A unified interpolatory subdivision scheme for quadrilateral meshes

2013 ◽  
Vol 32 (3) ◽  
pp. 1-11 ◽  
Author(s):  
Chongyang Deng ◽  
Weiyin Ma
Keyword(s):  
Subdivision Scheme ◽  
Quadrilateral Meshes ◽  
Interpolatory Subdivision

scholarly journals A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme

2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Rabia Hameed ◽  
Ghulam Mustafa ◽  
Amina Liaqat ◽  
Dumitru Baleanu ◽  
Faheem Khan ◽  
...  
Keyword(s):  
Tensor Product ◽  
Numerical Experiments ◽  
Subdivision Scheme ◽  
Shape Parameters ◽  
New Approach ◽  
Quadrilateral Meshes ◽  
Displacement Vectors ◽  
Approximating Subdivision Scheme ◽  
Interpolatory Subdivision

In this article, we present a new subdivision scheme by using an interpolatory subdivision scheme and an approximating subdivision scheme. The construction of the subdivision scheme is based on translation of points of the 4-point interpolatory subdivision scheme to the new position according to three displacement vectors containing two shape parameters. We first study the characteristics of the new subdivision scheme analytically and then present numerical experiments to justify these analytical characteristics geometrically. We also extend the new derived scheme into its bivariate/tensor product version. This bivariate scheme is applicable on quadrilateral meshes to produce smooth limiting surfaces up to C 3 continuity.

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.

Fractal range of a 3-point ternary interpolatory subdivision scheme with two parameters

2007 ◽  
Vol 32 (5) ◽  
pp. 1838-1845 ◽  
Author(s):  
Hongchan Zheng ◽  
Zhenglin Ye ◽  
Zuoping Chen ◽  
Hongxing Zhao
Keyword(s):  
Subdivision Scheme ◽  
Two Parameters ◽  
Interpolatory Subdivision
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