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Implementation of "Large Steps in Inverse Rendering of Geometry"


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ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia), December 2021.
Baptiste Nicolet · Alec Jacobson · Wenzel Jakob

Paper PDF Project Page

Table of Contents
  1. Installation
  2. Parameterization
  3. Running the experiments
  4. Repository structure
  5. License
  6. Citation
  7. Acknowledgments


This repository contains both the operators needed to use our parameterization of vertex positions of meshes as well as the code for the experiments we show in the paper.

Parameterization package installation

If you are only interested in using our parameterization in an existing (PyTorch based) pipeline, we have made it available to install via pip:

pip install largesteps

This will install the largesteps module. This only contains the parameterization logic implemented as a PyTorch custom operator. See the tutorial for an example use case.

Cloning the repository

Otherwise, if you want to reproduce the experiments from the paper, you can clone this repo and install the module locally.

git clone --recursive
cd large-steps-pytorch
pip install .

The experiments in this repository depend on PyTorch. Please follow instructions on the PyTorch website to install it.

To install nvdiffrast and the Botsch-Kobbelt remesher, which are provided as submodules, please run the script.

nvdiffrast relies on the cudatoolkit-dev package to compile modules at runtime. To install it with Anaconda:

conda install -c conda-forge cudatoolkit-dev

To install the other dependencies needed to run the experiments, also run:

pip install -r requirements.txt

⚠️ On Linux, nvdiffrast requires using g++ to compile some PyTorch extensions, make sure this is your default compiler:

export CC=gcc && CXX=g++

Rendering the figures will also require installing blender. You can specify the name of the blender executable you wish to use in scripts/

Downloading the scenes

The scenes for the experiments can be downloaded here. Please extract the archive at the toplevel of this repository.


In a nutshell, our parameterization can be obtained in just a few lines:

# Given tensors v and f containing vertex positions and faces
from largesteps.geometry import laplacian_uniform, compute_matrix
from largesteps.parameterize import to_differential, from_differential

# Compute the system matrix
M = compute_matrix(v, f, lambda_=10)

# Parameterize
u = to_differential(M, v)

compute_matrix returns the parameterization matrix M = I + λL. This function takes another parameter, alpha, which leads to a slightly different, but equivalent, formula for the matrix: M = (1-α)I + αL, with α ∈ [0,1[. With this formula, the scale of the matrix M has the same order of magnitude regardless of α.

M = compute_matrix(L, alpha=0.9)

Then, vertex coordinates can be retrieved as:

v = from_differential(u, M, method='Cholesky')

This will in practice perform a cache lookup for a solver associated to the matrix M (and instantiate one if not found) and solve the linear system Mv = u. Further calls to from_differential with the same matrix will use the solver stored in the cache. Since this operation is implemented as a differentiable PyTorch operation, there is nothing more to be done to optimize this parameterization.

Running the experiments

You can then run the experiments in the figures folder, in which each subfolder corresponds to a figure in the paper, and contains two files:

  • contains the script to run the experiment and write the output to the directory specified in scripts/
  • figure.ipynb: contains the script generating the figure, assuming has been run before and the output written to the directory specified in scripts/

We provide the scripts for the following figures:

  • Fig. 1 -> teaser
  • Fig. 3 -> multiscale
  • Fig. 5 -> remeshing
  • Fig. 6 -> reg_fail
  • Fig. 7 -> comparison
  • Fig. 8 -> viewpoints
  • Fig. 9 -> influence

⚠️ Several experiments are equal-time comparisons ran on a Linux Ryzen 3990X workstation with a TITAN RTX graphics card. In order to ensure reproducibility, we have frozen the step counts for each method in these experiments.

Repository structure

The largesteps folder contains the parameterization module made available via pip. It contains:

  • contains the laplacian matrix computation.
  • contains the AdamUniform optimizer implementation
  • contains the actual parameterization code, implemented as a to_differential and from_differential function.
  • contains the Cholesky and conjugate gradients solvers used to convert parameterized coordinates back to vertex coordinates.

Other functions used for the experiments are included in the scripts folder:

  • utility script to render meshes inside blender
  • contains paths to different useful folders (scenes, remesher, etc.)
  • utility geometry functions (normals computation, edge length, etc.)
  • PLY mesh file loading
  • XML scene file loading
  • contains the main optimization function
  • utility scipt to a import redundant modules for the figures
  • contains the rendering logic, using nvdiffrast


This code is provided under a 3-clause BSD license that can be found in the LICENSE file. By using, distributing, or contributing to this project, you agree to the terms and conditions of this license.


If you use this code for academic research, please cite our method using the following BibTeX entry:

    author = "Nicolet, Baptiste and Jacobson, Alec and Jakob, Wenzel",
    title = "Large Steps in Inverse Rendering of Geometry",
    journal = "ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia)",
    volume = "40",
    number = "6",
    year = "2021",
    month = dec,
    doi = "10.1145/3478513.3480501",
    url = ""


The authors would like to thank Delio Vicini for early discussions about this project, Silvia Sellán for sharing her remeshing implementation and help for the figures, as well as Hsueh-Ti Derek Liu for his advice in making the figures. Also, thanks to Miguel Crespo for making this README template.