B-Spline Curve Fitting with Intelligent Water Drops (IWD)

Abstract

The use of B-spline curves has spreaded too many fields such as computer aided design (CAD), data visualization, surface modelling, signal processing and statistics. The flexible and powerful mathematical properties of B-spline are the cause of being one of the most preferred curve in literature. They can represent a large variety of shapes efficiently. The curve behind of the model can be obtained by doing approximation of control points, approximation of knot points or parameterization. It is obvious that the selection of knot points in B-spline curve approximation has an important and considerable effect on the behaviour of final approximation. In addition to this, an unreasonable knot vector may introduce unpredictable and unacceptable shape. Recently, in literature, there has been a considerable attention on the algorithms inspired from natural processes or events to solve optimization problems such as simulated annealing, ant colony optimization, particle swarm optimization, artificial bee colony optimization, and genetic algorithms. This paper implements and analyses a solution to approximate B-spline curves using Intelligent Water Drops (IWD) algorithm. This algorithm is a swarm based optimization algorithm inspired from the processes that happen in the natural river systems. The algorithm is based on the actions and reactions that take place between water drops in the river and the changes that happen in the environment. Some basic properties of natural water drops are adopted in the algorithm here to solve B-spline curve fitting problem. Optimal knots are selected through IWD algorithm. The proposed algorithm convergences optimal solutions and finds good and promising results.