Computer Software Program for Representation and Visualization of Free-Form Curves through Bio-inspired Optimization Techniques

Free-form parametric curves are becoming increasingly popular in many theoretical and applied domains because of their ability to model a wide variety of complex shapes. In real-world applications those shapes are usually given in terms of data points, for which a fitting curve is to be obtained. Unfortunately, this is a very difficult task for classical optimization techniques. Recently, it has been shown that bio-inspired optimization techniques can be successfully applied to overcome this limitation. This paper introduces a new interactive, user-friendly computer software program for the representation and visualization of free-form parametric curves from sets of data points. Given a cloud of data points as initial input, the user is prompted to a graphical interface where he/she can choose the bio-inspired technique of his/her preference, set up the control parameters interactively, and obtain the mathematical representation and graphical visualization of the underlying shape. The paper discusses the main features of this software. An illustrative example of its application is also briefly reported.

[1]  Ahmet Arslan,et al.  Automatic knot adjustment using an artificial immune system for B-spline curve approximation , 2009, Inf. Sci..

[2]  Andrés Iglesias,et al.  Iterative two-step genetic-algorithm-based method for efficient polynomial B-spline surface reconstruction , 2012, Inf. Sci..

[3]  Andrés Iglesias,et al.  Efficient particle swarm optimization approach for data fitting with free knot B-splines , 2011, Comput. Aided Des..

[4]  Andrés Iglesias,et al.  Firefly Algorithm for Polynomial Bézier Surface Parameterization , 2013, J. Appl. Math..

[5]  Kathryn A. Ingle,et al.  Reverse Engineering , 1996, Springer US.

[6]  Andrés Iglesias,et al.  From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM , 2013, TheScientificWorldJournal.

[7]  Andrés Iglesias,et al.  A new iterative mutually coupled hybrid GA-PSO approach for curve fitting in manufacturing , 2013, Appl. Soft Comput..

[8]  Marina L. Gavrilova,et al.  Computational Science and Its Applications - ICCSA 2007, International Conference, Kuala Lumpur, Malaysia, August 26-29, 2007. Proceedings, Part I , 2007, ICCSA.

[9]  Leon G. Higley,et al.  Forensic Entomology: An Introduction , 2009 .

[10]  Paul Dierckx,et al.  Curve and surface fitting with splines , 1994, Monographs on numerical analysis.

[11]  Ling Jing,et al.  Fitting B-spline curves by least squares support vector machines , 2005, 2005 International Conference on Neural Networks and Brain.

[12]  Andrés Iglesias,et al.  Extending Neural Networks for B-Spline Surface Reconstruction , 2002, International Conference on Computational Science.

[13]  Caiming Zhang,et al.  Adaptive knot placement using a GMM-based continuous optimization algorithm in B-spline curve approximation , 2011, Comput. Aided Des..

[14]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[15]  Helmut Pottmann,et al.  Fitting B-spline curves to point clouds by curvature-based squared distance minimization , 2006, TOGS.

[16]  Andrés Iglesias,et al.  Particle swarm optimization for non-uniform rational B-spline surface reconstruction from clouds of 3D data points , 2012, Inf. Sci..

[17]  Ralph R. Martin,et al.  Reverse engineering of geometric models - an introduction , 1997, Comput. Aided Des..

[18]  Andries Petrus Engelbrecht,et al.  Fundamentals of Computational Swarm Intelligence , 2005 .

[19]  Weiyin Ma,et al.  Parameterization of randomly measured points for least squares fitting of B-spline curves and surfaces , 1995, Comput. Aided Des..

[20]  Toshinobu Harada,et al.  Data fitting with a spline using a real-coded genetic algorithm , 2003, Comput. Aided Des..

[21]  Andrés Iglesias,et al.  A New Artificial Intelligence Paradigm for Computer-Aided Geometric Design , 2000, AISC.

[22]  Kai-Uwe Kühnberger,et al.  Algorithmic Aspects of Theory Blending , 2014, AISC.

[23]  Enrique F. Castillo,et al.  Some characterizations of families of surfaces using functional equations , 1997, TOGS.

[24]  Josef Hoschek,et al.  Handbook of Computer Aided Geometric Design , 2002 .

[25]  Angel Cobo,et al.  Bézier Curve and Surface Fitting of 3D Point Clouds Through Genetic Algorithms, Functional Networks and Least-Squares Approximation , 2007, ICCSA.

[26]  Wenping Wang,et al.  Control point adjustment for B-spline curve approximation , 2004, Comput. Aided Des..

[27]  Muhammad Sarfraz,et al.  Capturing outline of fonts using genetic algorithm and splines , 2001, Proceedings Fifth International Conference on Information Visualisation.

[28]  Tamás Várady,et al.  Reverse Engineering , 2002, Handbook of Computer Aided Geometric Design.

[29]  Robert E. Barnhill,et al.  Geometry Processing for Design and Manufacturing , 1992 .

[30]  A. Iglesias,et al.  Firefly Algorithm for Explicit B-Spline Curve Fitting to Data Points , 2013 .

[31]  Miklós Hoffmann Numerical control of kohonen neural network for scattered data approximation , 2004, Numerical Algorithms.

[32]  Andrés Iglesias,et al.  Functional networks for B-spline surface reconstruction , 2004, Future Gener. Comput. Syst..

[33]  Jack Dongarra,et al.  Computational Science — ICCS 2002 , 2002, Lecture Notes in Computer Science.