A Rational Spline for Preserving the Shape of Positive Data (original) (raw)
Related papers
International Journal of Computer Applications, 2011
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.
Positivity-preserving C2 rational cubic spline interpolation
ScienceAsia, 2013
This work addresses the shape preserving interpolation problem for visualization of positive data. A piecewise rational function in cubic/quadratic form involving three shape parameters is presented. Simple data dependent conditions for a single shape parameter are derived to preserve the inherited shape feature (positivity) of data. The remaining two shape parameters are left free for the designer to modify the shape of positive curves as per industrial needs. The interpolant is not only C 2 , local, computationally economical, but it is also a visually pleasant and smooth in comparison with existing schemes. Several numerical examples are supplied to illustrate the proposed interpolant.
Shape preserving rational cubic spline for positive and convex data
Egyptian Informatics Journal, 2011
In this paper, the problem of shape preserving C 2 rational cubic spline has been proposed. The shapes of the positive and convex data are under discussion of the proposed spline solutions. A C 2 rational cubic function with two families of free parameters has been introduced to attain the C 2 positive curves from positive data and C 2 convex curves from convex data. Simple data dependent constraints are derived on free parameters in the description of rational cubic function to obtain the desired shape of the data. The rational cubic schemes have unique representations.
Visualization of positive and convex data by a rational cubic spline interpolation
Information Sciences, 2002
A curve interpolation scheme for the visualization of scientific data has been developed. This scheme uses piecewise rational cubic functions and is meant for positive and convex data. The two families of parameters, in the description of the rational interpolant, have been constrained to preserve the shape of the data. The rational spline scheme has a unique representation. In addition to preserve the shape of positive and/or convex data sets, it also possesses extra features to modify the shape of the design curve as and when desired. The degree of smoothness attained is C 1 .
Positive data modeling using spline function
Applied Mathematics and Computation, 2010
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 O h 3 i .
Positivity-preserving rational bi-cubic spline interpolation for 3D positive data
Applied Mathematics and Computation, 2014
This paper deals with the shape preserving interpolation problem for visualization of 3D positive data. A required display of 3D data looks smooth and pleasant. A rational bi-cubic function involving six shape parameters is presented for this objective which is an extension of piecewise rational function in the form of cubic/quadratic involving three shape parameters. Simple data dependent constraints for shape parameters are derived to conserve the inherited shape feature (positivity) of 3D data. Remaining shape parameters are left free for designer to modify the shape of positive surface as per industrial needs. The interpolant is not only local, C 1 but also it is a computationally economical in comparison with existing schemes. Several numerical examples are supplied to support the worth of proposed interpolant.
Totally positive bases for shape preserving curve design and optimality of B-splines
Computer Aided Geometric Design, 1994
Normalized totally positive (NTP) bases present good shape preserving properties when they are used in Computer Aided Geometric Design. Here we characterize all the NTP bases of a space and obtain a test to know if they exist. Furthermore, we construct the NTP basis with optimal shape preserving properties in the sense of (Goodman and Said, 1991), that is, the shape of the control polygon of a curve with respect to the optimal basis resembles with the highest fidelity the shape of the curve among all the control polygons of the same curve corresponding to NTP bases. In particular, this is the case of the B-spline basis in the space of polynomial splines. Further examples are given.
Curves and surfaces for computer aided design usingC 2 rational cubic splines
Engineering with Computers, 1995
This paper is concerned with the problem of fitting curves and surfaces, for computer aided design (CAD), via an ordered set of control points, so that the result is satisfactory for the user's needs. Piecewise rational functions with cubic numerator and quadratic denominator are used in the construction of the scheme, in such a way that the descriptions of the parameters control the shape of the picture in the desired area. A general solution is obtained for points in N-space, although the scheme is only meaningful in the cases where N = 2 and N = 3.
Visualization of shaped data by a rational cubic spline interpolation
Computers & Graphics, 2001
A smooth curve interpolation scheme for positive and monotonic data has been developed. This scheme uses piecewise rational cubic functions. The two families of parameters, in the description of the rational interpolant, have been constrained to preserve the shape of the data. The rational spline scheme has a unique representation. In addition to preserve the shape of positive and/or monotonic data sets, it also possesses extra features to modify the shape of the design curve as and when desired. The degree of smoothness attained is C 1 : r : S 0 0 9 7 -8 4 9 3 ( 0 1 ) 0 0 1 2 5 -X
Data Visualization using Spline Functions
Pakistan Journal of Statistics and Operation Research, 2013
A two parameter family of 1 C rational cubic spline functions is presented for the graphical representation of shape preserving curve interpolation for shaped data. These parameters have a direct impact on the shape of the curve. Constraints are developed on one family of the parameters to visualize positive, monotone and convex data while other family of parameters can assume any positive values. The problem of visualization of constrained data is also addressed when the data is lying above a straight line and curve is required to lie on the same side of the line. The approximation order of the proposed rational cubic function is also investigated and is found to be 3 i O h .