Patchwork: A compact representation for 3D polygonal shapes

TL;DR

Patchwork is a mathematically grounded, compact shape representation for 2D and 3D geometries that enables efficient fitting, high precision approximation, and supports inside-outside classification, suitable for geometric learning and reconstruction.

Contribution

We introduce Patchwork, a novel, compact, and mathematically rigorous shape representation with an efficient optimization scheme and regularization for high-precision modeling.

Findings

Requires fewer parameters than existing methods

Achieves high-precision shape approximation

Supports fast fitting and inside-outside classification

Abstract

We introduce Patchwork, a new general-purpose shape representation capable of modeling 2D and 3D geometry with a small number of parameters. Patchwork is grounded in a rigorous mathematical framework, providing provable complexity bounds and the ability to approximate arbitrary shapes with arbitrary precision in any dimension. We propose an efficient gradient-based optimization scheme to fit Patchwork representations to 2D and 3D data, along with a novel regularization loss that progressively prunes redundant elements, yielding high compactness after convergence. Our approach offers fast fitting performance, a fraction of the required parameters compared to existing alternatives, and native support for inside-outside classification, making it a versatile and compact representation for geometric learning and reconstruction tasks, with future potential for 3D generation. Our implementation is available at: https://github.com/Ankbzpx/patchwork-experiment.