# Variational Shape Approximation of Point Set Surfaces

arXiv: https://arxiv.org/abs/2005.01003 · HTML: https://mlsanity.com/paper/2005.01003/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2020.

## Built on by (most cited first, 2 of 2)

- [Split-and-Fit: Learning B-Reps via Structure-Aware Voronoi Partitioning](https://mlsanity.com/paper/2406.05261/) (2024)
- [ComplexGen: CAD Reconstruction by B-Rep Chain Complex Generation](https://mlsanity.com/paper/2205.14573/) (2022)

## Abstract (arXiv)

In this work, we present a translation of the complete pipeline for variational shape approximation (VSA) to the setting of point sets. First, we describe an explicit example for the theoretically known non-convergence of the currently available VSA approaches. The example motivates us to introduce an alternate version of VSA based on a switch operation for which we prove convergence. Second, we discuss how two operations - split and merge - can be included in a fully automatic pipeline that is in turn independent of the placement and number of initial seeds. Third and finally, we present two approaches how to obtain a simplified mesh from the output of the VSA procedure. This simplification is either based on simple plane intersection or based on a variational optimization problem. Several qualitative and quantitative results prove the relevance of our approach.