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 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.

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

A 4-point interpolatory subdivision scheme for curve design

1987 ◽  
Vol 4 (4) ◽  
pp. 257-268 ◽  
Author(s):  
Nira Dyn ◽  
David Levin ◽  
John A. Gregory
Keyword(s):  
Subdivision Scheme ◽  
Curve Design ◽  
Interpolatory Subdivision

Fractal generation using ternary 5-point interpolatory subdivision scheme

2014 ◽  
Vol 234 ◽  
pp. 402-411 ◽  
Author(s):  
Shahid S. Siddiqi ◽  
Saima Siddiqui ◽  
Nadeem Ahmad
Keyword(s):  
Subdivision Scheme ◽  
Interpolatory Subdivision

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 Generalized Four Point Interpolatory Subdivision Scheme for Curve Design

2012 ◽  
Vol 586 ◽  
pp. 378-383
Author(s):  
Xin Fen Zhang
Keyword(s):  
Subdivision Scheme ◽  
Curve Design ◽  
Curve Interpolation ◽  
Interpolatory Subdivision

ßIn this paper we propose a new kind of nonlinear and geometry driven subdivision scheme for curve interpolation. We introduce serval parameters in the new scheme.When the parameter ß is taken as 0, the new scheme presented in this paper regresses to the initial four point subdivision scheme, and when ß→∞ , the new scheme is convexity preserving. With proper choices of the subdßivision parameters,it can overcome the shortcoming of the initial four point subdivision scheme proposed.

scholarly journals Shape-Preserving Properties of a Relaxed Four-Point Interpolating Subdivision Scheme

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 806 ◽  
Author(s):  
Pakeeza Ashraf ◽  
Abdul Ghaffar ◽  
Dumitru Baleanu ◽  
Irem Sehar ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Graphical Representation ◽  
Subdivision Scheme ◽  
Control Points ◽  
Positivity Preserving ◽  
Shape Preserving ◽  
Numerical Examples ◽  
Initial Control ◽  
Point Scheme ◽  
Shape Preserving Properties ◽  
Monotonicity Preserving

In this paper, we analyze shape-preserving behavior of a relaxed four-point binary interpolating subdivision scheme. These shape-preserving properties include positivity-preserving, monotonicity-preserving and convexity-preserving. We establish the conditions on the initial control points that allow the generation of shape-preserving limit curves by the four-point scheme. Some numerical examples are given to illustrate the graphical representation of shape-preserving properties of the relaxed scheme.

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