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.

scholarly journals An Approximation Method of Bézier Curve

2017 ◽  
Vol 10 (4) ◽  
pp. 67
Author(s):  
Zhi Wu ◽  
Chu yi Song ◽  
De xi Bao
Keyword(s):  
Banach Space ◽  
Linear Combination ◽  
Linear Space ◽  
Approximation Method ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Base Function ◽  
Power Base ◽  
Approximation Element ◽  
Low Order

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.

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