A Unified Differentiable Boolean Operator with Fuzzy Logic

TL;DR

This paper introduces a differentiable boolean operator inspired by fuzzy logic, enabling continuous optimization of implicit shape models in CSG, which traditionally relies on discontinuous operators, thus facilitating smoother shape modeling and optimization.

Contribution

A novel unified differentiable boolean operator based on fuzzy logic that allows continuous optimization of CSG models, accommodating both sharp and smooth shapes.

Findings

Enables gradient-based optimization of CSG models.

Supports modeling of both sharp and smooth shapes.

Facilitates fully continuous CSG optimization.

Abstract

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.