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 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 Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xinru Liu ◽  
Yuanpeng Zhu ◽  
Shengjun Liu
Keyword(s):  
Sufficient Conditions ◽  
Rational Interpolation ◽  
Rectangular Domain ◽  
Interpolation Spline ◽  
Spline Surface ◽  
Surface Data ◽  
Shape Preserving Interpolation ◽  
The Given ◽  
Surface Construction ◽  
Special Case

A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively.

scholarly journals Shape Preserving Interpolation Using Rational Cubic Ball Function and Its Application in Image Interpolation

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Samsul Ariffin Abdul Karim ◽  
Azizan Saaban
Keyword(s):  
Tensor Product ◽  
Image Interpolation ◽  
Sufficient Condition ◽  
Shape Preserving ◽  
Straight Line ◽  
Shape Preserving Interpolation ◽  
Product Approach ◽  
The Given

New rational cubic Ball interpolation with one parameter is proposed for shape preserving interpolation such as positivity, monotonicity, and convexity preservations and constrained data lie on the same side of the given straight line. To produce shape preserving interpolant, the data dependent sufficient condition is derived on the parameter. The rational bicubic Ball function is constructed by using tensor product approach and it will be used for application in image upscaling. Numerical and graphical results are presented by using Mathematica and MATLAB including comparison with some existing scheme.

Cubic TP B-Spline Curves with a Shape Parameter

2013 ◽  
Vol 11 ◽  
pp. 59-72 ◽  
Author(s):  
Mridula Dube ◽  
Reenu Sharma
Keyword(s):  
Tensor Product ◽  
Shape Parameter ◽  
Control Points ◽  
Shape Parameters ◽  
Special Shape ◽  
B Spline ◽  
Control Polygon ◽  
Spline Curves ◽  
Trigonometric Spline ◽  
The Given

In this paper a new kind of splines, called cubic trigonometric polynomial B-spline (cubic TP B-spline) curves with a shape parameter, are constructed over the space spanned by As each piece of the curve is generated by three consecutive control points, they posses many properties of the quadratic B-spline curves. These trigonometric curves with a non-uniform knot vector are C1 and G2 continuous. They are C2 continuous when choosing special shape parameter for non-uniform knot vector. These curves are closer to the control polygon than the quadratic B-spline curves when choosing special shape parameters. With the increase of the shape parameter, the trigonometric spline curves approximate to the control polygon. The given curves posses many properties of the quadratic B-spline curves. The generation of tensor product surfaces by these new splines is straightforward.

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 A novel optimal multi-pattern matching method with wildcards for DNA sequence

2021 ◽  
Vol 29 ◽  
pp. 115-124
Author(s):  
Xinlu Wang ◽  
Ahmed A.F. Saif ◽  
Dayou Liu ◽  
Yungang Zhu ◽  
Jon Atli Benediktsson
Keyword(s):  
Dna Sequence ◽  
Pattern Matching ◽  
Health Informatics ◽  
State Of The Art ◽  
Machine Language ◽  
Data Sets ◽  
Fundamental Issue ◽  
Matching Method ◽  
Dna Sequence Alignment ◽  
The Given

BACKGROUND: DNA sequence alignment is one of the most fundamental and important operation to identify which gene family may contain this sequence, pattern matching for DNA sequence has been a fundamental issue in biomedical engineering, biotechnology and health informatics. OBJECTIVE: To solve this problem, this study proposes an optimal multi pattern matching with wildcards for DNA sequence. METHODS: This proposed method packs the patterns and a sliding window of texts, and the window slides along the given packed text, matching against stored packed patterns. RESULTS: Three data sets are used to test the performance of the proposed algorithm, and the algorithm was seen to be more efficient than the competitors because its operation is close to machine language. CONCLUSIONS: Theoretical analysis and experimental results both demonstrate that the proposed method outperforms the state-of-the-art methods and is especially effective for the DNA sequence.

scholarly journals Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Yuanpeng Zhu ◽  
Xuli Han ◽  
Shengjun Liu
Keyword(s):  
Error Estimate ◽  
Hermite Interpolation ◽  
Sufficient Conditions ◽  
Basis Functions ◽  
Shape Parameters ◽  
Interpolation Spline ◽  
Triangular Domain ◽  
Type Algorithm ◽  
Special Case ◽  
Monotonicity Preserving

Four new quartic rational Said-Ball-like basis functions, which include the cubic Said-Ball basis functions as a special case, are constructed in this paper. The new basis is applied to generate a class ofC1continuous quartic rational Hermite interpolation splines with local tension shape parameters. The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing aC1positivity- or monotonicity- preserving interpolation spline. In addition, we extend the quartic rational Said-Ball-like basis to a triangular domain which has three tension shape parameters and includes the cubic triangular Said-Ball basis as a special case. In order to compute the corresponding patch stably and efficiently, a new de Casteljau-type algorithm is developed. Moreover, theG1continuous conditions are deduced for the joining of two patches.

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