Fractal behavior of ternary 4-point interpolatory subdivision scheme with tension parameter

2015 ◽  
Vol 260 ◽  
pp. 148-158 ◽  
Author(s):  
Shahid S. Siddiqi ◽  
Wardat us Salam ◽  
Nadeem Ahmad Butt
Keyword(s):  
Subdivision Scheme ◽  
Tension Parameter ◽  
Interpolatory Subdivision

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 Recursive Process for Constructing the Refinement Rules of New Combined Subdivision Schemes and Its Extended Form

2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Rabia Hameed ◽  
Ghulam Mustafa ◽  
Jiansong Deng ◽  
Shafqat Ali
Keyword(s):  
New Method ◽  
Subdivision Scheme ◽  
Control Points ◽  
Local Translation ◽  
Extended Form ◽  
Subdivision Schemes ◽  
Tension Parameter ◽  
Displacement Vectors ◽  
The Family ◽  
Initial Control

In this article, we present a new method to construct a family of 2 N + 2 -point binary subdivision schemes with one tension parameter. The construction of the family of schemes is based on repeated local translation of points by certain displacement vectors. Therefore, refinement rules of the 2 N + 2 -point schemes are recursively obtained from refinement rules of the 2 N -point schemes. Thus, we get a new subdivision scheme at each iteration. Moreover, the complexity, polynomial reproduction, and polynomial generation of the schemes are increased by two at each iteration. Furthermore, a family of interproximate subdivision schemes with tension parameters is also introduced which is the extended form of the proposed family of schemes. This family of schemes allows a different tension value for each edge and vertex of the initial control polygon. These schemes generate curves and surfaces such that some initial control points are interpolated and others are approximated.

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