On Bézier surfaces in three-dimensional Minkowski space

Authors:
H. Ugail;M. C. Márquez;A. Yılmaz
Affiliations:
Centre for Visual Computing, University of Bradford, Bradford BD7 1DP, UK;Departamento de Geometría y Topología, Universidad de Sevilla, Apdo. 1160, Sevilla 41080, Spain;Department of Mathematics, Science Faculty, Akdeniz University, Antalya 07058, Turkey
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

In this paper, we study Bezier surfaces in R"1^3 three-dimensional Minkowski space. In particular, we focus on timelike and spacelike cases for Bezier surfaces. We also deal with the Plateau-Bezier problem in R"1^3, obtaining conditions over the control net to be extremal of the Dirichlet function for both timelike and spacelike Bezier surfaces. Moreover, we provide interesting examples showing the behavior of the Plateau-Bezier problem in R"1^3 and illustrating the relationship between it and the corresponding Plateau-Bezier problem in the Euclidean space R^3.