A novel Bézier curve with a shape parameter of the same degree

2018 ◽  
Vol 73 (4) ◽  
Author(s):  
Juncheng Li
Keyword(s):  
Shape Parameter ◽  
Bézier Curve ◽  
Bezier Curve

scholarly journals An Investigation on Image Compression Using the Trigonometric Bézier Curve with a Shape Parameter

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Juncheng Li ◽  
Dongbiao Zhao
Keyword(s):  
Image Compression ◽  
Approximation Method ◽  
Shape Parameter ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Control Polygon ◽  
Curve Approximation ◽  
Cubic Polynomial ◽  
The Given ◽  
Cubic Bezier Curve

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.

scholarly journals New Cubic Trigonometric Bezier-Like Functions with Shape Parameter: Curvature and Its Spiral Segment

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Abdul Majeed ◽  
Muhammad Abbas ◽  
Amna Abdul Sittar ◽  
Mohsin Kamran ◽  
Saba Tahseen ◽  
...  
Keyword(s):  
Shape Parameter ◽  
Partition Of Unity ◽  
Basis Functions ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Closed Curves ◽  
Geometric Invariance ◽  
And Control ◽  
Symmetric Property ◽  
Cubic Bezier Curve

This work presents the new cubic trigonometric Bézier-type functions with shape parameter. Basis functions and the curve satisfy all properties of classical Bézier curve-like partition of unity, symmetric property, linear independent, geometric invariance, and convex hull property and have been proved. The C 3 and G 3 continuity conditions between two curve segments have also been achieved. To check the applicability of proposed functions, different types of open and closed curves have been constructed. The effect of shape parameter and control points has been observed. It is observed that, by decreasing the value of shape parameter, the curve moves toward the control polygon and vice versa. The CT-Bézier curve is closer to the cubic Bézier curve for a fixed value of shape parameter. The proposed CT-Bézier curve can be used to represent ellipse. Using proposed basis functions, we have constructed the spiral segment which is very useful to construct fair curves and desirable to design trajectories of mobile robots, highway, and railway routes’ designing.

Optimal Bezier Curve Modification Function for Contrast Degraded Images

2021 ◽  
Vol 70 ◽  
pp. 1-10
Author(s):  
Bharath Subramani ◽  
Ashish Kumar Bhandari ◽  
Magudeeswaran Veluchamy
Keyword(s):  
Bézier Curve ◽  
Bezier Curve ◽  
Degraded Images

scholarly journals Automatic Lane-Changing Decision Based on Single-Step Dynamic Game with Incomplete Information and Collision-Free Path Planning

Actuators ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 173
Author(s):  
Hongbo Wang ◽  
Shihan Xu ◽  
Longze Deng
Keyword(s):  
Path Planning ◽  
Dynamic Game ◽  
Single Step ◽  
Bézier Curve ◽  
Vehicle Safety ◽  
Bezier Curve ◽  
Lane Change ◽  
Hardware In The Loop ◽  
Power Performance ◽  
Lane Changing

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.

Reconstruct unrecoverable data in real-time networks using Bézier curve

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