RealSurf { A GPU-based Realtime Ray Caster for Algebraic Surfaces
Abstract
We present a tool for the realtime visualization and animation of algebraic surfaces of moderate degree through GPU-based ray cast- ing. The overall ray casting task in the visualization is divided into a CPU-based preprocessing phase and a massive parallel GPU-based ray-surface intersection phase. The preprocessing phase compiles the surface equation into a shader program, which is afterwards used repeatedly during the realtime visualization. The shader pro- gram calculates for each ray a reduction of the trivariate surface representation into an univariate polynomial equation, calculates the real roots of that polynomial utilizing Descartes' rule of signs and finally applies some appealing shading to the point of the ray-surface intersection. Our method benefits from algebraic surfaces with few non-zero coefficients in its implicit representation and therefore ob- tains high frame rates for typical academic examples of algebraic surfaces.
References (7)
- HANRAHAN, P. 1983. Ray tracing algebraic surfaces. In SIG- GRAPH '83: Proceedings of the 10th annual conference on Com- puter graphics and interactive techniques, ACM, New York, NY, USA, 83-90.
- HART, J. 1996. Sphere tracing: A geometric method for the antialiased ray tracing of implicit surfaces. The Visual Computer 12, 10, 527-545.
- KNOLL, A., HIJAZI, Y., KENSLER, A., SCHOTT, M., HANSEN, C., AND HAGEN, H. 2007. Fast and Robust Ray Tracing of General Implicits on the GPU. Tech. Rep. UUSCI-2007-014, SCI Institute, University of Utah.
- LOOP, C., AND BLINN, J. 2006. Real-time gpu rendering of piecewise algebraic surfaces. ACM Trans. Graph. 25, 3, 664-670.
- REIMERS, M., AND SELAND, J. 2008. Ray Casting Algebraic Surfaces using the Frustum Form. In Computer Graphics Forum, vol. 27, Blackwell Science Ltd, Osney Mead, Oxford, OX 2 0 EL, UK, 361-370.
- SELAND, J. S., AND DOKKEN, T. 2007. Real-time algebraic surface visualization. In Geometric Modelling, Numerical Simulation, and Optimization, Springer Berlin Heidelberg, 163-183.
- STUSSAK, C. 2007. Echtzeit-Raytracing algebraischer Flächen auf der Graphics Processing Unit. Master's thesis, Martin Luther University Halle-Wittenberg, Institute of Computer Science.