publication . Article . 2005

Capturing planar shapes by approximating their outlines

Muhammad Sarfraz; M. Riyazuddin; M. H. Baig;
Open Access
  • Published: 23 Nov 2005 Journal: Journal of Computational and Applied Mathematics, volume 189, pages 494-512 (issn: 0377-0427, Copyright policy)
  • Publisher: Elsevier BV
AbstractA non-deterministic evolutionary approach for approximating the outlines of planar shapes has been developed. Non-uniform Rational B-splines (NURBS) have been utilized as an underlying approximation curve scheme. Simulated Annealing heuristic is used as an evolutionary methodology. In addition to independent studies of the optimization of weight and knot parameters of the NURBS, a separate scheme has also been developed for the optimization of weights and knots simultaneously. The optimized NURBS models have been fitted over the contour data of the planar shapes for the ultimate and automatic output. The output results are visually pleasing with respect ...
Persistent Identifiers
ACM Computing Classification System: ComputingMethodologies_COMPUTERGRAPHICS
free text keywords: Applied Mathematics, Computational Mathematics, NURBS, Digitization, Approximation, Simulated annealing, Shapes, Planar, Deterministic system (philosophy), Mathematics, Mathematical optimization, Knot (unit), Heuristic, Simulated annealing, B-spline, The Internet, business.industry, business, Numerical analysis
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23 references, page 1 of 2

[1] J.J. Chou, L.A. Piegl, Data reduction using cubic rational B-splines, IEEE Comput. Graphics Appl. 1992.

[2] D.E. Goldberg, Genetic algorithms in search, Optimization and Machine Learning, Addison-Wesley, Reading, MA, 1989.

[3] M. Hoffmann, I. Juhasz, Shape control of cubic B-spline and NURBS curves by knot modifications, IEEE, 2001.

[4] S. Kirkpatrick, C. Gelatt Jr., M. Vecchi, Optimization by Simulated Annealing, Science 220 (4598) (1983) 498-516.

[5] A. Limaiem, A. Nassef, H.A. Elmaghraby, Data fitting using dual Krigging and Genetic Algorithms, CIRP Ann. 45 (1996) 129-134.

[6] Matlab Web Server Manual, The math works Inc., 2000,

[7] N. Metropolis, A. Roshenbluth, M. Rosenbluth, A. Teller, E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys. 21 (6) (1953) 1087-1092.

[8] L. Piegl, On NURBS: a survey, IEEE Comput. Graphics Appl. 11 (1) (1991) 55-71.

[9] L. Piegl, W. Tiller, The NURBS Book, Springer, Berlin, 1995.

[10] F. Pontrandolfo, G. Monno, A.E. Uva, Simulated Annealing vs Genetic Algorithms for linear spline approximation of 2D scattered data, XII International Conference, Rimini, Italy, 2001.

[11] A. Quddus, Curvature analysis using multi-resolution techniques, Ph.D. Thesis, Department of Electric Engineering, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia, 1998.

[12] S.S. Rao, Engineering Optimization, Theory and Practice, Wiley, New York, 1999.

[13] S.A. Raza, Visualization with spline using a genetic algorithm, Master Thesis, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia, 2001.

[14] D.F. Rogers, An Introduction to NURBS With Historical Perspective, Morgan Kaufmann Publishers, Los Altos, CA, 2001.

[15] M.S. Sait, H. Youssef, Iterative computer algorithms with applications in engineering: solving combinatorial optimization problems, IEEE Computer Society Press, California, 1999.

23 references, page 1 of 2
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