Shape Preserving Positive Rational Trigonometric Spline Surfaces

2015 ◽  
Author(s):  
Muhammad Sarfraz ◽  
Farsia Hussain ◽  
Malik Zawwar Hussain
Keyword(s):  
Shape Preserving ◽  
Spline Surfaces ◽  
Trigonometric Spline

Shape-Preserving Positive Trigonometric Spline Curves

2016 ◽  
Vol 42 (2) ◽  
pp. 763-775
Author(s):  
Malik Zawwar Hussain ◽  
Farsia Hussain ◽  
Muhammad Sarfraz
Keyword(s):  
Shape Preserving ◽  
Spline Curves ◽  
Trigonometric Spline

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 C1Rational Quadratic Trigonometric Interpolation Spline for Data Visualization

2015 ◽  
Vol 2015 ◽  
pp. 1-20 ◽  
Author(s):  
Shengjun Liu ◽  
Zhili Chen ◽  
Yuanpeng Zhu
Keyword(s):  
Trigonometric Interpolation ◽  
Data Sets ◽  
Order Of Approximation ◽  
Shape Parameters ◽  
Interpolation Spline ◽  
Shape Preserving ◽  
Shape Preserving Interpolation ◽  
Trigonometric Spline ◽  
The Given ◽  
Data Constraints

A newC1piecewise rational quadratic trigonometric spline with four local positive shape parameters in each subinterval is constructed to visualize the given planar data. Constraints are derived on these free shape parameters to generate shape preserving interpolation curves for positive and/or monotonic data sets. Two of these shape parameters are constrained while the other two can be set free to interactively control the shape of the curves. Moreover, the order of approximation of developed interpolant is investigated asO(h3). Numeric experiments demonstrate that our method can construct nice shape preserving interpolation curves efficiently.

scholarly journals Convolution operators with trigonometric spline kernels

1988 ◽  
Vol 31 (2) ◽  
pp. 285-299 ◽  
Author(s):  
T. N. T. Goodman ◽  
S. L. Lee
Keyword(s):  
Algebraic Polynomial ◽  
Bernstein Polynomials ◽  
Spline Approximation ◽  
Convolution Operators ◽  
Shape Preserving ◽  
Approximation Operators ◽  
Trigonometric Spline ◽  
Polynomial Operators ◽  
Shape Preserving Properties ◽  
Schoenberg Spline

The Bernstein polynomials are algebraic polynomial approximation operators which possess shape preserving properties. These polynomial operators have been extended to spline approximation operators, the Bernstein-Schoenberg spline approximation operators, which are also shape preserving like the Bernstein polynomials [8].

PIECEWISE QUARTIC TRIGONOMETRIC POLYNOMIAL B-SPLINE CURVES WITH TWO SHAPE PARAMETERS

2012 ◽  
Vol 12 (04) ◽  
pp. 1250028
Author(s):  
MRIDULA DUBE ◽  
REENU SHARMA
Keyword(s):  
Trigonometric Polynomial ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curve ◽  
Control Polygon ◽  
Spline Curves ◽  
Spline Surfaces ◽  
Polynomial Curve ◽  
Trigonometric Spline ◽  
The Given

Analogous to the quartic B-splines curve, a piecewise quartic trigonometric polynomial B-spline curve with two shape parameters is presented in this paper. Each curve segment is generated by three consecutive control points. The given curve posses many properties of the B-spline curve. These curves are closer to the control polygon than the different other curves considered in this paper, for different values of shape parameters for each curve. With the increase of the value of shape parameters, the curve approach to the control polygon. For nonuniform and uniform knot vector the given curves have C0, G3; C1, G3; C1, G7; and C3 continuity for different choice of shape parameters. A quartic trigonometric Bézier curves are also introduced as a special case of the given trigonometric spline curves. A comparison of quartic trigonometric polynomial curve is made with different other curves. In the last, quartic trigonometric spline surfaces with two shape parameters are constructed. They have most properties of the corresponding curves.

scholarly journals Shape-preserving quasi-interpolation and interpolation by box spline surfaces

1989 ◽  
Vol 25 (2) ◽  
pp. 169-198 ◽  
Author(s):  
Charles K. Chui ◽  
Harvey Diamond ◽  
Louise Raphael
Keyword(s):  
Shape Preserving ◽  
Box Spline ◽  
Spline Surfaces

scholarly journals Shape preserving design of geometrically nonlinear structures using topology optimization

2019 ◽  
Vol 59 (4) ◽  
pp. 1033-1051 ◽  
Author(s):  
Yu Li ◽  
Jihong Zhu ◽  
Fengwen Wang ◽  
Weihong Zhang ◽  
Ole Sigmund
Keyword(s):  
Topology Optimization ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Shape Preserving
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