The equivalence problem for vectors in the two-dimensional Minkowski spacetime and its application to Bezier curves
Abstract
Let M(1,1) be the group of all transformations of the 2-dimensional Minkowski spacetime M generated by all pseudo-orthogonal transformations and parallel translations of M. Let SM(1,1) is the proper subgroup of M(1,1) and SL(1,1) is the ortochoronous proper subgroup of M(1,1). In this paper, conditions for the equivalence of two systems of vectors {x_{1},x_{2},..., x_{m}} and {y_{1},y_{2},..., y_{m}} are obtained for groups G=M(1,1), SM(1,1), SL(1,1). Finally, we present a necessary and sufficient conditions for judging whether Bezier curves in M of degree m are G-equivalent.
Copyright © 2016 Idris Oren. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
I. Oren, The equivalence problem for vectors in the two-dimensional Minkowski spacetime and its application to Bezier curves, J. Math. Comput. Sci. 6 (2016), 1–21.
BibTeX
@article{Oren2016,
author = {Oren, Idris},
title = {The equivalence problem for vectors in the two-dimensional Minkowski spacetime and its application to Bezier curves},
journal = {J. Math. Comput. Sci.},
volume = {6},
year = {2016},
pages = {1--21},
doi = {}
}