GEOMETRIC CONSTRAINT SOLVING WITH SOLUTION SELECTORS

Current parametric CAD systems are based on solving equality type of constraints between geometric objects and parameters. This includes algebraic equations constraining the values of variables, and geometric constraints, constraining the positions of geometric objects. However, to truly represent design intent, next-generation CAD systems must also allow users to input other types of constraints such as inequality constraints. Inequality constraints are expressed as inequality expressions on variables or as geometric constraints that force geometric objects to be on specific sides or have specific orientations with respect to other objects. To solve problems involving constraints, we use a graph-based constraint solving algorithm that can be used in CAD/CAM/CAE applications. This graph-based constraint solving algorithm, called the Modified Frontier Algorithm with Solution Selection (MFASS), has been implemented at Michigan Technological University to solve equality based constraints in a CAD/CAM/CAE testbed application. The objective of this research was to investigate whether the Frontier Algorithm can be extended to solve geometry positioning problems involving systems of equality and inequality based declarations in which the inequality based declaration are used as solution selectors to choose from multiple solutions inherently arising from these systems. It is hypothesized that these systems can be decomposed by the Frontier Algorithm in a manner similar to purely equality-based constraint systems however they require tracking and iterating through solutions and in many cases may require backtracking through the solution sequence. This capitalizes on the strength of the Frontier Algorithm which solves only one small subsystem at a time with resulting short processing times compared to alternative algorithms. In this research we generate a new algorithm/DR planner for handling inequality constraints, both theoretically and through implementation in a testbed to demonstrate the working of the algorithm.