Non-uniform shape-preserving subdivision scheme for surface interpolation

2000 ◽  
Author(s):  
Wenlong Dong ◽  
Jiankun Li ◽  
C.-C. Jay Kuo
Keyword(s):  
Subdivision Scheme ◽  
Shape Preserving ◽  
Surface Interpolation

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.

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.

A new four-point shape-preserving subdivision scheme

2014 ◽  
Vol 31 (1) ◽  
pp. 57-62 ◽  
Author(s):  
Jieqing Tan ◽  
Xinglong Zhuang ◽  
Li Zhang
Keyword(s):  
Subdivision Scheme ◽  
Shape Preserving

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 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.

A butterfly subdivision scheme for surface interpolation with tension control

1990 ◽  
Vol 9 (2) ◽  
pp. 160-169 ◽  
Author(s):  
Nira Dyn ◽  
David Levine ◽  
John A. Gregory
Keyword(s):  
Tension Control ◽  
Subdivision Scheme ◽  
Surface Interpolation
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