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A unified algebraic framework for fast and precise planar swept volumes and Minkowski sums.
- Source :
-
Computer Aided Geometric Design . Jun2022, Vol. 96, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- The topic of swept-volumes is well-studied. Yet, the high degree of underlying mathematical and computational complexity has prevented a general implementation which accepts freeform input, even for the planar case. Likewise for Minkowski sums. This paper proposes a unified approach to the two related problems, in 2D, via algebraic modeling of the underlying mathematical constraints. Handling self-intersections in the envelope has been the special focus of this work. Algebraic modeling results in a high degree of numerical precision and guarantee of topological correctness. A top-down computational strategy leads to a numerically robust algorithm. Further, an auxiliary point-cloud representation of the swept-volume yields a significant boost in computational efficiency. The robustness and numerical stability of our approach are demonstrated by tens of thousands of examples, generated from an implementation of our algorithm. • A novel, unified framework is proposed for swept volumes and Minkowski sums. • Algebraic modeling is employed to achieve high degree of numerical precision. • A top-down approach leads to a numerically robust algorithm. • Tens of thousands of examples demonstrate the robustness of our approach. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MATHEMATICAL models
*COMPUTATIONAL complexity
Subjects
Details
- Language :
- English
- ISSN :
- 01678396
- Volume :
- 96
- Database :
- Academic Search Index
- Journal :
- Computer Aided Geometric Design
- Publication Type :
- Academic Journal
- Accession number :
- 157711694
- Full Text :
- https://doi.org/10.1016/j.cagd.2022.102107