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About Conquer3D

Why it exists, how it is built, and what it stands on.

Motivation

A PhD side project, built to learn by building

Conquer3D is written during my PhD in Vision and Graphics. It exists to learn 3D differentiable geometry and graphics from the ground up — by implementing the algorithms rather than calling them.

Almost every component runs on the GPU: isosurface extraction, spatial acceleration structures, volumetric conversion, and the geometric primitives underneath them are written as CUDA kernels and exposed as PyTorch tensors.

Bibliography

Research papers

The algorithms implemented here come from published work. These are the primary sources.

A fast triangle-triangle intersection test

M"oller, Tomas · J. Graph. Tools · 1997

Surface mesh quality evaluation

Frey, Pascal J., Borouchaki, Houman · International Journal for Numerical Methods in Engineering · 1999

Discrete Differential-Geometry Operators for Triangulated 2-Manifolds

Meyer, Mark et al. · Visualization and Mathematics III · 2003

Dual Marching Cubes

Nielson, Gregory M. · Proceedings of the Conference on Visualization '04 · 2004

Sampling and meshing a surface with guaranteed topology and geometry

Cheng, Siu-Wing et al. · Proceedings of the Twentieth Annual Symposium on Computational Geometry · 2004

Fast, minimum storage ray/triangle intersection

M"oller, Tomas, Trumbore, Ben · ACM SIGGRAPH 2005 Courses · 2005

High quality triangulation of implicit surfaces

Shengjun Liu et al. · Ninth International Conference on Computer Aided Design and Computer Graphics (CAD-CG'05) · 2005

Manifold Dual Contouring

Schaefer, Scott, Ju, Tao, Warren, Joe · IEEE Transactions on Visualization and Computer Graphics · 2007

Edge Transformations for Improving Mesh Quality of Marching Cubes

Dietrich, Carlos A. et al. · IEEE Transactions on Visualization and Computer Graphics · 2009

Edge Transformations for Improving Mesh Quality of Marching Cubes

Dietrich, Carlos A. et al. · IEEE Transactions on Visualization and Computer Graphics · 2009

A robust feature-preserving semi-regular remeshing method triangular meshes

Chiang, Chien-Hsing, Jong, Bin-Shyan, Lin, Tsong-Wuu · Vis. Comput. · 2011

Maximizing parallelism in the construction of BVHs, octrees, and k-d trees

Karras, Tero · Proceedings of the Fourth ACM SIGGRAPH / Eurographics Conference on High-Performance Graphics · 2012

Aspect-ratio based triangular mesh smoothing

Huang, Xuan, Xu, Dianna · ACM SIGGRAPH 2017 Posters · 2017

Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement

Hu, Kaimo et al. · IEEE Transactions on Visualization and Computer Graphics · 2017

Isotropic Surface Remeshing without Large and Small Angles

Wang, Yiqun et al. · IEEE Transactions on Visualization and Computer Graphics · 2019

Surface Remeshing: A Systematic Literature Review of Methods and Research Directions

Khan, Dawar et al. · IEEE Transactions on Visualization and Computer Graphics · 2022

TetWeave: Isosurface Extraction using On-The-Fly Delaunay Tetrahedral Grids for Gradient-Based Mesh Optimization

Binninger, Alexandre et al. · ACM Trans. Graph. · 2025

Subgrid Marching Tetrahedra

Baktash, Hossein, Gillespie, Mark, Crane, Keenan · ACM Trans. Graph. · 2026

SuperFlex: Deformable Superquadrics for Point Cloud Decomposition

Tavernini, Gabriel et al. · arXiv preprint arXiv:2607.01015 · 2026

Bibliography

Books

Polygon Mesh Processing

Botsch, Mario et al. · A K Peters/CRC Press · 2010

Isosurfaces: Geometry, Topology, and Algorithms

Wenger, Rephael · A K Peters/CRC Press · 2013

Bibliography

Blog posts

Practical writing on GPU traversal and parallel construction.

Repositories

The open-source implementations this project learned from.

Using Conquer3D in your work

@software{conquer3d,
  title  = {Conquer3D: GPU-Accelerated Differentiable Geometry and Spatial Computing},
  author = {Do, Hoang Khoi},
  year   = {2025},
  url    = {https://github.com/KhoiDOO/conquer3d},
  version = {0.8.6}
}

Released under the MIT License.