Theory of Minkowski-Lorentz Spaces

Synonyms

Canal surface; Circles space; Spheres space

Definitions

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

Introduction

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 ${\mathrm{E}}_n$ of dimension nwhere its usual value in Computer...