Open AccessProceedings Article
Conversion of biquadratic rational Bézier surfaces into patches of particular Dupin cyclides: The torus and the double sphere
Lionel Garnier,Bertrand Belbis,Sebti Foufou +2 more
- pp 101-107
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TLDR
The condi ti s that the B́ezier surface should satisfy to be convertible are given, and a new conversion algorithm is presented to convert the torus or double sphere patch corresponding to a Bézier surface into Dupin cyclide patches.Abstract:
Toruses and double spheres are particular cases of Dupin cyc lides. In this paper, we study the conversion of rational biquadratic B́ezier surfaces into Dupin cyclide patches. We give the condi ti s that the B́ezier surface should satisfy to be convertible, and present a new conversion algorithm to cons truct the torus or double sphere patch corresponding to a giv en Bézier surface, some conversion examples are illustrated an d commented.read more
Citations
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Journal ArticleDOI
Construction of 3D Triangles on Dupin Cyclides
TL;DR: The properties of these surfaces are used to prove that three families of circles meridian arcs, parallel arcs, and Villarceau circles can be computed on every Dupin cyclide, and a geometric algorithm to compute these circles so that they define the edges of a 3D triangle on the Dupincyclide is presented.
Proceedings ArticleDOI
An Algorithm to Construct 3D Triangles with Circular Edges
TL;DR: The goal of this paper is to construct, onto a Dupin cyclide, 3D triangles with circular edges: a meridian arc, a parallel arc and a Villarceau circle arc.
References
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Book
Fundamentals of Computer Aided Geometric Design
TL;DR: A classic reference and text, this book introduces the foundations used to create an accurate computer screen image using mathematical tools.
Book
Curves and surfaces
Sebastián Montiel,Antonio Ros +1 more
TL;DR: In this paper, the authors present an introductory textbook on the differential geometry of curves and surfaces, which is suitable as an entry to a wider study of differential geometry and can also be used as a reference for a first-year course or an advanced undergraduate course.
Journal ArticleDOI
Cyclides in computer aided geometric design
TL;DR: Extensions are made to the methods of Pratt (1990) for the use of cyclides in solid modelling, with particular regard to their application as blend surfaces and new insights are given into the geometry and Bezier representation of cyclide surface patches.
Journal ArticleDOI
A menagerie of rational B-spline circles
Les A. Piegl,Wayne Tiller +1 more
TL;DR: The authors have found several other ways to represent the circle as a nonuniform rational B-spline curve, which they present.
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