G1-blend between a differentiable superquadric of revolution and a plane or a sphere using Dupin cyclides

Lionel Garnier, Sebti Foufou, Yohan Fougerolle

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this article, we present a method to perform G1- continuous blends between a differentiable superquadric of revolution and a plane or a sphere using Dupin cyclides. These blends are patches delimited by four lines of curvature. They allow to avoid parameterization problems that may occur when parametric surfaces are used. Rational quadratic B'ezier curves are used to approximate the principal circles of the Dupin cyclide blends and thus a complex 3D problem is now reduced to a simpler 2D problem. We present the necessary conditions to be satisfied to create the blending patches and illustrate our approach by a number of superellipsoid/plane and superellipsoid/sphere blending examples.

Original languageEnglish (US)
Title of host publicationSITIS 2008 - Proceedings of the 4th International Conference on Signal Image Technology and Internet Based Systems
Pages435-442
Number of pages8
DOIs
StatePublished - 2008
Event4th International Conference on Signal Image Technology and Internet Based Systems, SITIS 2008 - Bali, Indonesia
Duration: Nov 30 2008Dec 3 2008

Publication series

NameSITIS 2008 - Proceedings of the 4th International Conference on Signal Image Technology and Internet Based Systems

Other

Other4th International Conference on Signal Image Technology and Internet Based Systems, SITIS 2008
CountryIndonesia
CityBali
Period11/30/0812/3/08

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Software

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    Garnier, L., Foufou, S., & Fougerolle, Y. (2008). G1-blend between a differentiable superquadric of revolution and a plane or a sphere using Dupin cyclides. In SITIS 2008 - Proceedings of the 4th International Conference on Signal Image Technology and Internet Based Systems (pp. 435-442). [4725838] (SITIS 2008 - Proceedings of the 4th International Conference on Signal Image Technology and Internet Based Systems). https://doi.org/10.1109/SITIS.2008.73