3D Geometric Constraint Solving for Integrated Variational Design

A modified directed graph method is proposed to solve hybrid geometric constraint systems including 3D geometric constraints and assembly constraints derived from integrated variational design.Firstly,several basic constraints are defined to describe diverse geometric constraints,and two abstract dual objects are used to encapsulate various geometric entities.Then,the hybrid geometric constraint digraph model is established by introducing the irreversible directed arc to represent the intrinsic dependency between two interrelated objects.Subsequently,the optimal decomposition of geometric constraint system is achieved by optimal processing of the constraint digraph,from which the efficient parallel solving sequence can be obtained.Finally,a series of examples are presented to demonstrate the correctness and effectiveness of the proposed approach.