TY - GEN

T1 - An algorithm to construct 3D triangles with circular edges

AU - Belbis, Bertrand

AU - Garnier, Lionel

AU - Foufou, Sebti

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2009

Y1 - 2009

N2 - Dupin cyclides are non-spherical algebraic surfaces of degree 4, discovered by the French mathematician Pierre-Charles Dupin at the beginning of the 19th century. A Dupin cyclide has one parametric equation, two implicit equations, and a set of circular lines of curvature. It can be defined as the image of a torus, a cone of revolution, or a cylinder of revolution by an inversion. A torus has two families of circles: meridians and parallels. A ring torus has an additional third family, called Villarceau circles. As the image, by an inversion, of a circle is a circle or a straight line, there are three families of circles onto a Dupin cyclide too. The goal of this paper is to construct, onto a Dupin cyclide, 3D triangles with circular edges defined as a meridian arc, a parallel arc, and an arc of a Villarceau circle.

AB - Dupin cyclides are non-spherical algebraic surfaces of degree 4, discovered by the French mathematician Pierre-Charles Dupin at the beginning of the 19th century. A Dupin cyclide has one parametric equation, two implicit equations, and a set of circular lines of curvature. It can be defined as the image of a torus, a cone of revolution, or a cylinder of revolution by an inversion. A torus has two families of circles: meridians and parallels. A ring torus has an additional third family, called Villarceau circles. As the image, by an inversion, of a circle is a circle or a straight line, there are three families of circles onto a Dupin cyclide too. The goal of this paper is to construct, onto a Dupin cyclide, 3D triangles with circular edges defined as a meridian arc, a parallel arc, and an arc of a Villarceau circle.

KW - 3D triangles

KW - Circular edges

KW - Dupin cyclides

KW - Rational biquadratic Bézier surfaces

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U2 - 10.1109/SITIS.2009.13

DO - 10.1109/SITIS.2009.13

M3 - Conference contribution

AN - SCOPUS:79952085103

SN - 9780769539591

T3 - Proceedings - 5th International Conference on Signal Image Technology and Internet Based Systems, SITIS 2009

SP - 16

EP - 21

BT - Proceedings - 5th International Conference on Signal Image Technology and Internet Based Systems, SITIS 2009

PB - IEEE Computer Society

ER -