Mean value Bézier maps

Torsten Langer, Alexander Belyaev, Hans Peter Seidel

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

4 Citations (Scopus)

Abstract

Bernstein polynomials are a classical tool in Computer Aided Design to create smooth maps with a high degree of local control. They are used for the construction of Bézier surfaces, free-form deformations, and many other applications. However, classical Bernstein polynomials are only defined for simplices and parallelepipeds. These can in general not directly capture the shape of arbitrary objects. Instead, a tessellation of the desired domain has to be done first. We construct smooth maps on arbitrary sets of polytopes such that the restriction to each of the polytopes is a Bernstein polynomial in mean value coordinates (or any other generalized barycentric coordinates). In particular, we show how smooth transitions between different domain polytopes can be ensured. © 2008 Springer-Verlag Berlin Heidelberg.

Original languageEnglish
Title of host publicationAdvances in Geometric Modeling and Processing : 5th International Conference, GMP 2008, Proceedings
Pages231-243
Number of pages13
Volume4975 LNCS
DOIs
Publication statusPublished - 2008
Event5th International Conference on Geometric Modeling and Processing - Hangzhou, China
Duration: 23 Apr 200825 Apr 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4975 LNCS
ISSN (Print)0302-9743

Conference

Conference5th International Conference on Geometric Modeling and Processing
Abbreviated titleGMP 2008
CountryChina
CityHangzhou
Period23/04/0825/04/08

Keywords

  • Bézier surfaces
  • Computer Graphics
  • Curves and Surfaces
  • Mathematical foundations of CAGD
  • Mean value coordinates
  • Shape representation

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  • Cite this

    Langer, T., Belyaev, A., & Seidel, H. P. (2008). Mean value Bézier maps. In Advances in Geometric Modeling and Processing : 5th International Conference, GMP 2008, Proceedings (Vol. 4975 LNCS, pp. 231-243). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4975 LNCS). https://doi.org/10.1007/978-3-540-79246-8_18