Real-Time Algebraic Surface Visualization

Johan Simon Seland () and Tor Dokken ()
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Johan Simon Seland: University of Oslo, Center of Mathematics for Applications
Tor Dokken: SINTEF ICT, Applied Mathematics

A chapter in Geometric Modelling, Numerical Simulation, and Optimization, 2007, pp 163-183 from Springer

Abstract: Abstract We demonstrate a ray tracing type technique for rendering algebraic surfaces using programmable graphics hardware (GPUs). Our approach allows for real-time exploration and manipulation of arbitrary real algebraic surfaces, with no pre-processing step, except that of a possible change of polynomial basis. The algorithm is based on the blossoming principle of trivariate Bernstein-Bézier functions over a tetrahedron. By computing the blossom of the function describing the surface with respect to each ray, we obtain the coefficients of a univariate Bernstein polynomial, describing the surface’s value along each ray. We then use Bézier subdivision to find the first root of the curve along each ray to display the surface. These computations are performed in parallel for all rays and executed on a GPU.

Keywords: GPU; algebraic surface; ray tracing; root finding; blossoming (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/978-3-540-68783-2_6

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