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Poster Communications Year : 2016

The Minkowski-Lorentz space for Computer Aided Design purposes

Lionel Garnier
  • Function : Author
  • PersonId : 936575
Lucie Druoton
Rémi Langevin
  • Function : Author
  • PersonId : 1065225
Laurent Fuchs
Géraldine Morin

Abstract

This document deals with the Computer Aided Geometric Design with a short presentation of the Minkowski-Lorentz space. This space generalizes to R 5 the one used in the relativity theory. The Minkowski-Lorentz space oers a more intuitive writing of a sphere given by a point, a normal vector at the point and its curvature. It also eases the use of canal surfaces thus represented by curves. The quadratic computation in R 3 becomes linear in that space. The use of spheres, canal surfaces and their particular case known as Dupin cyclides is illustrated in a schematic seahorse. The seahorse applies the G 1 connection in the Minkowski-Lorentz space. Oriented spheres and Pencils An oriented sphere S with centre Ω and radius r > 0 satises the relationship − − → ΩM = ρ − → N with the rule ρ = r (resp. ρ = −r) if the unit normal vector − → N to the sphere at point M is getting outside (resp. inside). The power of the point M to the sphere S is dened by χ S (M) = ΩM 2 − ρ 2. The set of points solution of λ 1 χ S 1 (M) + λ 2 χ S 2 (M) = 0 is called the spheres pencil dened by S 1 et S 2 .
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Dates and versions

hal-02508282 , version 1 (14-03-2020)

Identifiers

  • HAL Id : hal-02508282 , version 1

Cite

Jean-Paul Becar, Lionel Garnier, Lucie Druoton, Rémi Langevin, Laurent Fuchs, et al.. The Minkowski-Lorentz space for Computer Aided Design purposes. Third International Conference and Expo on Computer Graphics & Animation, Nov 2016, Las Vegas, United States. 2016. ⟨hal-02508282⟩
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