An approach to applying constraints in geometric modelling

Abstract

A 2D constraint-based geometric modelling system is considered in the paper. Constraints are solved by local propagation of known states. The weakness of local propagation (it cannot solve cyclic constraints) is explained by an example. A biconnected constraint description graph is used to support local propagation. As a result of constraint solving an acyclic constraint description graph is obtained and it can be observed as a parametric description of a geometric object. The acyclic constraint description graph stores the sequence of applying constraints for generation of instances. It is shown that the time complexity of the algorithm for generation of an instance is 0(n2), where n is the number of basic geometrical elements included. In the last part of the paper we demonstrate how geometrical relations among geometrical objects can be established by the introduced geometrical constraints.