1Real-Time Algebraic Surface Visualization

Summary. We demonstrate a ray tracing type technique for rendering algebraic surfaces us-ing 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 func-tions 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, de-scribing 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