On the reducibility of geometric constraint graphs

TL;DR

This paper investigates the reducibility of geometric constraint graphs in 2D, aiming to improve understanding of solving geometric constraint systems used in CAD, mechanical design, and related fields.

Contribution

It provides a new analysis of the reducibility of geometric constraint graphs, enhancing the theoretical foundation for solving constraint systems in 2D.

Findings

Analysis of graph reducibility criteria

Identification of classes of reducible graphs

Implications for constraint solving algorithms

Abstract

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard modeling tools. In this discipline, a geometric form is specified by the relations that the components of this form must verify instead of explicitly specifying these components. The purpose of the resolution is to deduce the form satisfying all these constraints. Various methods have been proposed to solve this problem. We will focus on the so-called graph-based or graph-based methods with application to the two-dimensional space.