Convex Surface Visualization Using Rational Bi- cubic Function

Subject Areas : Operation Research

Malik Zawwar Hussain ¹ , Fareeha Saadia ² , Maria Hussain ³

1 - Department of Mathematics, University of the Punjab, Lahore, Pakistan
2 - Department of Mathematics, University of the Punjab, Lahore, Pakistan
3 - Department of Mathematics, Lahore College for Women University, Pakistan

Received: 2010-04-30 Accepted : 2010-05-30 Published : 2010-06-01

Keywords:

References:

[1]          Asaturyan, S., Shape preserving surface interpolation scheme, Ph.D. Thesis, Department of Mathematics and Computer Science, University of Dundee, Scotland, UK, 1990.

[2]          Asaturyan, S., Costantini P., and Manni C., Local shape preserving interpolation by space curves, IMA Journal of Numerical Analysis, 21(1), 301–325, 2001.

[3]          Carnicer, J.M., Garcia-Esnaol, M., and Peña, J. M., Convexity of rational curves and total positivity, Journal of Computational and Applied Mathematics, 71(2), 365–382, 1996.

[4]          Clements, J.C., A convexity preserving  parametric rational cubic interpolant, Numerische Mathemati, 63(1), 165-171, 1992.

[5]          Costantini, P., On monotone and convex spline interpolation, Mathematics of Computation, 46(173), 203-214, 1986.

[6]          Costantini, P. and Fontanella F., Shape preserving bivariate interpolation, SIAM Journal of Numerical Analysis, 27(2), 488-506,1990.

[7]          Dodd, S. L., McAllister, D. F., and Roulier J. A., Shape-preserving spline interpolation for specifying bivariate functions on grids, IEEE Computer Graphics and Applications, 3(6), 70-79,1983.

[8]          Floater, M. S., A weak condition for the convexity of tensor-product Bézier and B-spline surfaces, Advances in Computational Mathematics, 2(1), 67–80,1994. 

[9]          Hussain, M.Z. and Hussain, M., Visualization of 3D data preserving convexity, Journal of Applied Mathematics and Computing, 2, 170-186, 2006. 

[10]      Hussain, M.Z. and Hussain, M., Convex surface interpolation, Lecture Notes in Computer Science, 4975, 475-482, 2008.

[11]      Sarfraz, M., Al-Mulhem, M. and Ashraf, M., Preserving monotonic shape of data using piecewise rational cubic function, Computers & Graphics, 21(1), 5-14, 1997.

[12]      Zhang, Y., Duan, Q., and Twizell, E. H., Convexity control of bivariate interpolation spline surfaces, Computers & Graphics, 31(5), 679-687, 2007.