Solving Geometric Constraints by Auxiliary Constructions

This paper presents an approach for solving geometric constraint problems using auxiliary constructions. This approach converts a description of constrained geometry into a sequential ruler-and-compass construction, thereby converting variational geometry constraints into parametric geometry. The solution strategy is based on constructing auxiliary geometry and new constraints by systematically applying transformations to parts of the original constraint problem. The transformation of constraints results in creation of new constraint chains, yielding new paths in the constraint graph. Use of auxiliary constraints can thus decompose strongly connected components in the original constraint graph and provide an additional method for breaking loops due to simultaneous reference. The approach is demonstrated in two dimensions.