scholarly journals A Nonstationary Ternary 4-Point Shape-Preserving Subdivision Scheme

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Jieqing Tan ◽  
Guangyue Tong
Keyword(s):  
Continued Fraction ◽  
Subdivision Scheme ◽  
Limit Curve ◽  
Shape Preserving ◽  
Tension Parameter ◽  
Interpolatory Subdivision

This paper uses the continued fraction technique to construct a nonstationary 4-point ternary interpolatory subdivision scheme, which provides the user with a tension parameter that effectively handles cusps compared with a stationary 4-point ternary interpolatory subdivision scheme. Then, the continuous nonstationary 4-point ternary scheme is analyzed, and the limit curve is at least C 2 -continuous. Furthermore, the monotonicity preservation and convexity preservation are proved.

An Improved Four Point Interpolatory Subdivision Scheme

2013 ◽  
Vol 380-384 ◽  
pp. 1555-1557
Author(s):  
Xin Fen Zhang ◽  
Yu Zhen Liu
Keyword(s):  
Chord Length ◽  
Subdivision Scheme ◽  
Shape Preserving ◽  
Curve Interpolation ◽  
Interpolatory Polynomial ◽  
Interpolatory Subdivision

In this paper we propose a new kind of geometry driven subdivision scheme for curve interpolation. We use cubic Lagrange interpolatory polynomial to construct a new point, selecting parameters by accumulated chord length method. The new scheme is shape preserving. It can overcome the shortcoming of the initial four point subdivision scheme proposed.

A Nonlinear Ternary Circle-Preserving Interpolatory Subdivision Scheme

2013 ◽  
Vol 427-429 ◽  
pp. 2170-2173 ◽  
Author(s):  
Qian Song ◽  
Hong Chan Zheng ◽  
Guo Hua Peng
Keyword(s):  
Subdivision Scheme ◽  
Limit Curve ◽  
Numerical Examples ◽  
Interpolatory Subdivision

In this paper, we present a new nonlinear ternary interpolatory subdivision scheme which has the properties of convexity-preserving, circle-preserving and the limit curve iscontinuous. In each subdivision step, the newly generating points will be on the circle determined by the interpolatory point and its adjacent points. Numerical examples show that this algorithm is simple and curves generated by this subdivision scheme are fair curves.

scholarly journals Shape Preservation of Tension Controlled Ternary 4-point Non-Stationary Interpolating Subdivision Scheme

2018 ◽  
Author(s):  
Khurram Pervez ◽  
Syed Hussain Shah
Keyword(s):  
Shape Preservation ◽  
Subdivision Scheme ◽  
Control Points ◽  
Shape Preserving ◽  
Subdivision Schemes ◽  
Tension Parameter ◽  
Initial Control ◽  
Shape Preserving Properties ◽  
Limiting Case

The aim of this work is to analyze and investigate the shape preserving properties of ternary 4-point non-stationary interpolating subdivision schemes constructed by Beccari et al. [1] with a tension parameter !k+1 which can reproducing exponential. Moreover, the conditions on the initial control points are developed that allow user to generate shape preserving limit curves after a nite number of subdivision steps and generalize these results in limiting case. Signicance of derived conditions are illustrated through graphs and the whole discussion is followed by examples.

Shape Preserving Properties with Constraints on the Tension Parameter of Binary Three-Point Approximating Subdivision Scheme

2020 ◽  
Vol 20 (01) ◽  
pp. 2050005
Author(s):  
Khalida Bibi ◽  
Ghazala Akram ◽  
Kashif Rehan
Keyword(s):  
Initial Data ◽  
Subdivision Scheme ◽  
Shape Preserving ◽  
Tension Parameter ◽  
Approximating Subdivision Scheme ◽  
Shape Preserving Properties

The paper analyzes conditions for preserving the shape properties from the initial data to the limit curves of the binary three-point approximating subdivision scheme. We provide suitable conditions on the initial data utilizing the tension parameter [Formula: see text], thus the scheme can maintain three important shape properties, namely positivity, monotonicity and convexity in the limit curves. The use of derived conditions is illustrated in few examples, which offers more flexibility in the generation of smooth limit curves endowed with shape preserving properties.

scholarly journals Convexity preservation of the four-point interpolatory subdivision scheme

1999 ◽  
Vol 16 (8) ◽  
pp. 789-792 ◽  
Author(s):  
Nira Dyn ◽  
Frans Kuijt ◽  
David Levin ◽  
Ruud van Damme
Keyword(s):  
Subdivision Scheme ◽  
Interpolatory Subdivision

scholarly journals Univariate approximating schemes and their non-tensor product generalization

2018 ◽  
Vol 16 (1) ◽  
pp. 1501-1518 ◽  
Author(s):  
Ghulam Mustafa ◽  
Robina Bashir
Keyword(s):  
Initial Data ◽  
Tensor Product ◽  
Limit Curve ◽  
Subdivision Schemes ◽  
Tension Parameter ◽  
The Family

AbstractThis article deals with univariate binary approximating subdivision schemes and their generalization to non-tensor product bivariate subdivision schemes. The two algorithms are presented with one tension and two integer parameters which generate families of univariate and bivariate schemes. The tension parameter controls the shape of the limit curve and surface while integer parameters identify the members of the family. It is demonstrated that the proposed schemes preserve monotonicity of initial data. Moreover, continuity, polynomial reproduction and generation of the schemes are also discussed. Comparison with existing schemes is also given.

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