A subdivision method for modeling N-degree curves and surfaces

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

Abstract

During the last decade surface subdivision methods are leading in both industry and research interest due to their ability to generate surfaces defined by an arbitrary topology of vertices. A number of such methods have been developed and are used today in Computer Aided Geometric Design (CAGD). Most of them generate cubic or quadratic surfaces. Methods based on cubic polynomials are the most popular ones since they provide second derivative continuity (C2) on the surface, whereas quadratic methods have only C 1 continuity. There are many good reasons for using cubic polynomials: their theory is simple; they have a satisfactory C2 continuity; and they are easier to be developed. This paper presents a curve and surface subdivision method with n-degree polynomials. In the case of surfaces the method is generalized to handle surfaces defined by arbitrary topological meshes of vertices. It provides Cn-1 continuity and is fairly easy to be developed.

Original languageEnglish
Title of host publicationApplication of Mathematics in Technical and Natural Sciences - 3rd International Conference, AMiTaNS'11
Pages114-121
Number of pages8
Volume1404
DOIs
Publication statusPublished - 2011
Event3rd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'11 - Albena, Bulgaria
Duration: 20 Jun 201125 Jun 2011

Other

Other3rd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'11
CountryBulgaria
CityAlbena
Period20/06/1125/06/11

Keywords

  • Curve and surface fitting
  • geometric modeling
  • splines
  • surface subdivision

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  • Cite this

    Savva, A., & Stylianou, V. (2011). A subdivision method for modeling N-degree curves and surfaces. In Application of Mathematics in Technical and Natural Sciences - 3rd International Conference, AMiTaNS'11 (Vol. 1404, pp. 114-121) https://doi.org/10.1063/1.3659910