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Communication Dans Un Congrès Année : 2012

Expressing Discrete Geometry using the Conformal Model

Lilian Aveneau
SIC
Eric Andres
SIC
Frédéric Mora
DMI

Résumé

Primitives and transformations in discrete geometry, such as lines, circles, hyperspheres, hyperplanes, have been defined with classical linear algebra in dimension 2 and 3, leading to different expressions and algorithms. This paper explores the use of the conformal algebra to express these discrete primitives in arbitrary dimensions with a minimum of expressions and then algorithms. Starting with hyperspheres and hyperplanes, a generalization to $k$-sphere is then proposed. This gives one simple and compact formula, valid for all geometric conformal elements in R^n, from the circle to the hypersphere, and the line to the hyperplane.
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Dates et versions

hal-00865103 , version 1 (27-01-2014)

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  • HAL Id : hal-00865103 , version 1

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Lilian Aveneau, Eric Andres, Frédéric Mora. Expressing Discrete Geometry using the Conformal Model. AGACSE 2012, Jul 2012, La Rochelle, France. ⟨hal-00865103⟩
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