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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.





Author: Lilian Aveneau - Eric Andres - Frédéric Mora -

Source: https://hal.archives-ouvertes.fr/



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