Modeling of Objects Using Conic Splines


This paper contributes towards modeling for the designing of objects in the areas of Computer Graphics (CG), Computer-Aided Design (CAD), Computer-Aided Manufacturing (CAM), and Computer-Aided Engineering (CAE). It provides a modeling technique for the designing of objects. The model is based on a conic-like curve (rational quadratics) method and provides an extra degree of freedom to the user to fine tune the shape of the design to the satisfactory level. The 2D curve model has then been extended for the designing of 3D objects to produce fancy objects. The scheme has been also extended to automate the degree of freedom when a reverse engineering is required for images of the objects. A heuristic technique of genetic algorithm is applied to find optimal values of shape parameters in the description of conics.

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M. Sarfraz, M. Hussain and M. Ishaq, "Modeling of Objects Using Conic Splines," Journal of Software Engineering and Applications, Vol. 6 No. 3B, 2013, pp. 67-72. doi: 10.4236/jsea.2013.63B015.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. A. Gregory, and P.K. Yuen, An arbitrary mesh network scheme using rational splines, in: T. Lyche and L.L. Schumaker (eds.), Mathematical Methods in Computer Aided Geometric Design II, Academic Press, 321-329, 1992.
[2] J. A. Gregory, M. Sarfraz, and P.K. Yuen, Curves and Surfaces for Computer Aided Design using Rational Cubic Splines, Engineering with Computers, 11:94-102, 1995.
[3] J. Hoschek, Circular splines, Computer-Aided Design, 24:611-618, 1992.
[4] M. Sarfraz, M. Hussain, and Z. Habib, Local convexity preserving rational cubic spline curves, Proceedings of IEEE Conference on Information Visualization, IV'97, London, 211-218, 1997.
[5] T. A. Foley and H. S. Ely, Interpolation with interval and point tension controls using cubic weighted Nu-splines, ACM Transactions on Mathematical Software, 13(1): 68-96, 1987.
[6] L. Piegl, and W. Tiller, The NURBS Book, Springer, 1995.
[7] Sarfraz, M., Al-Mulhem, M., Al-Ghamdi, J., and Hussain, A., Quadratic Representation to a C1 Rational Cubic Spline with Interval Shape Control, Proc International Conference on Imaging Science, Systems, and Technology (CISST'98), USA, 322-329, 1998.
[8] J. S. Kouh, and S. W. Chau, Computer-aided geometric design and panel generation for hull forms based on rational cubic Bezier curves, , Computer Aided Geometric Design, 10:537-549, 1993.
[9] V. Pratt, Techniques for conic splines, Proceedings of SIGGRAPH, 151-159, 1985.
[10] T. Pavlidis, Curve fitting with conic splines, ACM Transactions on Graphics, 1-31, 1983.
[11] M. Plass and Maureen Stone, Curve-fitting with Piecewise Parametric Cubics, Computer Graphics, 17(3): 229-239, 1983.
[12] G. Nielson, Rectangular Nu-splines, IEEE Computer Graphics and Applications, 35-40, 1986.
[13] J. A. Gregory and M. Sarfraz, A rational cubic spline with tension, Computer Aided Geometric Design, 7:1-13, 1990.
[14] T. A. Foley and H. S. Ely, Interpolation with interval and point tension controls using cubic weighted Nu-splines, ACM Transactions on Mathematical Software, 13(1): 68-96, 1987.
[15] M. Paluszny and R. Patterson, A family of tangent continous cubic algebraic splines, ACM Transactions on Graphics, 12(3):209-232, 1993.
[16] J. C. Beatty R. Bartels and K. S. Booth, Experimental comparision of splines using the shape-matching paradigm, ACM Transactions on Graphics, 12(3):179-208, 1993.
[17] B. A. Barsky, Computer Graphics and Geometric Modeling using Beta-Splines, Springer-verlag, 1986, Tokyo.
[18] T. N. T. Goodman, Properties of Beta-Splines, Journal of Approximation Theory, 44(2):132-153, 1985.
[19] B. Barsky and J. Beatty, Local control of bias and tension in Beta-Splines, ACM Transactions on Graphics, 2(2):73-77, 1983.
[20] D. Joe, Multiple knot and rational cubic beta-splines, ACM Transactions on Graphics, 8(2):100-120, 1989.
[21] T. N. T. Goodman and K. Unsworth, Manipulating shape and producing geometric continuity in beta-splines curves, IEEE Computer Graphics and Applications, 6(2):50-56, 1986.
[22] M. Sarfraz, Interactive curve modeling with applications to computer graphics, vision and image processing. Springer, 2008.
[23] M. Sarfraz, M. Hussain, M. Irshad, and A. Khalid, Approximating boundary of bitmap characters using genetic algorithm, Seventh International Conference on Computer Graphics, Imaging and Visualization (CGIV'10), 2010, 671-680.
[24] Z.R. Yahya, A.R.M Piah and A.A. Majid, G1 continuity conics for curve fitting using particle swarm optimization, E. Banissi et al. (Eds.) 15th International Conference on Information Visualization,. IV, 2011, 497-501.
[25] M. Sarfraz, S. Raza and M. Baig, Capturing image outlines using soft computing approach with conic splines, International Conference of Soft Computing and Pattern Recognition, 2009, 289-294.
[26] P. Priza, S. M. Shamsuddin and A. Ali, Differential evolution optimization for Bezier curve fitting, Seventh In-ternational Conference on Computer Graphics, Imaging and Visualization, 2010, 68-72.
[27] M. Sarfraz, M. Al-Mulhem, J. Al-Ghamdi, and A. M. Hussain, Representing a C1 Rational Quadratic Spline with Interval Shape Control, Proceedings of International Conference on Imaging Science, Systems, and Technol-ogy (CISST'98), Las Vegas, Nevada, USA, CSREA Press, USA, 322-329, 1998.

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