Notice of Retraction: A novel BÉZier curve with multiple shape parameters

2010 ◽  
Author(s):  
Xinqiang Qin ◽  
Nianjuan Zhang ◽  
Gang Hu
Keyword(s):  
Bézier Curve ◽  
Bezier Curve ◽  
Shape Parameters

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 The cubic trigonometric Bézier curve with two shape parameters

2009 ◽  
Vol 22 (2) ◽  
pp. 226-231 ◽  
Author(s):  
Xi-An Han ◽  
YiChen Ma ◽  
XiLi Huang
Keyword(s):  
Bézier Curve ◽  
Bezier Curve ◽  
Shape Parameters

scholarly journals Generalized Fractional Bézier Curve with Shape Parameters

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2141
Author(s):  
Syed Ahmad Aidil Adha Said Mad Said Mad Zain ◽  
Md Yushalify Misro ◽  
Kenjiro T. Miura
Keyword(s):  
Basis Functions ◽  
Bézier Curve ◽  
Free Form ◽  
Bezier Curve ◽  
Geometric Continuity ◽  
Shape Parameters ◽  
Complex Curves ◽  
Curves And Surfaces ◽  
New Type ◽  
Fractional Parameter

The construction of new basis functions for the Bézier or B-spline curve has been one of the most popular themes in recent studies in Computer Aided Geometric Design (CAGD). Implementing the new basis functions with shape parameters provides a different viewpoint on how new types of basis functions can develop complex curves and surfaces beyond restricted formulation. The wide selection of shape parameters allows more control over the shape of the curves and surfaces without altering their control points. However, interpolated parametric curves with higher degrees tend to overshoot in the process of curve fitting, making it difficult to control the optimal length of the curved trajectory. Thus, a new parameter needs to be created to overcome this constraint to produce free-form shapes of curves and surfaces while still preserving the basic properties of the Bézier curve. In this work, a general fractional Bézier curve with shape parameters and a fractional parameter is presented. Furthermore, parametric and geometric continuity between two generalized fractional Bézier curves is discussed in this paper, as well as demonstrating the effect of the fractional parameter of curves and surfaces. However, the conventional parametric and geometric continuity can only be applied to connect curves at the endpoints. Hence, a new type of continuity called fractional continuity is proposed to overcome this limitation. Thus, with the curve flexibility and adjustability provided by the generalized fractional Bézier curve, the construction of complex engineering curves and surfaces will be more efficient.

scholarly journals Rail Optimization of Noncircular Curve of Crane Turning Based on Quasiquartic Bezier Curve with Three Shape Parameters

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Gang Liang ◽  
Zhangjie Wu ◽  
Weikun Yu
Keyword(s):  
Bézier Curve ◽  
Bezier Curve ◽  
Outer Side ◽  
Maximum Deviation ◽  
Optimal Parameters ◽  
Shape Parameters ◽  
Calculation Results ◽  
Geometric Relationship ◽  
Relationship Of ◽  
Specific Influence

In order to solve the problems of rail gnawing and jamming during turning of rail crane, a noncircular curve scheme of the crane based on Bezier curve is proposed. In the scheme, the quasiquartic Bezier curve with three shape parameters is chosen as the turning curve of the inner rail. According to the single-wheel and multiwheel situation of the crane, the tracks of the front and rear points on the outer side are calculated through the geometric relationship of the traveling mechanism of the crane cart. Taking the minimum deviation of the front and back points as the objective function of optimization, the optimal parameters of Bezier curve are searched by the multistart point heuristic global optimization algorithm, and the outer rail trajectory is fitted by Hermite interpolation. The calculation results show that the maximum deviation of the front and rear points on the outside of the crane during the turning process decreases significantly when the quartic Bezier curve is used as the turning track compared with the traditional circular turning track. When the quasiquartic Bezier curve with three shape parameters is used as the inner rail, the deviation can be further reduced by adjusting the three parameters. In addition, it is also analyzed the specific influence of turning parameters on the deviation. Finally, ADAMS is used to carry out dynamic simulation experiment and demonstrate the calculation.

The G2 and C2 rational quadratic trigonometric Bézier curve with two shape parameters with applications

2013 ◽  
Vol 219 (20) ◽  
pp. 10183-10197 ◽  
Author(s):  
Uzma Bashir ◽  
Muhammad Abbas ◽  
Jamaludin Md Ali
Keyword(s):  
Bézier Curve ◽  
Bezier Curve ◽  
Shape Parameters

scholarly journals A class of quasi-quintic trigonometric Bézier curve with two shape parameters

ScienceAsia ◽  
2013 ◽  
Vol 39S (1) ◽  
pp. 11 ◽  
Author(s):  
Uzma Bashir ◽  
Muhammad Abbas ◽  
Mohd Nain Hj Awang ◽  
Jamaludin Md. Ali
Keyword(s):  
Bézier Curve ◽  
Bezier Curve ◽  
Shape Parameters

scholarly journals Quintic Trigonometric Bezier Curve with Two Shape Parameters

2017 ◽  
Vol 46 (5) ◽  
pp. 825-831 ◽  
Author(s):  
Misro M.Y. ◽  
Ramli A. ◽  
Ali J.M.
Keyword(s):  
Bézier Curve ◽  
Bezier Curve ◽  
Shape Parameters
Sign in / Sign up

Export Citation Format

Share Document