Towards a Definition of Virtual Objects Using Partial Differential Equations

Hassan Ugail, Gabriela González Castro, Alexei Sourin, Olga Sourina
2009 2009 International Conference on CyberWorlds  
We propose an efficient alternative to commonly used parametric surfaces such as NURBS surfaces for definition of complex geometry in shared virtual spaces. Our mathematical model allows to define objects by only providing coordinates of the section curves in 3-space. The resulting parametric functions allow fast calculation of the coordinates of the points on the surface of the objects. We devise an algorithm which evaluates the coefficients of these functions in real time. Given the small
more » ... of the resulting formulas and interactive rates for their calculation, we are able to efficiently use such PDE-based models for making virtual objects in shared virtual spaces. We describe the modeling framework and illustrate the proposed theoretical concepts with our function-based extension of VRML and X3D.
doi:10.1109/cw.2009.8 dblp:conf/vw/UgailCSS09 fatcat:amcgac4vcbh6tdm6wyguqk5knq