# A Unified Differentiable Boolean Operator with Fuzzy Logic

arXiv: https://arxiv.org/abs/2407.10954 · HTML: https://mlsanity.com/paper/2407.10954/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 40 references that are in the map.
- First posted on arXiv 15 Jul 2024.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [CSGNet: Neural Shape Parser for Constructive Solid Geometry](https://mlsanity.com/paper/1712.08290/) (2017)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [UCSG-Net -- Unsupervised Discovering of Constructive Solid Geometry Tree](https://mlsanity.com/paper/2006.09102/) (2020)
- [CAPRI-Net: Learning Compact CAD Shapes with Adaptive Primitive Assembly](https://mlsanity.com/paper/2104.05652/) (2021)
- [CSG-Stump: A Learning Friendly CSG-Like Representation for Interpretable Shape Parsing](https://mlsanity.com/paper/2108.11305/) (2021)
- [Neurosymbolic Models for Computer Graphics](https://mlsanity.com/paper/2304.10320/) (2023)

## Built on by (most cited first, 1 of 1)

- [DiffCSG: Differentiable CSG via Rasterization](https://mlsanity.com/paper/2409.01421/) (2024)

## Abstract (arXiv)

This paper presents a unified differentiable boolean operator for implicit solid shape modeling using Constructive Solid Geometry (CSG). Traditional CSG relies on min, max operators to perform boolean operations on implicit shapes. But because these boolean operators are discontinuous and discrete in the choice of operations, this makes optimization over the CSG representation challenging. Drawing inspiration from fuzzy logic, we present a unified boolean operator that outputs a continuous function and is differentiable with respect to operator types. This enables optimization of both the primitives and the boolean operations employed in CSG with continuous optimization techniques, such as gradient descent. We further demonstrate that such a continuous boolean operator allows modeling of both sharp mechanical objects and smooth organic shapes with the same framework. Our proposed boolean operator opens up new possibilities for future research toward fully continuous CSG optimization.