The Hybrid Edge: a Topological Data Structure for Vertically Integrated Geometric Modeling

Generalizing the computational geometric support for the representation of designed artifacts over multiple different levels of symbolic abstraction (e.g. sketches, solid modelling, and drafting) is discussed. First, the need for integrating the representation and manipulation of points, lines, polygons and solids for the purpose of facilitating the design of artifacts at many levels of design abstractions established. Second, a vertically integrated model that supports the representation and manipulation of points, lines, polygons, and solids without redundancy, is presented. The particular roles of the operators and the operandi are discussed, along with their hierarchical integration. The utility of the model is demonstrated in performing operations that involve multiple different levels of data abstraction, such as splitting solids at an arbitrary polygon inscribed on their boundary. Finally, a particular implementation of the integrated model is presented. This implementation is based on the Hybrid Edge, a derivative from Baumgart's Winged Edge and Eastman's Split Edge models. The Hybrid Edge distinguishes between the roles of edges as topological adjacency information carriers and their role as carriers of directionality information. This distinction permits the Hybrid Edge to handle the different combinations of adjacency and directionality requirements imposed by different abstraction levels in the integrated model