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

## TL;DR

This paper introduces a geometric perturbation method to analyze free motions in variational B-rep models for direct 3D modeling, extending the witness method to handle complex boundary representations in STEP format.

## Contribution

It proposes a novel geometric perturbation approach that generalizes the witness method for systematic analysis of free motions in variational B-rep models.

## Key findings

- Effective analysis of free motions demonstrated through case studies
- Method generalizes existing techniques to standard STEP B-rep models
- Improves understanding of geometric constraints in direct modeling

## Abstract

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.

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Source: https://tomesphere.com/paper/1903.07770