Oriented projective geometry
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
Geometric Algebra for Computer Graphics
Geometric Algebra for Computer Graphics
A precision of computation in the projective space
Proceedings of the 15th WSEAS international conference on Computers
| Hi-index | 0.00 |
This paper presents solutions of some selected problems that can be easily solved by the projective space representation. If the principle of duality is used, quite surprising solutions can be found and new useful theorems can be generated as well. There are many algorithms based on computation of intersection of lines, planes, barycentric coordinates etc. Those algorithms are based on representation in the Euclidean space. Sometimes, very complex mathematical notations are used to express simple mathematical solutions. It will be shown that it is not necessary to solve linear system of equations to find the intersection of two lines in the case of E2 or the intersection of three planes in the case of E3. Plücker coordinates and principle of duality are used to derive an equation of a parametric line in E3 as an intersection of two planes. This new formulation avoids division operations and increases the robustness of computation.