Geometric constraints and reasoning for geometrical CAD systems

Abstract

Many design tools, including CAD systems, are developed for improving the productivity of the design process. However, these tools are generally not powerful enough to support designers in their knowledge-intensive work. In this paper we propose a system based on geometric constraints and reasoning which is useful for enhancing the function of computers from mere tools for conventional geometric modeling. We regard design process as a series of tasks to solve design constraints. We also assume that an essential portion of design constraints is replaced by their equivalent geometrical constraints. Therefore, we think it is important for Intelligent CAD systems to have capabilities to solve geometrical design constraints. Among important geometrical design constraints, we treat dimensional constraints and discuss a method of determining the geometric properties of a geometric model by a given set of geometric constraints. We show a logical framework to represent geometric models and constraints, and a geometric reasoning mechanism to solve these constraints. Key ideas are constraint propagation at geometric element level and utilization of dependency information among geometric elements. We use ATMS (Assumption based Truth Maintenance System) techniques to keep track of dimensional dependencies derived by the propagation process. This dependency information is used for partial parametric modification, for detecting over and under constraint conditions, and for explaining constraint relationships. A default reasoning technique is also used for supplementing incomplete geometric constraints for determining the geometry.