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Theory of Minkowski-Lorentz Spaces


Canal surface; Circles space; Spheres space


Introduction of Minkowski-Lorentz spaces to simplify Euclidean 2- or 3-dimensional problems.


In this entry, the authors propose a survey on Minkowski-Lorentz spaces which are a generalization of the space-time used in Einstein’s theory, equipped of the nondegenerate indefinite quadratic form

where (x,y,z) are the spacial components of the vector \( \overrightarrow{u} \) and t is the time component of \( \overrightarrow{u} \) and c is the constant of the speed of light. Computer Graphics computations involving families of circles or spheres are simplified in this space. One can note that a canal surface of the usual 3D Euclidean affine space is represented in the suitable Minkowski-Lorentz space by a curve. Moreover, in order to realize a G1-blend between two canal surfaces, it is enough to make a G1 join between two curves. From an affine Euclidean space E n of dimension nwhere its usual value in Computer...

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Correspondence to Lionel Garnier .

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Garnier, L., Bécar, JP., Druoton, L., Fuchs, L., Morin, G. (2018). Theory of Minkowski-Lorentz Spaces. In: Lee, N. (eds) Encyclopedia of Computer Graphics and Games. Springer, Cham.

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