Differentiable Voxelization of Surface Representations

SIGGRAPH 2026 Conference Proceedings
Tobias Djuren · Ugo Finnendahl* · Markus Worchel* · Hendrik Meyer · Marc Alexa

*Equal contribution (shared second author)

About

This repository contains the official implementation of the paper "Differentiable Voxelization of Surface Representations". The paper introduces an efficient method for converting the surface representation of a shape, in particular a triangle mesh, into a volumetric representation in a differentiable manner. The resulting voxel grid of winding numbers makes it straightforward to define volumetric objectives that drive the optimization of the underlying surface (e.g. for intersection avoidance).

The algorithms are implement in C++, targeting the CPU (a CUDA GPU implementation is work in progress). The dvx package exposes these algorithms to Python, where they are readily usable with PyTorch.

Getting Started

The easiest way to install the Python package is via pip

pip install dvx-python

Optional: Test the Installation

To test the installation, run

pip install numpy pytest svgpathtools trimesh
python -m pytest ./tests -v

Some tests may be skipped, depending on the availability of packages.

Usage

This is a minimal PyTorch example that demonstrates triangle mesh voxelization in $\mathbb{R}^3$:

import dvx.torch as dvx

# Triangle mesh as indexed face set within the [-1,1]^3 cube (v: vertices, f: faces)
v, f = ...
v.requires_grad_(True)

# Resolution of the voxel grid (same resolution in all dimensions)
n = 64 

# Voxelize the mesh -> returns a grid with shape (n,n,n) of smoothed winding numbers
voxels = dvx.voxelize(n, v, f)

loss = some_loss(voxels)
loss.backward() # Gradients are propagated to the mesh vertices v

For more usage examples, see the demos folder. The demos include examples for bandsaw cutting, space tilings in $\mathbb{R}^3$ and for self-intersection resolving to generate results similar to the ones in the paper.

Conventions for Coordinates and Data Layout

The volume considered for voxelization is the $[-1, 1]^d$ cube, where $d$ is the dimensionality of the space. The input shape (e.g., a triangle mesh) must be fully contained within this volume, otherwise the output is undefined $\space^1$.

The voxel grid covers this volume exactly, which means it reaches from $(-1, -1, \ldots, -1) \in \mathbb{R}^d$ to $(1, 1, \ldots, 1) \in \mathbb{R}^d$. We use standard naming conventions to denote points in space: $(x, y)$ for $\mathbb{R}^2$ and $(x, y, z)$ for $\mathbb{R}^3$.

For two-dimensional input and a resolution of $w$ in x-direction and $h$ in y-direction, the result is an array of shape $(h, w)$. Similarly, for three-dimensional input with the same resolutions in x- and y-directions, and a resolution of $d$ in z-direction, the result is an array of shape $(d, h, w)$. The voxel data is stored in row-major order, i.e., the index in x-direction is the fastest varying, followed by y and z.

The value of a voxel is the smoothed winding number field evaluated at its center.

The following sketch summarizes our conventions for coordinates and the data layout in $\mathbb{R}^2$ and $\mathbb{R}^3$:

$\space^1$ This restriction is not a limitation of the method itself, but rather a consequence of how the closed-form integration is currently implemented. It will be lifted in a future release.

License and Copyright

The code in this repository is provided under a BSD 3-clause license.

Citation

If you use this code or our method in your research, please cite our paper:

@inproceedings{Djuren:2026:DVX,
    author = {Djuren, Tobias and Finnendahl, Ugo and Worchel, Markus and Meyer, Hendrik and Alexa, Marc},
    title = {Differentiable Voxelization of Surface Representations},
    year = {2026},
    isbn = {9798400725548},
    publisher = {Association for Computing Machinery},
    address = {New York, NY, USA},
    url = {https://doi.org/10.1145/3799902.3811203},
    doi = {10.1145/3799902.3811203},
    booktitle = {Proceedings of the Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers},
    articleno = {22},
    numpages = {12},
    keywords = {differentiable voxelization, efficient voxelization, smoothed winding numbers, shape optimization},
    location = {
    },
    series = {SIGGRAPH Conference Papers '26}
}

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dvx-python 0.1.0

Differentiable Voxelization of Surface Representations

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BLAKE2b-256	`ce6fdbeb46371f58096a5c32df8ce096222762025e0fc3e55588a3c2f8659e32`

Algorithm	Hash digest
SHA256	`ed336f6bf9d92f1aa3b3440e4ff5cc5d93c5a6023b1e42f6f0debce58e2375d7`
MD5	`6156576ba525c773d4f6525efd2a0798`
BLAKE2b-256	`0b903d0a8545ee4e0b73e2b5efb46d53728db3068841bb533cf3c0df4d5a7ed9`