Abstract
This paper summarizes the experience of authors in solving a broad range of CAD modeling problems where the formalism of graph theory demonstrates its expressive power. Some results reported in this paper have never been published elsewhere. The set of topological and geometric heuristics backing the subgraph isomorphism algorithm is presented to achieve decent performance in our extensible feature recognition framework. By the example of sheet metal features, we show that using wise topological and geometric heuristics speeds up the search process up to interactive performance rates. For detecting CAD part’s type, we present the connected components’ analysis in the attributed adjacency graph. Our approach allows for identifying two-sided CAD parts, such as sheet metals, tubes, and flat plates. We use the notion of face transition graph for the unfoldability analysis. The basic operations on hierarchical assembly graphs are formalized in terms of graph theory for handling CAD assemblies. We describe instance singling operation that allows for addressing unique part’s occurrences in the component tree of an assembly. The presented algorithms and ideas demonstrated their efficiency and accuracy in the bunch of industrial applications developed by our team.
Highlights
Because of its inherent simplicity, the apparatus of graph theory found extensive use in industrial geometric modeling
This paper summarizes the experience of authors in solving a broad range of CAD modeling problems where the formalism of graph theory demonstrates its expressive power
By the example of sheet metal features, we show that using wise topological and geometric heuristics speeds up the search process up to interactive performance rates
Summary
Because of its inherent simplicity, the apparatus of graph theory found extensive use in industrial geometric modeling. In the boundary representation scheme [15], the topology can be expressed in the form of an acyclic directed simple graph (having no self-loops and parallel edges [4]). The topology graph determines how the primary topological elements (faces, edges, and vertices) are nested. Graph structures persist in the very foundation of the geometric modeling systems. Many other graph structures arise in the modeling systems for solving specific problems. Additional specialized graph structures serve at solving specific design problems, such as recognition of a model type or digital shape reconstruction. We review some of the commonly used graph structures following our CAD software development experience. We use the terms ”nodes,” ”vertices,” ”arcs,” and ”edges” interchangeably as the meaning of each term should be clear from the context
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