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Geometric Modelling, Numerical Simulation, and Optimization pp 163–183Cite as

Real-Time Algebraic Surface Visualization

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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.

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Author information

Authors and Affiliations

  1. Center of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, NO-0316, Oslo, Norway

    Johan Simon Seland

  2. Applied Mathematics, SINTEF ICT, P.O. Box 124, Blindern, NO-0314, Oslo, Norway

    Tor Dokken

Authors
  1. Johan Simon Seland
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  2. Tor Dokken
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Editor information

Editors and Affiliations

  1. Applied Mathematics, SINTEF ICT, P.O. Box 124, Blindern, NO-0314, Oslo, Norway

    Geir Hasle , Knut-Andreas Lie  & Ewald Quak ,  & 

  2. Centre for Nonlinear Studies (CENS) Institute of Cybernetics, Tallinn University of Technology, Akadeemia tee 21, EE-12618, Tallinn, Estonia

    Ewald Quak

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Seland, J.S., Dokken, T. (2007). Real-Time Algebraic Surface Visualization. In: Hasle, G., Lie, KA., Quak, E. (eds) Geometric Modelling, Numerical Simulation, and Optimization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68783-2_6

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