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Pré-Publication, Document De Travail Année : 2024

PENCILS AND SET OPERATORS IN 3D CGA

FAISCEAUX ET OPÉRATEURS ENSEMBLISTES DANS CGA 3D

Clément Chomicki
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Stéphane Breuils
Venceslas Biri
Vincent Nozick

Résumé

Geometric Algebra can be considered as a language that unifies mathematics, physics and computer sciences etc. Among other, CGA is of special interest for its powerful transformations and its ability to represent any hypersphere or hyperplane. Moreover, CGA is an algebra capable of representing pencils of spheres. This paper presents a reinterpretation of every objects of 3D CGA as pencils of spheres and introduces set operators on its elements (i.e. union, intersection, complement, etc). As an application, these operators are used to find the smallest tangent sphere of two skew lines.
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Dates et versions

hal-04569529 , version 1 (06-05-2024)

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  • HAL Id : hal-04569529 , version 1

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Clément Chomicki, Stéphane Breuils, Venceslas Biri, Vincent Nozick. PENCILS AND SET OPERATORS IN 3D CGA. 2024. ⟨hal-04569529⟩
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