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 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

scholarly journals Shape Preserving Data Interpolation Using Rational Cubic Ball Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Ayser Nasir Hassan Tahat ◽  
Abd Rahni Mt Piah ◽  
Zainor Ridzuan Yahya
Keyword(s):  
Numerical Experiments ◽  
Smooth Curve ◽  
The Other ◽  
Data Interpolation ◽  
Shape Parameters ◽  
Interpolation Scheme ◽  
Shape Preserving ◽  
Curve Interpolation ◽  
Two Parameters

A smooth curve interpolation scheme for positive, monotone, and convex data is developed. This scheme uses rational cubic Ball representation with four shape parameters in its description. Conditions of two shape parameters are derived in such a way that they preserve the shape of the data, whereas the other two parameters remain free to enable the user to modify the shape of the curve. The degree of smoothness isC1. The outputs from a number of numerical experiments are presented.

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
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