A Comprehensive Evaluation of the DFP Method for Geometric Constraint Solving Algorithm Using PlaneGCS

Abstract

The development of open-source geometric constraint solvers is a pressing research topic, as commercially available solvers may not meet the research requirements. In this paper, we examine the use of numerical methods in PlaneGCS, an open-source geometric constraint solver within the FreeCAD CAD software. Our study focuses on PlaneGCS's constraint solving algorithms and the three built-in single-subsystem solving methods: BFGS, LM, and Dogleg. Based on our research results, the DFP method was implemented in PlaneGCS and was successfully verified in FreeCAD. To evaluate the performance of the algorithms, we used the solving state of the constraint system as a test criterion, and analysed their solving time, adaptability, and number of iterations. Our results highlight the performance differences between the algorithms and provide empirical guidance for selection of constraint solving algorithms and research based on open-source geometric constraint solvers.

Keywords

• algorithm testing
• DFP method
• numerical constraint solving algorithm
• open-source geometric constraint solver