# Variational B-rep Model Analysis for Direct Modeling using Geometric Perturbation

arXiv: https://arxiv.org/abs/1903.07770 · HTML: https://mlsanity.com/paper/1903.07770/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2019.

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

- [Deep Learning Assisted Optimization for 3D Reconstruction from Single 2D Line Drawings](https://mlsanity.com/paper/2209.02692/) (2022)
- [XVoxel-Based Parametric Design Optimization of Feature Models](https://mlsanity.com/paper/2303.15316/) (2023)

## Abstract (arXiv)

The very recent CAD paradigm of direct modeling gives rise to the need of processing 3D geometric constraint systems defined on boundary representation (B-rep) models. The major issue of processing such variational B-rep models (in the STEP format) is that free motions of a well-constrained model involve more than just rigid-body motions. The fundamental difficulty lies in having a systematic description of what pattern these free motions follow. This paper proposes a geometric perturbation method to study these free motions. This method is a generalization of the witness method, allowing it to directly deal with variational B-rep models represented with the standard STEP scheme. This generalization is essentially achieved by using a direct, geometric representation of the free motions, and then expressing the free motions in terms of composites of several basis motions. To demonstrate the effectiveness of the proposed method, a series of comparisons and case studies are presented.