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.

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.