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

Year 2016, Volume: 4 Issue: Special Issue-1, 204 - 210, 26.12.2016

Kübra Uyar , Erkan Ülker , Ahmet Arslan

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.

Keywords

Intelligent water drops, natural water drops, evolutionary algorithms, B-spline curves, knot points, optimization, reverse engineering

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