Sammendrag
When making algorithms for Computer Aided Geometric Design it is very advantageous to combine parametric and algebraic representations for curves and surface. The high degrees of the exact algebraic representation of rational parametric surfaces, and the missing computational speed of exact algebraic methods have restricted the combined use of representations in industrial systems, and created a demand for approximate methods that can use floating point arithmetic exploit the performance of many core processors such as GPUs and multi-core CPUs The talk will address the potential of the use of approximate algebraic methods in CAGD systems, with a focus on intersection and self-intersection algorithms. An introduction to the original approach to approximate implicitization will be given.