The equivalence problem for vectors in the two-dimensional Minkowski spacetime and its application to Bezier curves

Idris Oren

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.

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How to Cite this Article:

Idris 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

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.

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