding_mode == "zeros":
+        padding_mode_enum = 0
+    elif padding_mode == "border":
+        padding_mode_enum = 1
+    else:  # padding_mode == 'reflection'
+        padding_mode_enum = 2
+
+    if align_corners is None:
+        align_corners = False
+
+    return th.ops.mipmap_grid_sampler_ext.mipmap_grid_sampler_2d(
+        input,
+        grid,
+        vt_dxdy_img,
+        max_aniso,
+        padding_mode_enum,
+        mode_enum,
+        align_corners,
+        force_max_aniso,
+        clip_grad,
+    )
+
+
+def mipmap_grid_sample_ref(
+    input: List[th.Tensor],
+    grid: th.Tensor,
+    vt_dxdy_img: th.Tensor,
+    max_aniso: int,
+    mode: str = "bilinear",
+    padding_mode: str = "border",
+    align_corners: Optional[bool] = False,
+    high_quality: bool = False,
+) -> th.Tensor:
+    """
+    A reference implementation for `mipmap_grid_sample`. See the doc string from `mipmap_grid_sample`
+    The CUDA version of `mipmap_grid_sample` should behave the same as this referense implementation when:
+        - `force_max_aniso` argument of `mipmap_grid_sample` is set to True
+        - `clip_grad` argument of `mipmap_grid_sample` is set to False
+        - `high_quality` argument of `mipmap_grid_sample_ref` is set to False
+    """
+
+    q = len(input)
+    base_level_size = list(input[0].shape[2:])
+
+    with th.no_grad():
+        # vt_dxdy_img has assumes uv in range 0..1.
+        # For the comutations below we need to convert from normalized units to pixels
+        size = th.as_tensor(
+            [base_level_size[0], base_level_size[1]],
+            dtype=th.float32,
+            device=vt_dxdy_img.device,
+        )
+        vt_dxdy_img_pixel = vt_dxdy_img * size[None, None, None, :]
+
+        # x and y gradients magnitudes. We then need to find direction of maximum gradient and
+        # minimum gradients direction (principal axis)
+        px, py = _compute_grad_magnitude(vt_dxdy_img_pixel)
+
+        if not high_quality:
+            # This is what hardware implements.
+            # We assume that maximum and minimum direction is either x or y.
+            # This assumption is a quite grude approximation
+            p_max = th.max(px, py)
+            p_min = th.min(px, py) if max_aniso != 1 else None
+        else:
+            # Instead, a more correct way would be to find principal axis using SVD
+            # Note this is not practical as it is very slow
+            u, s, v = th.linalg.svd(vt_dxdy_img_pixel)
+            p_max = s[..., 0]
+            p_min = s[..., 1]
+
+        # Given the max and min gradients, select mipmap levels (assumes linear interpolation
+        # between mipmaps)
+        d1, a = _mipmap_selection(q, p_max, p_min, max_aniso)
+
+        if max_aniso != 1:
+            if not high_quality:
+                uv_step_x = vt_dxdy_img[..., 0, :]
+                uv_step_y = vt_dxdy_img[..., 1, :]
+
+                with th.enable_grad():
+                    uv_ext_x = th.cat(
+                        [
+                            grid + uv_step_x * ((j + 1) / (max_aniso + 1) * 2.0 - 1.0)
+                            for j in range(max_aniso)
+                        ],
+                        dim=0,
+                    )
+                    uv_ext_y = th.cat(
+                        [
+                            grid + uv_step_y * ((j + 1) / (max_aniso + 1) * 2.0 - 1.0)
+                            for j in range(max_aniso)
+                        ],
+                        dim=0,
+                    )
+                    uv_ext = th.where(
+                        (px > py)[..., None].tile(max_aniso, 1, 1, 2),
+                        uv_ext_x,
+                        uv_ext_y,
+                    )
+            else:
+                # From SVD we have direction of the maximum gradient in the uv space.
+                # We ntegrate along this direction using `max_aniso` samples
+                uv_step = (v[..., 0, :] * s[..., 0:1]) / size[None, None, None, :]
+                with th.enable_grad():
+                    uv_ext = th.cat(
+                        [
+                            grid + uv_step * ((j + 1) / (max_aniso + 1) * 2.0 - 1.0)
+                            for j in range(max_aniso)
+                        ],
+                        dim=0,
+                    )
+
+    result = []
+    if max_aniso == 1:
+        for level in input:
+            r = thf.grid_sample(
+                level,
+                grid,
+                mode=mode,
+                padding_mode=padding_mode,
+                align_corners=align_corners,
+            )
+            result.append(r)
+    else:
+        for level in input:
+            r = thf.grid_sample(
+                th.tile(level, (max_aniso, 1, 1, 1)),
+                uv_ext,
+                mode=mode,
+                padding_mode=padding_mode,
+                align_corners=align_corners,
+            )
+            r = r.view(max_aniso, r.shape[0] // max_aniso, *r.shape[1:]).mean(dim=0)
+            result.append(r)
+    return _combine_sampled_mipmaps(result, d1, a)
+
+
+def _mipmap_selection(
+    q: int,
+    p_max: th.Tensor,
+    p_min: Optional[th.Tensor],
+    max_aniso: int = 1,
+) -> Tuple[th.Tensor, th.Tensor]:
+    if max_aniso != 1:
+        # See p.255 of OpenGL Core Profile
+        # N = min(ceil(Pmax/Pmin),maxAniso)
+        N = th.clamp(th.ceil(p_max / p_min), max=max_aniso)
+        N[th.isnan(N)] = 1
+
+        # Lambda' = log2(Pmax/N)
+        lambda_ = th.log2(p_max / N)
+    else:
+        lambda_ = th.log2(p_max)
+
+    lambda_[th.isinf(lambda_)] = 0
+
+    # See eq. 8.15, 8.16
+    # Substract small number (1e-6) so that `lambda_` is always < q - 1
+    lambda_ = th.clamp(lambda_, min=0, max=q - 1 - 1e-6)
+    d1 = th.floor(lambda_).long()
+    a = lambda_ - d1.float()
+    return d1, a
+
+
+def _compute_grad_magnitude(vt_dxdy_img: th.Tensor) -> Tuple[th.Tensor, th.Tensor]:
+    # See p.255 of OpenGL Core Profile
+    # Px = sqrt(dudx^2 + dvdx^2)
+    # Py = sqrt(dudy^2 + dvdy^2)
+    px = th.norm(vt_dxdy_img[..., 0, :], dim=-1)
+    py = th.norm(vt_dxdy_img[..., 1, :], dim=-1)
+    return px, py
+
+
+def _combine_sampled_mipmaps(
+    sampled_mipmaps: List[th.Tensor], d1: th.Tensor, a: th.Tensor
+) -> th.Tensor:
+    if len(sampled_mipmaps) == 1:
+        return sampled_mipmaps[0]
+    sampled_mipmaps = th.stack(sampled_mipmaps, dim=0)
+    indices = th.cat([d1[None, :, None], d1[None, :, None] + 1], dim=0)
+    samples = th.gather(
+        sampled_mipmaps,
+        dim=0,
+        index=indices.expand(-1, *sampled_mipmaps.shape[1:3], -1, -1),
+    )
+    # Interpolate two nearest mipmaps. See p.266
+    return th.lerp(samples[0], samples[1], a[:, None])

drtk/mipmap_grid_sample_ext.pyi

+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+from typing import List
+
+from torch import Tensor
+
+def mipmap_grid_sample_2d(
+    x: List[Tensor],
+    grid: Tensor,
+    vt_dxdy_img: Tensor,
+    max_aniso: int,
+    padding_mode: int,
+    interpolation_mode: int,
+    align_corners: bool,
+    force_max_ansio: bool,
+    clip_grad: bool,
+) -> Tensor: ...

drtk/msi.py

+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+import torch as th
+from drtk import msi_ext
+
+th.ops.load_library(msi_ext.__file__)
+
+
+def msi(
+    ray_o: th.Tensor,
+    ray_d: th.Tensor,
+    texture: th.Tensor,
+    sub_step_count: int = 2,
+    min_inv_r: float = 1.0,
+    max_inv_r: float = 0.0,
+    stop_thresh: float = 1e-7,
+) -> th.Tensor:
+    """
+    Renders a Multi-Sphere Image which is similar to the one described in "NeRF++: Analyzing and Improving
+    Neural Radiance Fields"
+    The implementation performs bilinear sampling in the spatial dimensions of each layer and cubic between
+    the layers.
+
+    Args:
+        ray_o (th.Tensor): Ray origins [N x 3]
+
+        ray_d (th.Tensor): Ray directions [N x 3]
+
+        texture (th.Tensor): The MSI texture [L x 4 x H x W], where L - number of layers.
+            The first 3 channels are the color channels, and the fourth one is the sigma (transmittance)
+            channel (negative log of alpha).
+
+        sub_step_count (int, optional): Rate of the subsampling of the layers. Default is 2.
+
+        min_inv_r (float, optional): Inverse of the minimum sphere radius. Default is 1 for unit radius.
+
+        max_inv_r (float, optional): Inverse of the maximum sphere radius. Default is 0 for infinite radius.
+
+        stop_thresh (bool, optional): The threshold for early ray termination when the accumulated
+            transmittance goes beyond the specified value.
+
+    Returns:
+        output (Tensor): Result of the sampled MSI. First three channels are the color channels, and the 4th
+        one is sigma (transmittance). [N x 4]
+    """
+    return th.ops.msi_ext.msi(
+        ray_o, ray_d, texture, sub_step_count, min_inv_r, max_inv_r, stop_thresh
+    )

drtk/msi_ext.pyi

+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+from torch import Tensor
+
+def msi(
+    ray_o: th.Tensor,
+    ray_d: th.Tensor,
+    texture: th.Tensor,
+    sub_step_count: int,
+    min_inv_r: float,
+    max_inv_r: float,
+    stop_thresh: float,
+) -> th.Tensor: ...

drtk/rasterize.py

+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+from typing import Tuple
+
+import torch as th
+
+from drtk import rasterize_ext
+
+th.ops.load_library(rasterize_ext.__file__)
+
+
+def rasterize(
+    v: th.Tensor,
+    vi: th.Tensor,
+    height: int,
+    width: int,
+    wireframe: bool = False,
+) -> th.Tensor:
+    """
+    Rasterizes a mesh defined by v and vi.
+
+    Args:
+        v (th.Tensor):  vertex positions. The first two components are the projected vertex's location (x, y)
+        on the image plane. The coordinates of the top left corner are (-0.5, -0.5), and the coordinates of
+        the bottom right corner are (width - 0.5, height - 0.5). The z component is expected to be in the
+        camera space coordinate frame (before projection).
+            N x V x 3
+
+        vi (th.Tensor): face vertex index list tensor. The most significant nibble of vi is reserved for
+        controlling visibility of the edges in wireframe mode. In non-wireframe mode, content of the most
+        significant nibble of vi will be ignored.
+            V x 3
+
+        height (int): height of the image in pixels.
+
+        width (int): width of the image in pixels.
+
+        wireframe (bool): If False (default), rasterizes triangles. If True, rasterizes lines, where the most
+        significant nibble of vi is reinterpreted as a bit field controlling the visibility of the edges. The
+        least significant bit controls the visibility of the first edge, the second bit controls the
+        visibility of the second edge, and the third bit controls the visibility of the third edge. This
+        limits the maximum number of vertices to 268435455.
+
+    Returns:
+        The rasterized image of triangle indices which is represented with an index tensor of a shape
+        [N, H, W] of type int32 that stores a triangle ID for each pixel. If a triangle covers a pixel and is
+        the closest triangle to the camera, then the pixel will have the ID of that triangle. If no triangles
+        cover a pixel, then its ID is -1.
+
+    Note:
+        This function is not differentiable. The gradients should be computed with `edge_grad_estimator`
+        instead.
+    """
+    _, index_img = th.ops.rasterize_ext.rasterize(v, vi, height, width, wireframe)
+    return index_img
+
+
+def rasterize_with_depth(
+    v: th.Tensor,
+    vi: th.Tensor,
+    height: int,
+    width: int,
+    wireframe: bool = False,
+) -> Tuple[th.Tensor, th.Tensor]:
+    """
+    Same as `rasterize` function, additionally returns depth image. Internally it uses the same implementation
+    as the rasterize function which still computes depth but does not return depth.
+
+    Notes:
+        The function is not differentiable, including the depth output.
+
+    The split is done intentionally to hide the depth image from the user as it is not differentiable which
+    may cause errors if assumed otherwise. Instead, the`barycentrics` function should be used instead to
+    compute the differentiable version of depth.
+
+    However, we still provide `rasterize_with_depth` which returns non-differentiable depth which could allow
+    to avoid call to `barycentrics` function when differentiability is not required.
+
+    Returns:
+        The rasterized image of triangle indices of shape [N, H, W] and a depth image of shape [N, H, W].
+        Values in of pixels in the depth image not covered by any pixel are 0.
+
+    """
+    depth_img, index_img = th.ops.rasterize_ext.rasterize(
+        v, vi, height, width, wireframe
+    )
+    return depth_img, index_img

drtk/rasterize_ext.pyi

+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+from typing import List
+
+from torch import Tensor
+
+def rasterize(
+    v: Tensor,
+    vi: Tensor,
+    height: int,
+    width: int,
+) -> List[Tensor]: ...

drtk/render.py

+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+from functools import lru_cache
+from typing import Tuple
+
+import torch as th
+
+from drtk import render_ext
+
+th.ops.load_library(render_ext.__file__)
+
+
+def render(
+    v: th.Tensor,
+    vi: th.Tensor,
+    index_img: th.Tensor,
+) -> Tuple[th.Tensor, th.Tensor]:
+    depth_img, bary_img = th.ops.render_ext.render(v, vi, index_img)
+    return depth_img, bary_img
+
+
+def index(x, I, dim):
+    target_shape = [*x.shape]
+    del target_shape[dim]
+    target_shape[dim:dim] = [*I.shape]
+    return x.index_select(dim, I.view(-1)).reshape(target_shape)
+
+
+@lru_cache
+def _get_grid(width: int, height: int, device: th.device):
+    return th.stack(
+        th.meshgrid(th.arange(height, device=device), th.arange(width, device=device))[
+            ::-1
+        ],
+        dim=2,
+    )
+
+
+def render_ref(
+    v: th.Tensor, vi: th.Tensor, index_img: th.Tensor
+) -> Tuple[th.Tensor, th.Tensor]:
+    # Run reference implementation in double precision to get as good reference as possible
+
+    orig_dtype = v.dtype
+    v = v.double()
+    b = v.shape[0]
+    mask = th.ne(index_img, -1)
+    float_mask = mask.float()[:, None]
+    index_img_clamped = index_img.clamp(min=0).long()
+
+    grid = _get_grid(index_img.shape[-1], index_img.shape[-2], device=v.device)
+
+    # compute barycentric coordinates
+    vi_img = index(vi, index_img_clamped, 0).long()
+    v_img0 = th.cat(
+        [index(v[i], vi_img[i, ..., 0].data, 0)[None, ...] for i in range(b)], dim=0
+    )
+    v_img1 = th.cat(
+        [index(v[i], vi_img[i, ..., 1].data, 0)[None, ...] for i in range(b)], dim=0
+    )
+    v_img2 = th.cat(
+        [index(v[i], vi_img[i, ..., 2].data, 0)[None, ...] for i in range(b)], dim=0
+    )
+
+    vec01 = v_img1 - v_img0
+    vec02 = v_img2 - v_img0
+    vec12 = v_img2 - v_img1
+
+    def epsclamp(x: th.Tensor) -> th.Tensor:
+        return th.where(x < 0, x.clamp(max=-1e-16), x.clamp(min=1e-16))
+
+    det = vec01[..., 0] * vec02[..., 1] - vec01[..., 1] * vec02[..., 0]
+    denominator = epsclamp(det)
+
+    vp0 = grid[None, ...] - v_img0[..., :2]
+    vp1 = grid[None, ...] - v_img1[..., :2]
+
+    lambda_0 = (vp1[..., 1] * vec12[..., 0] - vp1[..., 0] * vec12[..., 1]) / denominator
+    lambda_1 = (vp0[..., 0] * vec02[..., 1] - vp0[..., 1] * vec02[..., 0]) / denominator
+    lambda_2 = (vp0[..., 1] * vec01[..., 0] - vp0[..., 0] * vec01[..., 1]) / denominator
+
+    assert th.allclose(lambda_0 + lambda_1 + lambda_2, th.ones_like(lambda_0))
+
+    lambda_0_mul_w0 = lambda_0 / epsclamp(v_img0[:, :, :, 2])
+    lambda_1_mul_w1 = lambda_1 / epsclamp(v_img1[:, :, :, 2])
+    lambda_2_mul_w2 = lambda_2 / epsclamp(v_img2[:, :, :, 2])
+    zi = 1.0 / epsclamp(lambda_0_mul_w0 + lambda_1_mul_w1 + lambda_2_mul_w2)
+
+    bary_0 = lambda_0_mul_w0 * zi
+    bary_1 = lambda_1_mul_w1 * zi
+    bary_2 = lambda_2_mul_w2 * zi
+
+    bary_img = (
+        th.cat(
+            (bary_0[:, None, :, :], bary_1[:, None, :, :], bary_2[:, None, :, :]),
+            dim=1,
+        )
+        * float_mask
+    )
+
+    depth_img = zi * float_mask[:, 0]
+
+    return depth_img.to(orig_dtype), bary_img.to(orig_dtype)

drtk/render_ext.pyi

+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+from typing import List
+
+from torch import Tensor
+
+def render(
+    v: Tensor,
+    vi: Tensor,
+    index_img: Tensor,
+) -> List[Tensor]: ...

drtk/screen_space_uv_derivative.py

+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+from typing import Optional, Sequence
+
+import torch as th
+
+from drtk.interpolate import interpolate
+
+from drtk.utils import face_dpdt, project_points_grad
+
+
+def screen_space_uv_derivative(
+    v: th.Tensor,
+    vt: th.Tensor,
+    vi: th.Tensor,
+    vti: th.Tensor,
+    index_img: th.Tensor,
+    bary_img: th.Tensor,
+    mask: th.Tensor,
+    campos: th.Tensor,
+    camrot: th.Tensor,
+    focal: th.Tensor,
+    dist_mode: Optional[Sequence[str]] = None,
+    dist_coeff: Optional[th.Tensor] = None,
+) -> th.Tensor:
+    """
+    Computes per-pixel uv derivative - vt_dxdy_img with respect to the pixel-space position.
+    vt_dxdy_img is an image of 2x2 Jacobian matrices of the form: [[du/dx, dv/dx],
+                                                                   [du/dy, dv/dy]]
+    Shape: N x H x W x 2 x 2
+    """
+
+    dpdt_t, vf = face_dpdt(v, vt, vi.long(), vti.long())
+
+    # make three of this for each vertex of the face
+    dpdt_t = dpdt_t[:, :, None]
+    dpdt_t = dpdt_t.expand(-1, -1, 3, -1, -1)
+
+    # UV grads are not quite well interpolated with barycentrics
+    # We computes uv grads at per-pixel basis. For faster compute it is better to use CUDA kernel
+
+    # make new index list, because gradients have discontinuities and we do not want to interpolate them
+    vi_dis = th.arange(0, 3 * vi.shape[0], dtype=th.int32, device=v.device).view(-1, 3)
+    dpdt_t_img = interpolate(
+        dpdt_t.reshape(dpdt_t.shape[0], dpdt_t.shape[1] * dpdt_t.shape[2], -1),
+        vi_dis,
+        index_img,
+        bary_img,
+    ).permute(0, 2, 3, 1)
+    dpdt_t_img = dpdt_t_img.view(*dpdt_t_img.shape[:3], 2, 3)
+    vf_img = interpolate(
+        vf.reshape(vf.shape[0], vf.shape[1] * vf.shape[2], -1),
+        vi_dis,
+        index_img,
+        bary_img,
+    ).permute(0, 2, 3, 1)
+    # duplicate vertex position vector for u and v
+    vf_img = vf_img[:, :, :, None].expand(-1, -1, -1, 2, -1)
+    # Compute 2D pixel-space gradients (d p_pix / dt)^T.
+    dp_pix_dt_t_img = project_points_grad(
+        dpdt_t_img.reshape(v.shape[0], -1, 3),
+        vf_img.reshape(v.shape[0], -1, 3),
+        campos,
+        camrot,
+        focal,
+        dist_mode,
+        dist_coeff,
+    )
+    # Uncollapse dimension. The result is (d p_pix / dt)^T
+    # Where: dp_pix_dt[..., i, j] = d p_pix[j] / dt[i]
+    dp_pix_dt_t_img = dp_pix_dt_t_img.view(*dpdt_t_img.shape[:3], 2, 2)
+    # Inverse Jacobian: (dt / d p_pix)^T = ((d p_pix / dt)^T)^-1
+    # Where: dt_dp_pix_t[..., i, j] = dt[j] / dp_pix[i]
+    vt_dxdy_img, _ = th.linalg.inv_ex(dp_pix_dt_t_img)
+    # pyre-fixme[16] Undefined attribute: `th.Tensor` has no attribute `__invert__`.
+    vt_dxdy_img[~mask, :, :] = 0
+    return vt_dxdy_img