Symmetries of canal surfaces and Dupin cyclides

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2018Embargo end date: 01 Jan 2016 Norway English Publisher:Elsevier BVJournal:Computer Aided Geometric Design, volume 59, pages 68-85 (issn: 0167-8396,

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Authors: Juan Gerardo Alcázar; Heidi E. I. Dahl; Georg Muntingh;

doi: 10.1016/j.cagd.2017.10.001 , 10.48550/arxiv.1611.06768

arXiv: 1611.06768

handle: 11250/2476556

Symmetries of canal surfaces and Dupin cyclides

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Abstract

We develop a characterization for the existence of symmetries of canal surfaces defined by a rational spine curve and rational radius function. In turn, this characterization inspires an algorithm for computing the symmetries of such canal surfaces. For Dupin cyclides in canonical form, we apply the characterization to derive an intrinsic description of their symmetries and symmetry groups, which gives rise to a method for computing the symmetries of a Dupin cyclide not necessarily in canonical form. As a final application, we discuss the construction of patches and blends of rational canal surfaces with a prescribed symmetry.

27 pages

Country

Norway

Related Organizations

SINTEF AS
Norway
University of Alcalá
Spain

Keywords

Computer Science - Symbolic Computation, Computational Geometry (cs.CG), FOS: Computer and information sciences, blending, canal surfaces, algorithm, rational surfaces, Symbolic Computation (cs.SC), 14Q10, 68W30, symmetries of surfaces, rational spine curve, Computer-aided design (modeling of curves and surfaces), Mathematics - Algebraic Geometry, Dupin cyclides, FOS: Mathematics, Computer Science - Computational Geometry, Algebraic Geometry (math.AG)

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