scholarly journals A Class of Sextic Trigonometric Bézier Curve with Two Shape Parameters

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Salma Naseer ◽  
Muhammad Abbas ◽  
Homan Emadifar ◽  
Samia Bi Bi ◽  
Tahir Nazir ◽  
...  
Keyword(s):  
Shape Control ◽  
Basis Functions ◽  
Control Parameters ◽  
Shape Parameters ◽  
Bernstein Basis ◽  
Closed Curves ◽  
Geometric Characteristics ◽  
New Class ◽  
Bernstein Basis Functions ◽  
Short Basis

In this paper, we present a new class of sextic trigonometric Bernstein (ST-Bernstein, for short) basis functions with two shape parameters along with their geometric properties which are similar to the classical Bernstein basis functions. A sextic trigonometric Bézier (ST-Bézier, for short) curve with two shape parameters and their geometric characteristics is also constructed. The continuity constraints for the connection of two adjacent ST-Bézier curves segments are discussed. Shape control parameters can provide an opportunity to modify the shape of curve as designer desired. Some open and closed curves are also part of this study.

scholarly journals On a New Construction of Generalized q-Bernstein Polynomials Based on Shape Parameter λ

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1919
Author(s):  
Qing-Bo Cai ◽  
Reşat Aslan
Keyword(s):  
Error Estimation ◽  
Shape Parameter ◽  
Bernstein Polynomials ◽  
Modulus Of Smoothness ◽  
Basis Functions ◽  
Approximation Properties ◽  
Bernstein Basis ◽  
New Class ◽  
New Construction ◽  
Bernstein Basis Functions

This paper deals with several approximation properties for a new class of q-Bernstein polynomials based on new Bernstein basis functions with shape parameter λ on the symmetric interval [−1,1]. Firstly, we computed some moments and central moments. Then, we constructed a Korovkin-type convergence theorem, bounding the error in terms of the ordinary modulus of smoothness, providing estimates for Lipschitz-type functions. Finally, with the aid of Maple software, we present the comparison of the convergence of these newly constructed polynomials to the certain functions with some graphical illustrations and error estimation tables.

Cubic Uniform B-Spline Curve and Surface with Multiple Shape Parameters

2014 ◽  
Vol 543-547 ◽  
pp. 1860-1863
Author(s):  
Xi Wang ◽  
Cui Cui Gao ◽  
Chen Jiang
Keyword(s):  
Shape Control ◽  
Basis Functions ◽  
Control Parameters ◽  
Shape Parameters ◽  
Surface Design ◽  
Local Shape ◽  
B Spline ◽  
Spline Curves ◽  
Curve Fit ◽  
Polynomial Curve

In order to construct B-spline curves with local shape control parameters, a class of polynomial basis functions with two local shape parameters is presented. Properties of the proposed basis functions are analyzed and the corresponding piecewise polynomial curve is constructed with two local shape control parameters accordingly. In particular, the G1 continuous and the shapes of other segments of the curve can remain unchangeably during the manipulation on the shape of each segment on the curve. Numerical examples illustrate that the constructed curve fit to the control polygon very well. Furthermore, its applications in curve design is discussed and an extend application on surface design is also presented. Modeling examples show that the new curve is very valuable for the design of curves and surfaces.

scholarly journals A Novel Generalization of Trigonometric Bézier Curve and Surface with Shape Parameters and Its Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-25 ◽  
Author(s):  
Sidra Maqsood ◽  
Muhammad Abbas ◽  
Gang Hu ◽  
Ahmad Lutfi Amri Ramli ◽  
Kenjiro T. Miura
Keyword(s):  
Basis Functions ◽  
Geometric Continuity ◽  
Shape Parameters ◽  
Bernstein Basis ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Surface Design ◽  
Curves And Surfaces ◽  
Bernstein Basis Functions ◽  
Parametric Continuity

Adopting a recurrence technique, generalized trigonometric basis (or GT-basis, for short) functions along with two shape parameters are formulated in this paper. These basis functions carry a lot of geometric features of classical Bernstein basis functions and maintain the shape of the curve and surface as well. The generalized trigonometric Bézier (or GT-Bézier, for short) curves and surfaces are defined on these basis functions and also analyze their geometric properties which are analogous to classical Bézier curves and surfaces. This analysis shows that the existence of shape parameters brings a convenience to adjust the shape of the curve and surface by simply modifying their values. These GT-Bézier curves meet the conditions required for parametric continuity (C0, C1, C2, and C3) as well as for geometric continuity (G0, G1, and G2). Furthermore, some curve and surface design applications have been discussed. The demonstrating examples clarify that the new curves and surfaces provide a flexible approach and mathematical sketch of Bézier curves and surfaces which make them a treasured way for the project of curve and surface modeling.

8-node quasi-conforming plane element by using Bernstein basis functions

2018 ◽  
Vol 70 ◽  
pp. 127-140 ◽  
Author(s):  
Changsheng Wang ◽  
Xingtong Lu ◽  
Xiangkui Zhang ◽  
Ping Hu
Keyword(s):  
Basis Functions ◽  
Bernstein Basis ◽  
Plane Element ◽  
Bernstein Basis Functions

scholarly journals Geometric Modeling of Novel Generalized Hybrid Trigonometric Bézier-Like Curve with Shape Parameters and Its Applications

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 967 ◽  
Author(s):  
Samia BiBi ◽  
Muhammad Abbas ◽  
Kenjiro T. Miura ◽  
Md Yushalify Misro
Keyword(s):  
Geometric Modeling ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Geometric Continuity ◽  
Shape Parameters ◽  
Bernstein Basis ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Curvature Continuity ◽  
Bernstein Basis Functions

The main objective of this paper is to construct the various shapes and font designing of curves and to describe the curvature by using parametric and geometric continuity constraints of generalized hybrid trigonometric Bézier (GHT-Bézier) curves. The GHT-Bernstein basis functions and Bézier curve with shape parameters are presented. The parametric and geometric continuity constraints for GHT-Bézier curves are constructed. The curvature continuity provides a guarantee of smoothness geometrically between curve segments. Furthermore, we present the curvature junction of complex figures and also compare it with the curvature of the classical Bézier curve and some other applications by using the proposed GHT-Bézier curves. This approach is one of the pivotal parts of construction, which is basically due to the existence of continuity conditions and different shape parameters that permit the curve to change easily and be more flexible without altering its control points. Therefore, by adjusting the values of shape parameters, the curve still preserve its characteristics and geometrical configuration. These modeling examples illustrate that our method can be easily performed, and it can also provide us an alternative strong strategy for the modeling of complex figures.

scholarly journals Decomposition of mixed pixels in MODIS data using Bernstein basis functions

2019 ◽  
Vol 13 (04) ◽  
pp. 1
Author(s):  
Yi Qin ◽  
Feng Guo ◽  
Yupeng Ren ◽  
Xin Wang ◽  
Juan Gu ◽  
...  
Keyword(s):  
Basis Functions ◽  
Bernstein Basis ◽  
Modis Data ◽  
Mixed Pixels ◽  
Bernstein Basis Functions

scholarly journals Construction of Local Shape Adjustable Surfaces Using Quintic Trigonometric Bézier Curve

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1205
Author(s):  
Muhammad Ammad ◽  
Md Yushalify Misro
Keyword(s):  
Basis Functions ◽  
Bézier Curve ◽  
Shape Parameters ◽  
Bernstein Basis ◽  
Suggested Approach ◽  
Local Shape ◽  
General Surface ◽  
Different Types ◽  
Swept Surface ◽  
Shape Adjustment

Based on quintic trigonometric Bézier like basis functions, the biquintic Bézier surfaces are modeled with four shape parameters that not only possess the key properties of the traditional Bézier surface but also have exceptional shape adjustment. In order to construct Bézier like curves with shape parameters, we present a class of quintic trigonometric Bézier like basis functions, which is an extension of a traditional Bernstein basis. Then, according to these basis functions, we construct three different types of shape adjustable surfaces such as general surface, swept surface and swung surface. In addition to the application of the proposed method, we also discuss the shape adjustment of surfaces showing with curvature nephogram (with and without fixing the boundaries). However, the modeling examples shows that the suggested approach is efficient and easy to implement.

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