Shape preserving surface data visualization using rational bi-cubic functions

2011 ◽  
Vol 19 (4) ◽  
Author(s):  
M.Z. HUSSAIN ◽  
S. BASHIR
Keyword(s):  
Data Visualization ◽  
Shape Preserving ◽  
Surface Data

scholarly journals Data Visualization Using Rational Trigonometric Spline

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Uzma Bashir ◽  
Jamaludin Md. Ali
Keyword(s):  
Data Visualization ◽  
The Other ◽  
Shape Features ◽  
Shape Parameters ◽  
Shape Preserving ◽  
Numerical Examples ◽  
Data Points ◽  
Trigonometric Spline ◽  
The Given

This paper describes the use of trigonometric spline to visualize the given planar data. The goal of this work is to determine the smoothest possible curve that passes through its data points while simultaneously satisfying the shape preserving features of the data. Positive, monotone, and constrained curve interpolating schemes, by using aC1piecewise rational cubic trigonometric spline with four shape parameters, are developed. Two of these shape parameters are constrained and the other two are set free to preserve the inherited shape features of the data as well as to control the shape of the curve. Numerical examples are given to illustrate the worth of the work.

scholarly journals Monotone Data Visualization Using Rational Trigonometric Spline Interpolation

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Farheen Ibraheem ◽  
Maria Hussain ◽  
Malik Zawwar Hussain
Keyword(s):  
Data Visualization ◽  
Spline Interpolation ◽  
Trigonometric Functions ◽  
Rectangular Patch ◽  
Surface Data ◽  
Trigonometric Spline ◽  
Monotone Data ◽  
Cubic Function

Rational cubic and bicubic trigonometric schemes are developed to conserve monotonicity of curve and surface data, respectively. The rational cubic function has four parameters in each subinterval, while the rational bicubic partially blended function has eight parameters in each rectangular patch. The monotonicity of curve and surface data is retained by developing constraints on some of these parameters in description of rational cubic and bicubic trigonometric functions. The remaining parameters are kept free to modify the shape of curve and surface if required. The developed algorithm is verified mathematically and demonstrated graphically.

scholarly journals Local Convexity Shape-Preserving Data Visualization by Spline Function

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Muhammad Abbas ◽  
Ahmad Abd Majid ◽  
Mohd Nain Hj Awang ◽  
Jamaludin Md Ali
Keyword(s):  
Error Bound ◽  
Data Visualization ◽  
Free Parameter ◽  
Spline Function ◽  
Convex Curve ◽  
Local Convexity ◽  
Shape Preserving ◽  
User Choice ◽  
Free Parameters ◽  
Cubic Function

The main purpose of this paper is the visualization of convex data that results in a smooth, pleasant, and interactive convexity-preserving curve. The rational cubic function with three free parameters is constructed to preserve the shape of convex data. The free parameters are arranged in a way that two of them are left free for user choice to refine the convex curve as desired, and the remaining one free parameter is constrained to preserve the convexity everywhere. Simple data-dependent constraints are derived on one free parameter, which guarantee to preserve the convexity of curve. Moreover, the scheme under discussion is, C1 flexible, simple, local, and economical as compared to existing schemes. The error bound for the rational cubic function is O(h3).

scholarly journals Shape Preserving Positive and Convex Data Visualization using Rational Bi-cubic Functions

2012 ◽  
Vol 8 (1) ◽  
pp. 121 ◽  
Author(s):  
Tahira Sumbal Shaikh ◽  
Muhammad Sarfraz ◽  
Malik Zawwar Hussain
Keyword(s):  
Data Visualization ◽  
Shape Preserving
Sign in / Sign up

Export Citation Format

Share Document