Similarity Detection for Free-Form Parametric Models

Abstract

In this article, we propose a framework for detecting local similarities in free-form parametric models, in particular on B-Splines or NURBS based B-reps: patches similar up to an approximated isometry are identified. Many recent articles have tackled similarity detection on 3D objects, in particular on 3D meshes. The parametric B-splines, or NURBS models are standard in the CAD (Computer Aided Design) industry, and similarity detection opens the door to interesting applications in this domain, such as model editing, objects comparison or efficient coding. Our contributions are twofold: we adapt the current technique called votes transformation space for parametric surfaces and we improve the identification of isometries. First, an orientation technique independent of the parameterization permits to identify direct versus indirect transformations. Second, the validation step is generalized to extend to the whole B-rep. Then, by classifying the isometries according to their fixed points, we simplify the clustering step. We also apply an unsupervised spectral clustering method which improves the results but also automatically estimates the number of clusters.