scholarly journals Model Matematika Kurva Kuartik Bezier Hasil Modifikasi Kubik Bezier

2021 ◽  
Vol 1 (1) ◽  
pp. 40-46
Author(s):  
Juhari Juhari
Keyword(s):  
Parameter Selection ◽  
Creative Industries ◽  
Surface Shape ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Control Points ◽  
Bézier Curves ◽  
Artistic Creativity ◽  
Space Geometry ◽  
Selection For

The creative industries have become the government's attention for contributing to economic accretion. But due the lack of artistic creativity and appeal, the evolution of creative industries craft section is not optimal. So that it was needed a variations of relief items to increase the attractiveness. In general, industrial objects design are still limited to the space geometry objects or a Bezier curve of degree two. Therefore, Bezier curves of degree is selected and modified it into a quartic Bezier forms and then applied to the design of industrial objects (glassware). The purpose of this research is to determine the formula of quartic Bezier from of qubic Bezier modifications and to determine the rotary surface shape of quartic Bezier from cubic Bezier modifications. Then, from some form of revolving surface of modified cubic Bezier the glassware designs are generated. The results of this research are, first, the formula of quartic Bezier result of Bezier cubic modifications. Second, the form of revolving surface of modified cubic Bezier which is influenced by five control points  and parameter selection . For further Research it is expected to develop a modification of cubic Bezier into Bezier of degree-

scholarly journals Mathematical Model Quartic Curve Bezier of Modification Cubic Curve Bezier

CAUCHY ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. 77
Author(s):  
Juhari Juhari
Keyword(s):  
Mathematical Model ◽  
Creative Industries ◽  
Surface Shape ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Control Points ◽  
Artistic Creativity ◽  
Quartic Curve ◽  
Cubic Curve ◽  
Space Geometry

<div><p>The creative industries have become the government's attention for contributing to economic accretion. But due to the lack of artistic creativity and appeal, the evolution of the creative industries' craft section is not optimal. So that it was needed a variation of relief items to increase attractiveness. In general, an industrial object's design is still limited to the space geometry objects or a Bezier curve of degree two. Therefore, Bezier curves of degree are selected and modified it into a quartic Bezier forms and then applied to the design of industrial objects (glassware). The purpose of this research is to determine the formula of the quartic Bezier form of cubic Bezier modifications and to determine the rotary surface shape of quartic Bezier from cubic Bezier modifications. Then, from some form of the revolving surface of modified cubic Bezier, the glassware designs are generated. The results of this research are, first, the formula of the quartic Bezier result of Bezier cubic modifications. Second, the form of the revolving surface of modified cubic Bezier which is influenced by five control points P0, NP31, NP32, NP33, P3, and parameter lambda. For further research, it is expected to develop a modification of cubic Bezier into Bezier of degree-n</p></div>

scholarly journals Approximate Multidegree Reduction ofλ-Bézier Curves

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Gang Hu ◽  
Huanxin Cao ◽  
Suxia Zhang
Keyword(s):  
Shape Control ◽  
Control Parameter ◽  
Linear Equations ◽  
Least Square ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Control Points ◽  
Degree Reduction ◽  
Bezier Curves ◽  
Bézier Curves

Besides inheriting the properties of classical Bézier curves of degreen, the correspondingλ-Bézier curves have a good performance in adjusting their shapes by changing shape control parameter. In this paper, we derive an approximation algorithm for multidegree reduction ofλ-Bézier curves in theL2-norm. By analysing the properties ofλ-Bézier curves of degreen, a method which can deal with approximatingλ-Bézier curve of degreen+1byλ-Bézier curve of degreem  (m≤n)is presented. Then, in unrestricted andC0,C1constraint conditions, the new control points of approximatingλ-Bézier curve can be obtained by solving linear equations, which can minimize the least square error between the approximating curves and the original ones. Finally, several numerical examples of degree reduction are given and the errors are computed in three conditions. The results indicate that the proposed method is effective and easy to implement.

A Bezier Curve Based Key Management Scheme for Hierarchical Wireless Sensor Networks

2012 ◽  
Vol 263-266 ◽  
pp. 2979-2985
Author(s):  
Yong Luo Shen ◽  
Jun Zhang ◽  
Di Wei Yang ◽  
Lin Bo Luo
Keyword(s):  
Key Management ◽  
Wireless Sensor ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Control Points ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Management Scheme ◽  
Secret Keys ◽  
Key Management Scheme

In this paper, we propose a novel key management scheme based on Bezier curves for hierarchical wireless sensor networks (WSNs). The design of our scheme is motivated by the idea that a Bezier curve can be subdivided into arbitrarily continuous pieces of sub Bezier curves. The subdivided sub Bezier curves are easily organized to a hierarchical architecture that is similar to hierarchical WSNs. The subdivided Bezier curves are unique and independent from each other so that it is suitable to assign each node in the WSN with a sub Bezier curve. Since a piece of Bezier curve can be presented by its control points, in the proposed key management scheme, the secret keys for each node are selected from the corresponding Bezier curve’s control points. Comparing with existing key management schemes, the proposed scheme is more suitable for distributing secret keys for hierarchical WSNs and more efficient in terms of computational and storage cost.

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 Approximate conversion of Bézier curves

1995 ◽  
Vol 51 (1) ◽  
pp. 153-162 ◽  
Author(s):  
Yungeom Park ◽  
U Jin Choi ◽  
Ha-Jine Kimn
Keyword(s):  
Error Analysis ◽  
A Priori ◽  
Approximation Error ◽  
Bézier Curve ◽  
Bezier Curve ◽  
A Priori Bounds ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Geometric Properties

The methods for generating a polynomial Bézier approximation of degree n − 1 to an nth degree Bézier curve, and error analysis, are presented. The methods are based on observations of the geometric properties of Bézier curves. The approximation agrees at the two endpoints up to a preselected smoothness order. The methods allow a detailed error analysis, providing a priori bounds of the point-wise approximation error. The error analysis for other authors’ methods is also presented.

scholarly journals Path Planning Optimization for Driverless Vehicle in Parallel Parking Integrating Radial Basis Function Neural Network

2021 ◽  
Vol 11 (17) ◽  
pp. 8178
Author(s):  
Leiyan Yu ◽  
Xianyu Wang ◽  
Zeyu Hou ◽  
Zaiyou Du ◽  
Yufeng Zeng ◽  
...  
Keyword(s):  
Neural Network ◽  
Radial Basis Function ◽  
Basis Function ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Control Points ◽  
Parallel Parking ◽  
Radial Basis ◽  
Initial Path ◽  
Continuous Curvature

To optimize performances such as continuous curvature, safety, and satisfying curvature constraints of the initial planning path for driverless vehicles in parallel parking, a novel method is proposed to train control points of the Bézier curve using the radial basis function neural network method. Firstly, the composition and working process of an autonomous parking system are analyzed. An experiment concerning parking space detection is conducted using an Arduino intelligent minicar with ultrasonic sensor. Based on the analysis of the parallel parking process of experienced drivers and the idea of simulating a human driver, the initial path is planned via an arc-line-arc three segment composite curve and fitted by a quintic Bézier curve to make up for the discontinuity of curvature. Then, the radial basis function neural network is established, and slopes of points of the initial path are used as input to train and obtain horizontal ordinates of four control points in the middle of the Bézier curve. Finally, simulation experiments are carried out by MATLAB, whereby parallel parking of driverless vehicle is simulated, and the effects of the proposed method are verified. Results show the trained and optimized Bézier curve as a planning path meets the requirements of continuous curvature, safety, and curvature constraints, thus improving the abilities for parallel parking in small parking spaces.

scholarly journals On the Involute of the Cubic Bezier Curve by Using Matrix Representation in E3

2020 ◽  
Vol 13 (2) ◽  
pp. 216-226
Author(s):  
Şeyda Kılıçoğlu ◽  
Süleyman Şenyurt
Keyword(s):  
Vector Fields ◽  
Matrix Representation ◽  
Matrix Form ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Control Points ◽  
Cubic Bezier Curve

In this study we have examined, involute of the cubic Bezier curve based on the control points with matrix form in E3. Frenet vector fields and also curvatures of involute of the cubic Bezier curve are examined based on the Frenet apparatus of the first cubic Bezier curve in E3.  

A Concurrent Search Algorithm for Multiple Phase Transition Pathways

2013 ◽  
Author(s):  
Lijuan He ◽  
Yan Wang
Keyword(s):  
Phase Transition ◽  
Search Algorithm ◽  
Minimum Energy ◽  
Saddle Points ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Conjugate Directions ◽  
Control Points ◽  
True Value ◽  
Transition Paths

The challenge of accurately predicting a phase transition in computer-aided nano-design is estimating the true value of transition rate, which is determined by the saddle point with the minimum energy barrier between stable states on the potential energy surface (PES). In this paper, a new algorithm for searching the minimum energy path (MEP) is presented. Unlike existing pathway search methods, the new algorithm is able to locate both the saddle points and local minima simultaneously. Therefore no prior knowledge of the precise positions for the reactant and product on the PES is required. In addition, the algorithm is able to search multiple transition paths on the PES simultaneously. In this method, a Bézier curve is used to represent each transition path. Starting from a single Bézier curve, multiple curves with ends connected can be generated during the search process. For each Bézier curve, the reactant and product states are located by minimizing the two end control points of the curve, while the transition pathway is refined by moving the intermediate control points of the curve in the conjugate directions. A curve subdivision scheme is developed so that multiple transition paths can be located. The algorithm is demonstrated by examples.

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