Local Convexity Shape-Preserving Data Visualization by Spline Function (original) (raw)
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Local convexity-preserving C2 rational cubic spline for convex data
TheScientificWorldJournal, 2014
We present the smooth and visually pleasant display of 2D data when it is convex, which is contribution towards the improvements over existing methods. This improvement can be used to get the more accurate results. An attempt has been made in order to develop the local convexity-preserving interpolant for convex data using C(2) rational cubic spline. It involves three families of shape parameters in its representation. Data dependent sufficient constraints are imposed on single shape parameter to conserve the inherited shape feature of data. Remaining two of these shape parameters are used for the modification of convex curve to get a visually pleasing curve according to industrial demand. The scheme is tested through several numerical examples, showing that the scheme is local, computationally economical, and visually pleasing.
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.
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 .
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 .
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 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
Visualization of 3D data preserving convexity
Journal of Applied Mathematics and Computing, 2007
Visualization of 2D and 3D data, which arises from some scientific phenomena, physical model or mathematical formula, in the form of curve or surface view is one of the important topics in Computer Graphics. The problem gets critically important when data possesses some inherent shape feature. For example, it may have positive feature in one instance and monotone in the other. This paper is concerned with the solution of similar problems when data has convex shape and its visualization is required to have similar inherent features to that of data. A rational cubic function [5] has been used for the review of visualization of 2D data. After that it has been generalized for the visualization of 3D data. Moreover, simple sufficient constraints are made on the free parameters in the description of rational bicubic functions to visualize the 3D convex data in the view of convex surfaces.
A Rational Spline for Preserving the Shape of Positive Data
International Journal of Computer and Electrical Engineering, 2013
In Computer Aided Geometric Design (CAGD), it is often needed to produce a positivity-preserving curve according to the given positive data. The main focus of this work is to address the problem of visualizing positive data in such a way that its display looks smooth and pleasant. A rational cubic spline function with three shape parameters has been developed. Simple data dependent constraints are derived for single shape parameter to preserve the positivity through positive data. Remaining two shape parameters are provided extra freedom to user for modification of curves as desired. The scheme is local, computationally economical and time saving as compared to existing schemes. The curve scheme under discussion is attained 1 C continuity.
Data visualization using rational spline interpolation
Journal of Computational and Applied Mathematics, 2006
A smooth curve interpolation scheme for positive, monotonic, and convex 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. The degree of smoothness attained is C 1 .