Positive data modeling using spline function

A rational cubic function with two parameters has been constructed to visualize the positive data. The main focus of the work is the representation of the data in such a way that its view looks smooth and attractive. In the first step simple data dependent constraints are derived on the parameters in the description of the rational cubic function to visualize the shape of positive data then, it is extended to a rational bi-cubic partially blended functions (Coons-patches) and derived constraints on parameters to visualize the shape of positive surface data. The developed scheme is locally positive and economical. The approximation order of rational cubic spline function is Oh"i^3.

[1]  B. I. Kvasov,et al.  Algorithms for shape preserving local approximation with automatic selection of tension parameters , 2000, Comput. Aided Geom. Des..

[2]  Muhammad Sarfraz,et al.  Data visualization using rational spline interpolation , 2006 .

[3]  Muhammad Sarfraz,et al.  A rational spline for visualizing positive data , 2000, 2000 IEEE Conference on Information Visualization. An International Conference on Computer Visualization and Graphics.

[4]  Tim N. T. Goodman.  Shape Preserving Interpolation by Curves , 2001 .

[5]  Carla Manni,et al.  Shape-Preserving C2 Functional Interpolation via Parametric Cubics , 2004, Numerical Algorithms.

[6]  Edward H. Twizell,et al.  Error estimation of a kind of rational spline , 2007 .

[7]  Jochen W. Schmidt,et al.  Positivity of cubic polynomials on intervals and positive spline interpolation , 1988 .

[8]  Michael Kallay,et al.  Monotone linear rational spline interpolation , 1992, Comput. Aided Geom. Des..

[9]  John A. Gregory,et al.  A rational cubic spline with tension , 1990, Comput. Aided Geom. Des..

[10]  Carla Manni,et al.  Constructing C3 shape preserving interpolating space curves , 2001, Adv. Comput. Math..

[11]  Gleb Beliakov,et al.  Monotonicity Preserving Approximation of Multivariate Scattered Data , 2005 .

[12]  J. Mason,et al.  Algorithms for approximation , 1987 .

[13]  S. BUTT,et al.  Preserving positivity using piecewise cubic interpolation , 1993, Comput. Graph..

[14]  Ken Brodlie,et al.  Preserving convexity using piecewise cubic interpolation , 1991, Comput. Graph..

[15]  Malik Zawwar Hussain.  Shape Preserving Curves and Surfaces for Computer Graphics. , 2002 .

[16]  Muhammad Sarfraz,et al.  Visualization of shaped data by a rational cubic spline interpolation , 2001, Comput. Graph..

[17]  Muhammad Sarfraz,et al.  Positivity-preserving interpolation of positive data by rational cubics , 2008 .

[18]  Muhammad Sarfraz.  A rational cubic spline for the visualization of monotonic data , 2000, Comput. Graph..

[19]  Tim N. T. Goodman,et al.  Automatic interpolation by fair, shape-preserving, G2 space curves , 1998, Comput. Aided Des..

[20]  N. Dejdumrong,et al.  The Generation of G1 Cubic Bézier Curve Fitting for Thai Consonant Contour , 2007, Geometric Modeling and Imaging (GMAI '07).