Proceedings of the World Congress on Engineering 2008 Vol IWCE 2008, July 2 - 4, 2008, London, U.KAbstract
— As shape parameterization defines the designvariables for the optimization of some object (geometricknowledge representation), it is very important to applyparameterizations with a low number of control points in orderto reduce the dimensionality of the search space. Aparameterization for 2D and 3D geometries based on piecewiseBezier curves and surfaces is proposed here. The requested C
1
inter- segment continuity is accomplished by automaticallygenerating additional control points without increasing thenumber of optimization variables. The computationalprocedure takes the initially given complex surface or pointscloud (2D or 3D), adaptively splits the domain into 2D or 3Dpatches and iteratively tries to reduce the necessary number of control points while satisfying the requested modeling accuracy.This adaptive parameterization procedure can serve as ageometric data-set compression utility and fits well intoevolutionary optimization.
Index Terms
—Geometry parameterization, piecewise Bezierpatches, shape optimization, aerofoils and blades
