Applying Rational Envelope curves for skinning purposes

Kinga KRUPPA

doi:10.1631/FITEE.1900377

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Applying Rational Envelope curves for skinning purposes

Regular Papers | Updated：2022-05-19

- Applying Rational Envelope curves for skinning purposes
- 有理包络线的蒙皮应用
- Frontiers of Information Technology & Electronic Engineering Vol. 22, Issue 2, Pages: 202-209(2021)
- Affiliations：
  
  Faculty of Informatics, University of Debrecen, Debrecen H-4028, Hungary
  Doctoral School of Informatics, University of Debrecen, Debrecen H-4028, Hungary
- Author bio：
  
  [ "Kinga KRUPPA, E-mail: kruppa.kinga@inf.unideb.hu" ]
- Funds：
- DOI：10.1631/FITEE.1900377
  CLC： TP391
- Received：25 July 2019，
  
  Revised：2020-;9-16，
  
  Published Online：28 November 2020，
  
  Published：2021-02
- Accepted：
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Kinga KRUPPA. Applying Rational Envelope curves for skinning purposes[J]. Frontiers of Information Technology & Electronic Engineering, 2021, 22(2): 202-209.
DOI：

Kinga KRUPPA. Applying Rational Envelope curves for skinning purposes[J]. Frontiers of Information Technology & Electronic Engineering, 2021, 22(2): 202-209. DOI： 10.1631/FITEE.1900377.

摘要

闵可夫斯基空间中的特殊曲线如闵可夫斯基毕达哥拉斯矢端线，在计算机辅助几何设计中有着重要作用，其应用近年来得到深入研究。Bizzarri等人在2016年介绍了一类有理包络（RE）曲线；提出用于

Hermite数据的插值方法，其合成的RE曲线能对所表示的区域生成有理边界。本文提出RE曲线的一类新的应用领域--离散输入圆集的蒙皮。若未选择正确的Hermite数据进行插值，得到的RE曲线将不适合蒙皮。本文介绍一种新颖的方法，按此方法得到的包络曲线能够接触每个圆预定的接触点。因此，我们克服了因接触点位置导致不适合蒙皮的问题。本文所提方法的一个显著优点在于其边界偏移量修剪的效率，这在计算机数控方面非常有用。

Abstract

Special curves in the Minkowski space such as Minkowski Pythagorean hodograph curves play an important role in computer-aided geometric design

and their usages are thoroughly studied in recent years.

Bizzarri et al. (2016)

introduced the class of Rational Envelope (RE) curves

and an interpolation method for $G^{1}$ Hermite data was presented

where the resulting RE curve yielded a rational boundary for the represented domain. We now propose a new application area for RE curves: skinning of a discrete set of input circles. We show that if we do not choose the Hermite data correctly for interpolation

then the resulting RE curves are not suitable for skinning. We introduce a novel approach so that the obtained envelope curves touch each circle at previously defined points of contact. Thus

we overcome those problematic scenarios in which the location of touching points would not be appropriate for skinning purposes. A significant advantage of our proposed method lies in the efficiency of trimming offsets of boundaries

which is highly beneficial in computer numerical control machining.

关键词

Keywords

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