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978-3-8439-2051-3, Reihe Informatik
Advanced Distance Metrics Defined on Complex Geometries
196 Seiten, Dissertation Universität Erlangen-Nürnberg (2014), Softcover, A5
In almost all modern manufacturing processes, the use of Computer Aided Design (CAD) has become an inevitable part. Before any real part is produced, everything is virtually designed and assembled in a computer and modern hardware allows for realistic visualizations, simulations and measurements on these virtual 3D data. As a consequence, there is a constant need for efficient algorithms to handle these complex tasks, creating a large amount of challenges in the field of computer graphics.
This theses particularly deals with distance metrics defined on complex 3D data. The first part handles the computation of shortest paths on the surface of polygonal meshes under a complex, hybrid metric. In this metric, the paths are not strictly constrained to stay on the surface, as in the geodesic metric, but are allowed to take Euclidean shortcuts through the air up to a certain maximum distance.
The computation of shortest paths under consideration of this metric can assist the quality assurance of electric assemblies, where individual components, carrying different electric potentials, have to comply with strict regulations concerning their distance. We provide the fundamental theoretical basis for the underlying distance metric and introduce an efficient algorithm for the computation of shortest paths.
In the second part of the thesis, the term "distance metric" gets a more abstract meaning. We examine geometric as well as feature-based distances between entire 3D objects and thereby create similarity measures which allow for shape-based object retrieval, the determination of symmetries and the efficient matching of similar parts in complex geometries. These are important tasks in the automatic analysis of 3D shapes and facilitate the administration of large 3D databases.