Conditions on shape preserving of stationary polynomial reproducing subdivision schemes

2018 ◽  
pp. 283-291
Author(s):  
Yeon Kim
Keyword(s):  
Shape Preserving ◽  
Subdivision Schemes ◽  
Polynomial Reproducing

scholarly journals Abel–Goncharov Type Multiquadric Quasi-Interpolation Operators with Higher Approximation Order

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ruifeng Wu
Keyword(s):  
Error Estimates ◽  
Error Bounds ◽  
Nonnegative Integer ◽  
Convergence Rates ◽  
Approximation Order ◽  
Degree Polynomial ◽  
Shape Preserving ◽  
Interpolation Operators ◽  
Interpolation Polynomials ◽  
Polynomial Reproducing

A kind of Abel–Goncharov type operators is surveyed. The presented method is studied by combining the known multiquadric quasi-interpolant with univariate Abel–Goncharov interpolation polynomials. The construction of new quasi-interpolants ℒ m AG f has the property of m m ∈ ℤ , m > 0 degree polynomial reproducing and converges up to a rate of m + 1 . In this study, some error bounds and convergence rates of the combined operators are studied. Error estimates indicate that our operators could provide the desired precision by choosing the suitable shape-preserving parameter c and a nonnegative integer m. Several numerical comparisons are carried out to verify a higher degree of accuracy based on the obtained scheme. Furthermore, the advantage of our method is that the associated algorithm is very simple and easy to implement.

scholarly journals A Family of High Continuity Subdivision Schemes Based on Probability Distribution

2019 ◽  
Vol 38 (2) ◽  
pp. 389-398 ◽  
Author(s):  
Muhammad Asghar ◽  
Muhammad Javed Iqbal ◽  
Ghulam Mustafa
Keyword(s):  
Probability Distribution ◽  
Geometric Modeling ◽  
Probability Generating Function ◽  
Hölder Regularity ◽  
Binomial Probability ◽  
Shape Preserving ◽  
Subdivision Schemes ◽  
Smooth Curves ◽  
The Family ◽  
Holder Regularity

Subdivision schemes are famous for the generation of smooth curves and surfaces in CAGD (Computer Aided Geometric Design). The continuity is an important property of subdivision schemes. Subdivision schemes having high continuity are always required for geometric modeling. Probability distribution is the branch of statistics which is used to find the probability of an event. We use probability distribution in the field of subdivision schemes. In this paper, a simplest way is introduced to increase the continuity of subdivision schemes. A family of binary approximating subdivision schemes with probability parameter p is constructed by using binomial probability generating function. We have derived some family members and analyzed the important properties such as continuity, Holder regularity, degree of generation, degree of reproduction and limit stencils. It is observed that, when the probability parameter p = 1/2, the family of subdivision schemes have maximum continuity, generation degree and Holder regularity. Comparison shows that our proposed family has high continuity as compare to the existing subdivision schemes. The proposed family also preserves the shape preserving property such as convexity preservation. Subdivision schemes give negatively skewed, normal and positively skewed behavior on convex data due to the probability parameter. Visual performances of the family are also presented.

scholarly journals 3n-Point Quaternary Shape Preserving Subdivision Schemes

2017 ◽  
Vol 36 (3) ◽  
pp. 489-500 ◽  
Author(s):  
Mehwish Bari ◽  
◽  
Robina Bashir ◽  
Ghulam Mustafa ◽  
◽  
...  
Keyword(s):  
Shape Preserving ◽  
Subdivision Schemes

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.

scholarly journals Shape preserving design of geometrically nonlinear structures using topology optimization

2019 ◽  
Vol 59 (4) ◽  
pp. 1033-1051 ◽  
Author(s):  
Yu Li ◽  
Jihong Zhu ◽  
Fengwen Wang ◽  
Weihong Zhang ◽  
Ole Sigmund
Keyword(s):  
Topology Optimization ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Shape Preserving

scholarly journals Clothoid fitting and geometric Hermite subdivision

2021 ◽  
Vol 47 (4) ◽  
Author(s):  
Ulrich Reif ◽  
Andreas Weinmann
Keyword(s):  
Building Block ◽  
Numerical Results ◽  
Normal Vector ◽  
Subdivision Schemes ◽  
Planar Curves ◽  
Nonlinear Subdivision ◽  
New Strategy ◽  
Vector Information ◽  
Hermite Subdivision

AbstractWe consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertices. The building block for the (nonlinear) subdivision schemes we propose is based on clothoidal averaging, i.e., averaging w.r.t. locally interpolating clothoids, which are curves of linear curvature. To this end, we derive a new strategy to approximate Hermite interpolating clothoids. We employ the proposed approach to define the geometric Hermite analogues of the well-known Lane-Riesenfeld and four-point schemes. We present numerical results produced by the proposed schemes and discuss their features.

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