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Real-Time Algebraic Surface Visualization

In: Geometric Modelling, Numerical Simulation, and Optimization

Author

Listed:
  • Johan Simon Seland

    (University of Oslo, Center of Mathematics for Applications)

  • Tor Dokken

    (SINTEF ICT, Applied Mathematics)

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.

Suggested Citation

  • Johan Simon Seland & Tor Dokken, 2007. "Real-Time Algebraic Surface Visualization," Springer Books, in: Geir Hasle & Knut-Andreas Lie & Ewald Quak (ed.), Geometric Modelling, Numerical Simulation, and Optimization, pages 163-183, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-68783-2_6
    DOI: 10.1007/978-3-540-68783-2_6
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