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2009
Springer

Towards a Definition of Virtual Objects Using Partial Differential Equations

12 years 4 months ago
Towards a Definition of Virtual Objects Using Partial Differential Equations
—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 size 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. Keywords-PDE; shape modeling; shared virtual spaces; X3D, VRML
Hassan Ugail, Gabriela González Castro, Ale
Added 27 Jul 2010
Updated 27 Jul 2010
Type Conference
Year 2009
Where VW
Authors Hassan Ugail, Gabriela González Castro, Alexei Sourin, Olga Sourina
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