Construction of smooth branching surfaces using T-splines
| Autor: | K.V. Kostas, Panagiotis Kaklis, A. I. Ginnis |
|---|---|
| Přispěvatelé: | National Technical University of Athens [Athens] (NTUA), Nazarbayev University [Kazakhstan], University of Strathclyde [Glasgow], AlgebRe, geOmetrie, Modelisation et AlgoriTHmes (AROMATH), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-National and Kapodistrian University of Athens (NKUA) |
| Rok vydání: | 2017 |
| Předmět: |
Surface (mathematics)
discrete Fréchet distance Geometry 02 engineering and technology T-splines 01 natural sciences Branching surface Industrial and Manufacturing Engineering Planar Euclidean geometry 0202 electrical engineering electronic engineering information engineering Mathematics::Metric Geometry [INFO]Computer Science [cs] surrounding curve Voronoi diagram 0101 mathematics Representation (mathematics) Finite set Mathematics Smoothness 020207 software engineering [INFO.INFO-IA]Computer Science [cs]/Computer Aided Engineering Computer Graphics and Computer-Aided Design Weighted Voronoi diagram Computer Science Applications 010101 applied mathematics |
| Zdroj: | Computer-Aided Design. 92:22-32 |
| ISSN: | 0010-4485 |
| Popis: | The request for designing or reconstructing objects from planar cross sections arises in various applications, ranging from CAD to GIS and Medical Imaging. The present work focuses on the one-to-many branching problem, where one of the planes can be populated with many, possibly tortuous and densely packed, contours. The proposed method combines the proximity information offered by the Euclidean Voronoi diagram with the concept of surrounding curve, introduced inGabrielides etal. (2007), and T-splines technologySederberg etal. (2003) for securing a flexible and portable representation. Our algorithm delivers a single cubic T-spline that deviates from the given contours less than a user-specified tolerance, measured via the so-called discrete Frchet distanceEiter and Mannila (1994) and is C2 everywhere except from a finite set of point-neighborhoods. Subject to minor enrichment, the algorithm is also capable to handle the many-to-many configuration as well as the global reconstruction problem involving contours on several planes. Construction of smooth branching surfaces from parallel planar contours using T-splines.Branching surface is C2 everywhere except from a finite set of point-neighborhoods where smoothness degrades to G1.Approximation of planar contours using discrete Frchet distance. |
| Databáze: | OpenAIRE |
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