Performance comparison of adapted delaunay triangulation method over nurbs for surface optimization problems

Abstract

Traditionally NURBS (Non-Uniform Rational Basis Spline) are used as the basis for defining free-form surfaces as they can define non-regular surfaces with minimal control points. However, they require parameters such as knot vectors and weights to configure a surface. Similarly, DT (Delaunay Triangulation) is proven and used widely for meshing, rendering and surface reconstruction applications, but its capability in freeform surface design for optimization is untested. Thus, this paper proposes Adapted Delaunay Triangulation (ADT) method which can generate a surface from scattered data points without any parameters. The paper presents a comparison of the performance of ADT method and NURBS fitting method for surface generation from scattered 3D coordinate points. This method was suggested so that the generated surface could be used in Stochastic Optimization Algorithm (SOA) methods and computational fluid dynamics applications (CFD) simultaneously. Data points that other 3D point clouds fitting methods would ignore as outliers are included in ADT method. Small change in each data point during optimization cycle should show a distinctive change in its output as SOA approaches depend on such differences for its optimal performance. Special consideration has been made for fast processing and rendering of the surface with minimum complexity (removing parameters such as knots and weights) and storage requirements as SOA methods demand generation of numerous surfaces to solve any problem.