scholarly journals Construction and Analysis of Binary Subdivision Schemes for Curves and Surfaces Originated from Chaikin Points

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Rabia Hameed ◽  
Ghulam Mustafa
Keyword(s):  
Shape Parameter ◽  
Weighted Average ◽  
Subdivision Schemes ◽  
Smoothing Operator ◽  
Curves And Surfaces ◽  
New Variant ◽  
Subdivision Operator ◽  
Cubic Polynomial ◽  
Smoothing Parameters ◽  
Two Parameters

We present a new variant of Lane-Riesenfeld algorithm for curves and surfaces both. Our refining operator is the modification of Chaikin/Doo-Sabin subdivision operator, while each smoothing operator is the weighted average of the four/sixteen adjacent points. Our refining operator depends on two parameters (shape and smoothing parameters). So we get new families of univariate and bivariate approximating subdivision schemes with two parameters. The bivariate schemes are the nontensor product schemes for quadrilateral meshes. Moreover, we also present analysis of our families of schemes. Furthermore, our schemes give cubic polynomial reproduction for a specific value of the shape parameter. The nonuniform setting of our univariate and bivariate schemes gives better performance than that of the uniform schemes.

scholarly journals A Family of Integer-Point Ternary Parametric Subdivision Schemes

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ghulam Mustafa ◽  
Muhammad Asghar ◽  
Shafqat Ali ◽  
Ayesha Afzal ◽  
Jia-Bao Liu
Keyword(s):  
General Formula ◽  
Integer Point ◽  
Laurent Polynomial ◽  
Polynomial Method ◽  
Subdivision Schemes ◽  
Smooth Curves ◽  
Curves And Surfaces

New subdivision schemes are always required for the generation of smooth curves and surfaces. The purpose of this paper is to present a general formula for family of parametric ternary subdivision schemes based on the Laurent polynomial method. The different complexity subdivision schemes are obtained by substituting the different values of the parameter. The important properties of the proposed family of subdivision schemes are also presented. The continuity of the proposed family is C 2 m . Comparison shows that the proposed family of subdivision schemes has higher degree of polynomial generation, degree of polynomial reproduction, and continuity compared with the exiting subdivision schemes. Maple software is used for mathematical calculations and plotting of graphs.

scholarly journals Modeling and prediction for gas production during coalbed methane drainage based on two indirect reservoir parameters

2018 ◽  
Vol 36 (6) ◽  
pp. 1424-1437 ◽  
Author(s):  
Mingjun Zou ◽  
Xiaochun Lv ◽  
Zhiquan Huang ◽  
Simin Wei ◽  
Miao Zhang ◽  
...  
Keyword(s):  
Coalbed Methane ◽  
Good Accuracy ◽  
Simulated Data ◽  
Gas Production ◽  
Methane Drainage ◽  
Modeling And Prediction ◽  
Cubic Polynomial ◽  
Southern Qinshui Basin ◽  
Two Parameters ◽  
Gas Production Prediction

Two indirect parameters influencing coalbed methane (CBM) drainage performances are proposed in this paper, which are effective desorption radius and difference between reservoir pressure and critical desorption pressure (DRPCDP). Variations of the two parameters during CBM drainage are investigated, which shows that they have a linear relationship. By using formula derivations, a theoretical model for gas production prediction is built. It suggests that the cumulative gas production is a product of square of effective desorption radius with DRPCDP, and there is also a cubic polynomial relationship between cumulative gas production and linear average DRPCDP. Furthermore, well PM01 located at southern Qinshui basin of China is selected as a case, and a commercial software is adopted to predict the gas production. Compared with the simulated and modeled cumulative gas productions, the simulated data match well with the modeled data, which indicates that the model has a good accuracy.

scholarly journals Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2102
Author(s):  
Abdul Majeed ◽  
Muhammad Abbas ◽  
Faiza Qayyum ◽  
Kenjiro T. Miura ◽  
Md Yushalify Misro ◽  
...  
Keyword(s):  
Geometric Modeling ◽  
Shape Parameter ◽  
3D Models ◽  
Basis Functions ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curves ◽  
Spline Basis ◽  
Cubic Polynomial ◽  
2D And 3D

Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ∈[0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.

scholarly journals A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 66 ◽  
Author(s):  
Aamir Shahzad ◽  
Faheem Khan ◽  
Abdul Ghaffar ◽  
Ghulam Mustafa ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Numerical Algorithm ◽  
Subdivision Schemes ◽  
Practical Applications ◽  
Curves And Surfaces ◽  
Geometrical Shapes ◽  
Subdivision Depth ◽  
Subdivision Curves

Subdivision schemes are extensively used in scientific and practical applications to produce continuous geometrical shapes in an iterative manner. We construct a numerical algorithm to estimate subdivision depth between the limit curves/surfaces and their control polygons after k-fold subdivisions. In this paper, the proposed numerical algorithm for subdivision depths of binary subdivision curves and surfaces are obtained after some modification of the results given by Mustafa et al in 2006. This algorithm is very useful for implementation of the parametrization.

Biquadratic TC-Bézier Curves with Shape Parameter

2011 ◽  
Vol 467-469 ◽  
pp. 57-62
Author(s):  
Xu Min Liu ◽  
Xian Peng Yang ◽  
Yan Ling Wu
Keyword(s):  
Shape Parameter ◽  
Free Form ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Curves And Surfaces ◽  
G1 Continuity ◽  
Shape Controlling

Shape controlling is a popular topic in curves and surfaces design with free form. In this paper, a new curve, to be called Biquadratic TC-Bézier curves with shape parameter , is constructed in the space . We show that such curves share the same properties as the traditional Bézier curves in polynomial spaces. The shape of new curves, representing circle and ellipse accurately, can be adjusted by changing the value of the parameter . Then we give the G1 continuity conditions of Biquadratic TC-Bézier curves with shape parameter and its application in surfaces modeling.

scholarly journals Self-select target neighboring base station assisted handover for natural disaster in LTE-A network

2020 ◽  
Vol 19 (1) ◽  
pp. 309
Author(s):  
Azita Laily Yusof ◽  
Ainnur Eiza Azhar ◽  
Norsuzila Ya’acob
Keyword(s):  
Natural Disaster ◽  
Weighted Average ◽  
Signal Strength ◽  
Received Signal Strength ◽  
Base Station ◽  
Average Score ◽  
Battery Life ◽  
Power Outage ◽  
Two Parameters ◽  
Selection Of

This paper presents Self-Select Target Neighboring Base Station Assisted Handover for Natural Disaster in LTE-A Network. In this study, two parameters have been introduced which are known as received signal strength of user (RSS) and left over power of base station (LoP) in order to maintained good QoS of UE and prolong battery life of base station when there is power outage. A distance fraction coefficient (α) with value 0.2 has been introduced to RSS expression to improve the signal strength by reducing the area that the UE’s covered. Both parameters are used to calculate weighted-average score (WAS) for selection of potential target base station to avoid more users to connect to the affected base station. From the results, sRSS=0.8 gave the highest WAS with value of WAS=0.84 for users from 1 to 100 compares to other value of sRSS. Moreover, by using no natural disaster condition as reference, Condition 1 (wRSS=80%, wLoP=20% ) with the lowest percentage of improvement (3.75%.) will be chosen as handover condition as it near to base station, avoid overloaded users to the affected base station, hence prolong battery life as it only use 20% of battery usage.

scholarly journals A New Quasi Cubic Rational System with Two Parameters

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1070
Author(s):  
Ming-Xiu Tuo ◽  
Gui-Cang Zhang ◽  
Kai Wang
Keyword(s):  
Positive System ◽  
Local Shape ◽  
B Spline ◽  
Triangular Domain ◽  
Complex Curves ◽  
Curves And Surfaces ◽  
Spline Curves ◽  
Totally Positive ◽  
Two Parameters ◽  
New System

The purpose of this article is to develop a new system for the construction of curves and surfaces. Making the new system not only has excellent properties of the orthodox Bézier and the B-spline method but also has practical properties such as variation diminishing and local shape adjustability. First, a new set of the quasi-cubic rational (QCR) system with two parameters is given, which is verified on an optimal normalized totally positive system (B-system). The related QCR Bézier curve is defined, and the de Casteljau-type algorithm are given. Next, a group of non-uniform QCR B-spline system is shown based on the linear combination of the proposed QCR system, the relative properties of the B-spline system are analyzed. Then, the definition and properties of non-uniform QCR B-spline curves are discussed in detail. Finally, the proposed QCR system is extended to the triangular domain, which is called the quasi-cubic rational Bernstein-Bézier (QCR-BB) system, and its related definition and properties of patches are given at length. The experimental image obtained by using MATLAB shows that the newly constructed system has excellent properties such as symmetry, totally positive, and C 2 continuity, and its corresponding curve has the properties of local shape adjustability and C 2 continuity. These extended systems in the extended triangular domain have symmetry, linear independence, etc. Hence, the methods in this article are suitable for the modeling design of complex curves and surfaces.

scholarly journals A New 4-PointC3Quaternary Approximating Subdivision Scheme

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Ghulam Mustafa ◽  
Faheem Khan
Keyword(s):  
Shape Parameter ◽  
Approximation Order ◽  
Subdivision Scheme ◽  
Subdivision Schemes ◽  
Approximating Subdivision Scheme

A new 4-pointC3quaternary approximating subdivision scheme with one shape parameter is proposed and analyzed. Its smoothness and approximation order are higher but support is smaller in comparison with the existing binary and ternary 4-point subdivision schemes.

scholarly journals A Family of Even-Point Ternary Approximating Schemes

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Abdul Ghaffar ◽  
Ghulam Mustafa
Keyword(s):  
General Formula ◽  
Shape Parameter ◽  
Sufficient Conditions ◽  
Approximation Order ◽  
Subdivision Schemes ◽  
The Family ◽  
Curvature And Torsion

We presented a general formula to generate the family of even-point ternary approximating subdivision schemes with a shape parameter for describing curves. Some sufficient conditions for C0 to C7 continuity and approximation order for certain ranges of parameter are discussed. The proposed even-point ternary schemes compare remarkably with existing even-point ternary schemes because they are able to generate limit functions with higher smoothness and approximation order. In addition, we measured curvature and torsion that assist the quality of subdivided curves.

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