Expressing Discrete Geometry using the Conformal Model

Lilian Aveneau 1 Eric Andres 1 Frédéric Mora 2
1 XLIM-SIC - SIC
Université de Poitiers, XLIM - XLIM
2 XLIM-DMI - DMI
XLIM - XLIM
Abstract : 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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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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