Topological and Geometric Consistency in Boundary Representations of Solid Models of Mechanical Components

Abstract

This paper describes a method of verifying the consistency (i.e., agreement) between the topology and geometry of boundary representation (B-rep) solid models of mechanical components. This verification is well-suited for implementation as an algorithm and has been implemented as such in a polyhedral boundary representation solid modeling system (Jablokow, 1989). This technique and algorithm is important in the design of mechanical components for design documentation, integration with analysis and manufacturing applications, and design data exchange between solid modeling systems. Information regarding boundary representations has typically divided into the geometry and topology. It is important that the two are consistent for a valid solid model. In this work the genus of a solid model of an object is calculated topologically and geometrically and then compared to verify the consistency of the solid model. The genus of an object gives insight as to the geometric complexity of the object. This is equivalent to verifying the Gauss-Bonnet Theorem for the model, and is discussed in the paper.