“Extended Cross-Product” and Solution of a Linear System of Equations

Conference paper

DOI: 10.1007/978-3-319-42085-1_2

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9786)
Cite this paper as:
Skala V. (2016) “Extended Cross-Product” and Solution of a Linear System of Equations. In: Gervasi O. et al. (eds) Computational Science and Its Applications – ICCSA 2016. ICCSA 2016. Lecture Notes in Computer Science, vol 9786. Springer, Cham

Abstract

Many problems, not only in computer vision and visualization, lead to a system of linear equations Ax = 0 or Ax = b and fast and robust solution is required. A vast majority of computational problems in computer vision, visualization and computer graphics are three dimensional in principle. This paper presents equivalence of the cross–product operation and solution of a system of linear equations Ax = 0 or Ax = b using projective space representation and homogeneous coordinates. This leads to a conclusion that division operation for a solution of a system of linear equations is not required, if projective representation and homogeneous coordinates are used. An efficient solution on CPU and GPU based architectures is presented with an application to barycentric coordinates computation as well.

Keywords

Linear system of equations Extended cross-product Projective space computation Geometric algebra Scientific computation 

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of Applied SciencesUniversity of West BohemiaPlzenCzech Republic

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