The Non-Degenerate Dupin Cyclides in the Space of Spheres Using Geometric Algebra

被引：4

作者：

Druoton, Lucie ^{[1
,2
,3
]}

Fuchs, Laurent ^{[4
]}

Garnier, Lionel ^{[3
]}

Langevin, Remi ^{[2
]}

机构：

[1] CEA, DAM, F-21120 Valduc, Is Sur Tille, France

[2] Univ Burgundy, CNRS, UMR 5584, Inst Math Bourgogne,Fac Mirande, F-21000 Dijon, France

[3] Univ Burgundy, CNRS, UMR 6306, LE2I,Fac Mirande, F-21000 Dijon, France

[4] Univ Poitiers, CNRS, UMR 7252, XLIM SIC,SP2MI, F-86962 Futuroscope, France

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2014年 / 24卷 / 02期

关键词：

Dupin cyclide; space of spheres; Conformal Geometric Algebra;

D O I：

10.1007/s00006-014-0453-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Dupin cyclides are algebraic surfaces of degree 4 discovered by the French mathematician Pierre-Charles Dupin early in the 19th century and were introduced in CAD by R. Martin in 1982. A Dupin cyclide can be defined, in two different ways, as the envelope of a oneparameter family of oriented spheres. So, it is very interesting to model the Dupin cyclides in the space of spheres, space wherein each family of spheres can be seen as a conic curve. In this paper, we model the nondegenerate Dupin cyclides and the space of spheres using Conformal Geometric Algebra. This new approach permits us to benefit from the advantages of the use of Geometric Algebra.

引用

页码：515 / 532

页数：18

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