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Heterogeneous Computing and Computational Geometry


Moore's Law (1965) is the observation that the number of transistors on an integrated circuit for minimum component cost doubles every 24 months. Until 2004 the evolution of CPU frequency and consequently performance of single kernel CPUs followed a similar evolution. Consequently programs implemented according to a sequential paradigm could directly benefit from Moore’s law. However, in 2004 the growth of CPU frequency almost stopped, and multi-kernel commodity CPUs started to be introduced. In 2007 most new PCs have dual core CPUs, Intel recently introduced quad core CPUs. Parallel to this evolution, driven by the computer game market, graphics cards and their GPUs (Graphics Processing Units) have changed from being fixed functionality pipelines to becoming programmable data stream processors with a performance at least one order of magnitude higher than a CPU core. A modern PC with a multi-core CPU and a modern programmable graphics card is a heterogeneous parallel computational resource that offers a total computational performance of more than 500 Gflops. We use the word heterogeneous to point of that there are computational resources of different types as the CPU kernels are program driven and the GPU is data stream driven.To a great extent research and development within Computer Aided Geometric Design has been held back by what is feasible to be computed on a typical PC. Heterogeneous computing combining multi-kernel CPUs and GPUs consequently opens an opportunity to develop new algorithms and addresses computational problems that until now have been regarded as too resource consuming to be addressed. Since spatial subdivision of geometric objects is a natural strategy for breaking a complex geometrical problem into smaller (and hopefully simpler) subproblems, geometric computing has potentially much to benefit from exploiting heterogeneous computational resources. The talk will focus on the potential of heterogeneous computing in approximate implicitization


Academic lecture





  • SINTEF Digital / Mathematics and Cybernetics

Presented at

FSP Workshop on Computational Methods for Algebraic Spline Surfaces


Strobl, Østerrike


10.09.2007 - 14.09.2007


Institute of Applied Geometry, Johannes Kepler Universität Linz



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