scholarly journals An Approximation Method of Bézier Curve

2017 ◽  
Vol 10 (4) ◽  
pp. 67
Author(s):  
Zhi Wu ◽  
Chu yi Song ◽  
De xi Bao

It is proved that the linear space constructed by power base is a banach space under 2-norm by using approximation method. For the Bézier curve--the elements in banach space, the linear combination of the low-order S power base is used to approximate optimal the high-order Bernstein base function. The original Bézier curve is instituted by the linear combination of low-order S power base and the optimal approximation element of the original Bézier curve is obtained.

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Juncheng Li ◽  
Dongbiao Zhao

A trigonometric Bézier curve analogous to the cubic polynomial Bézier curve, with a shape parameter, is presented in this work. The proposed curve inherits properties similar to those of cubic polynomial Bézier curve, and the shape of the curve can be adjusted by altering the value of the shape parameter while the control polygon is fixed. With the shape parameter, the proposed curve can be made closer to the given control polygon than the general cubic Bézier curve. Then, image compression using the trigonometric Bézier curve approximation method is investigated. Experimental results show that the trigonometric Bézier curve approximation is an effective method for dealing with image compression problems.


2021 ◽  
Vol 70 ◽  
pp. 1-10
Author(s):  
Bharath Subramani ◽  
Ashish Kumar Bhandari ◽  
Magudeeswaran Veluchamy

Actuators ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 173
Author(s):  
Hongbo Wang ◽  
Shihan Xu ◽  
Longze Deng

Traffic accidents are often caused by improper lane changes. Although the safety of lane-changing has attracted extensive attention in the vehicle and traffic fields, there are few studies considering the lateral comfort of vehicle users in lane-changing decision-making. Lane-changing decision-making by single-step dynamic game with incomplete information and path planning based on Bézier curve are proposed in this paper to coordinate vehicle lane-changing performance from safety payoff, velocity payoff, and comfort payoff. First, the lane-changing safety distance which is improved by collecting lane-changing data through simulated driving, and lane-changing time obtained by Bézier curve path planning are introduced into the game payoff, so that the selection of the lane-changing start time considers the vehicle safety, power performance and passenger comfort of the lane-changing process. Second, the lane-changing path without collision to the forward vehicle is obtained through the constrained Bézier curve, and the Bézier curve is further constrained to obtain a smoother lane-changing path. The path tracking sliding mode controller of front wheel angle compensation by radical basis function neural network is designed. Finally, the model in the loop simulation and the hardware in the loop experiment are carried out to verify the advantages of the proposed method. The results of three lane-changing conditions designed in the hardware in the loop experiment show that the vehicle safety, power performance, and passenger comfort of the vehicle controlled by the proposed method are better than that of human drivers in discretionary lane change and mandatory lane change scenarios.


2015 ◽  
Vol 9 (5) ◽  
pp. 596-602
Author(s):  
Dwi Agung Nugroho ◽  
Syamsul Rizal ◽  
Dong-Seong Kim
Keyword(s):  

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