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Shape Preserving Surfaces for the Visualization of Positive and Convex Data using Rational Bi-quadratic Splines

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International Journal of Computer Applications
© 2011 by IJCA Journal
Number 10 - Article 3
Year of Publication: 2011
Authors:
Malik Zawwar Hussain
Muhammad Sarfraz
Ayesha Shakeel
10.5120/3338-4594

Malik Zawwar Hussain, Muhammad Sarfraz and Ayesha Shakeel. Article: Shape Preserving Surfaces for the Visualization of Positive and Convex Data using Rational Bi-quadratic Splines. International Journal of Computer Applications 27(10):12-20, August 2011. Full text available. BibTeX

@article{key:article,
	author = {Malik Zawwar Hussain and Muhammad Sarfraz and Ayesha Shakeel},
	title = {Article: Shape Preserving Surfaces for the Visualization of Positive and Convex Data using Rational Bi-quadratic Splines},
	journal = {International Journal of Computer Applications},
	year = {2011},
	volume = {27},
	number = {10},
	pages = {12-20},
	month = {August},
	note = {Full text available}
}

Abstract

A smooth surface interpolation scheme for positive and convex data has been developed. This scheme has been extended from the rational quadratic spline function of Sarfraz [11] to a rational bi-quadratic spline function. Simple data dependent constraints are derived on the free parameters in the description of rational bi-quadratic spline function to preserve the shape of 3D positive and convex data. The rational spline scheme has a unique representation. The developed scheme is computationally economical and visually pleasant.

Reference

  • Asaturyan, S., 1990. Shape preserving surface interpolation, Ph.D. Thesis, Department of Mathematics and Computer Science, University of Dundee, Scotland, UK.
  • 2 Brodlie, K. W., Mashwama, P. and Butt, S., 1995. Visualization of surface to preserve positivity and other simple constraints, Computers and Graphics, 19(4), p. 585-594.
  • 3 Butt, S. and Brodlie, K. W., 1993. Preserving positivity using piecewise cubic interpolation, Computers and Graphics, 17 (1), p. 55-64.
  • 4 Chang, G. and Sederberg, T. W., 1994. Non-negative quadratic Bézier triangular patches, Computer Aided Geometric Design, 11, p. 113-116.
  • 5 Constantini, P. and Fontanella, F., 1990. Shape preserving bivariate interpolation, SIAM Journal of Numerical Analysis, 27, p. 488-506.
  • 6 Dodd, S. L., McAllister and Roulier, J. A., 1983. Shape preserving spline interpolation for specifying bivariate functions of grids, IEEE Computer Graphics and Applications, 3(6), p. 70-79.
  • 7 Hussain, M. Z. and Sarfraz, M., 2007. Positivity-preserving interpolation of positive data by rational cubics, Journal of Computation and Applied Mathematics, 218(2), p. 446-458.
  • 8 Hussain, M. Z. and Maria Hussain, 2008. Convex surface interpolation, Lecture Notes in Computer Sciences, 4975, p. 475-482.
  • 9 Nadler, E. (1992), Non-negativity of bivariate quadratic function on triangle, Computer Aided Geometric Design, 9, p. 195-205.
  • 10 Piah, A. R. Mt., Goodman, T. N. T. and Unsworth, K., 2005. Positivity preserving scattered data interpolation, Lecture Notes in Computer Sciences, 3604, p. 336-349.
  • 11 Sarfraz, M., 1993. Monotonocity preserving interpolation with tension control using quadratic by linear functions, Journal of Scientific Research, 22 (1), p. 1-12.
  • 12 Sarfraz, M., Hussain, M. Z. and Chaudary, F. S., 2005. Shape preserving cubic spline for data visualization, Computer Graphics and CAD/CAM, 1(6), p. 185-193.
  • 13 Schmidt, J. W. and Hess, W., 1987. Positivity interpolation with rational quadratic splines interpolation, Computing, 38, p. 261-267.
  • 14 Schumaker, L. L., 1983. On shape preserving quadratic spline interpolation, SIAM Journal of Numerical Analysis, 20, p. 854–864.
  • 15 K.W. Brodlie and S. Butt, (1991), Preserving convexity using piecewise cubic interpolation, Comput. & Graphics, 15, p. 15-23.
  • 16 Paolo, C., 1997, Boundary-Valued Shape Preserving Interpolating Splines, ACM Transactions on Mathematical Software, 23(2), p. 229-251.
  • 17 Dejdumrong, N. and Tongtar, S., 2007. The Generation of G1 Cubic Bezier Curve Fitting for Thai Consonant Contour, Geometic Modeling and Imaging – New Advances, Sarfraz, M., and Banissi, E., (Eds.) ISBN: 0-7695-2901-1, IEEE Computer Society, USA, p. 48 – 53.
  • 18 Zulfiqar, H., and Manabu, S., 2008, Transition between concentric or tangent circles with a single segment of G2 PH quintic curve, Computer Aided Geometric Design 25(4-5): p. 247-257.
  • 19 Sebti, F., Dominique, M. and Jean-Paul, J., 2005, Numerical decomposition of geometric constraints, Proceedings of the 2005 ACM symposium on Solid and physical modeling, ACM Symposium on Solid and Physical Modeling, Cambridge, Massachusetts, ACM, New York, NY, USA, p. 143 – 151.
  • 20 Fougerolle, Y.D., Gribok, A., Foufou, S., Truchetet, F., Abidi, M.A., 2005, Boolean operations with implicit and parametric representation of primitives using R-functions, IEEE Transactions, on Visualization and Computer Graphics, 11(5), p. 529 – 539.