Possibilities and Advantages of Rational Envelope and Minkowski Pythagorean Hodograph Curves for Circle Skinning

Kinga Kruppa, Roland Kunkli and Miklós Hoffmann
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Kinga Kruppa: Faculty of Informatics, University of Debrecen, 4028 Debrecen, Hungary
Roland Kunkli: Faculty of Informatics, University of Debrecen, 4028 Debrecen, Hungary
Miklós Hoffmann: Faculty of Informatics, University of Debrecen, 4028 Debrecen, Hungary

Mathematics, 2021, vol. 9, issue 8, 1-13

Abstract: Minkowski Pythagorean hodograph curves are widely studied in computer-aided geometric design, and several methods exist which construct Minkowski Pythagorean hodograph (MPH) curves by interpolating Hermite data in the R 2 , 1 Minkowski space. Extending the class of MPH curves, a new class of Rational Envelope (RE) curve has been introduced. These are special curves in R 2 , 1 that define rational boundaries for the corresponding domain. A method to use RE and MPH curves for skinning purposes, i.e., for circle-based modeling, has been developed recently. In this paper, we continue this study by proposing a new, more flexible way how these curves can be used for skinning a discrete set of circles. We give a thorough overview of our algorithm, and we show a significant advantage of using RE and MPH curves for skinning purposes: as opposed to traditional skinning methods, unintended intersections can be detected and eliminated efficiently.

Keywords: medial axis transform; Minkowski Pythagorean hodograph curves; Rational Envelope curves; envelope; interpolation; skinning; intersection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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