Topology-based geometry representation to support geometric reasoning

The geometry of parts and components is traditionally represented in the computer using some form of coordinate data in three dimensional Euclidean space. While such a representation facilitates operations such as graphics transformations and mass property calculations, it is too low a level of detail to enable deep reasoning based on an understanding of the geometric relationships that exist in the part. It is suggested here that an application-specific hierarchic representation of part geometry, where geometric details at lower levels of the hierarchy are embedded within the higher-level topological description of the object, provides a powerful framework for enabling such geometric reasoning capabilities. Such a representation can facilitate high-level topological queries, linguistic means for human-machine interaction, development of an intelligent interactive design aid, and an extension to more complex geometries. It can provide a language for expressing the appropriate domain heuristics, thereby leading to a smooth interface between the heuristics and the geometry representation. The paper analyzes these issues and illustrates the concepts in the context of blocker design, which is encountered in the process of forging die design.