Oriented projective geometry
The Visual Computer: International Journal of Computer Graphics
Multiple view geometry in computer vision
Multiple view geometry in computer vision
Computer Graphics Using OpenGL
Computer Graphics Using OpenGL
A homogeneous formulation for lines in 3 space
SIGGRAPH '77 Proceedings of the 4th annual conference on Computer graphics and interactive techniques
A New Line Clipping Algorithm with Hardware Acceleration
CGI '04 Proceedings of the Computer Graphics International
Geometry For Computer Graphics: Formulae, Examples And Proofs
Geometry For Computer Graphics: Formulae, Examples And Proofs
Duality and intersection computation in projective space with GPU support
ASM'10 Proceedings of the 4th international conference on Applied mathematics, simulation, modelling
Duality, barycentric coordinates and intersection computation in projective space with GPU support
WSEAS Transactions on Mathematics
Duality and intersection computation in projective space with GPU support
ASM'10 Proceedings of the 4th international conference on Applied mathematics, simulation, modelling
A precision of computation in the projective space
Proceedings of the 15th WSEAS international conference on Computers
Scattered data interpolation in N-dimensional space
SITE'12 Proceedings of the 11th international conference on Telecommunications and Informatics, Proceedings of the 11th international conference on Signal Processing
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There are many geometric algorithms based on computation of intersection of lines, planes etc. Sometimes, very complex mathematical notations are used to express simple mathematical solutions, even if their formulation in the projective space offers much more simple solution. This paper presents solution of selected problems using principle of duality and projective space representation. It will be shown that alternative formulation in the projective space offers quite surprisingly simple solutions that lead to more robust and faster algorithms which are convenient for use within parallel architectures as GPU (Graphical Processor Units-NVIDIA-TESLA/Fermi) or SCC (Intel-Single-chip Cloud Computing), which can speed up solutions of numerical problems in magnitude of 10-100. It is shown that a solution of a system of linear equations is equivalent to generalized cross product, which leads with the duality principle to new algorithms. This is presented on a new formulation of a line in 3D given as intersection of two planes which is robust and fast, based on duality of Plücker coordinates. The presented approach for intersection computation is well suited especially for applications where robustness is required, e.g. large GIS/CAD/CAM systems etc.