Curvature computations for the intersection curves of hypersurfaces in Euclidean n-space

Özçetin B. M., DÜLDÜL M.

Computer Aided Geometric Design, vol.84, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 84
  • Publication Date: 2021
  • Doi Number: 10.1016/j.cagd.2020.101954
  • Journal Name: Computer Aided Geometric Design
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Curvatures, Implicit curve, Intersection curve, Transversal intersection, Willmore's method
  • Istanbul Gelisim University Affiliated: No

Abstract

The aim of this paper is to derive the curvatures and Frenet vectors of the intersection curve of (n−1) transversally intersecting hypersurfaces represented either in implicit or in parametric form in Euclidean n-space. Since the intersection of (n−1) implicit hypersurfaces defines an implicit curve in n-dimensions, the method derived for the implicit case can be considered as a partial answer to the open problem posed by Ron Goldman in 2005. Also, an application is provided for the implicit case where the results are presented by using computer codes currently produced in MATLAB.