scholarly journals Planar Typical Bézier Curves with a Single Curvature Extremum

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2148
Author(s):  
Chuan He ◽  
Gang Zhao ◽  
Aizeng Wang ◽  
Shaolin Li ◽  
Zhanchuan Cai
Keyword(s):  
Interpolation Problem ◽  
Numerical Experiments ◽  
Sufficient Condition ◽  
Calculation Formula ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Fast Calculation ◽  
Effectiveness And Efficiency ◽  
Curvature Extremum

This paper focuses on planar typical Bézier curves with a single curvature extremum, which is a supplement of typical curves with monotonic curvature by Y. Mineur et al. We have proven that the typical curve has at most one curvature extremum and given a fast calculation formula of the parameter at the curvature extremum. This will allow designers to execute a subdivision at the curvature extremum to obtain two pieces of typical curves with monotonic curvature. In addition, we put forward a sufficient condition for typical curve solutions under arbitrary degrees for the G1 interpolation problem. Some numerical experiments are provided to demonstrate the effectiveness and efficiency of our approach.

scholarly journals Planar Typical Bézier Curves Made Simple

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3017
Author(s):  
Javier Sánchez-Reyes
Keyword(s):  
Explicit Formula ◽  
18Th Century ◽  
Arbitrary Point ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Axis Of Symmetry ◽  
Curvature Extremum ◽  
Early 18Th Century

Recently, He et al. derived several remarkable properties of the so-called typical Bézier curves, a subset of constrained Bézier curves introduced by Mineur et al. In particular, He et al. proved that such curves display at most one curvature extremum, give an explicit formula of the parameter at the extremum, and show that subdividing a curve at this point furnishes two new typical curves. We recall that typical curves amount to segments of a special family of sinusoidal spirals, curves already studied by Maclaurin in the early 18th century and whose properties are well-known. These sinusoidal spirals display only one curvature extremum (i.e., vertex), whose parameter is simply that corresponding to the axis of symmetry. Subdividing a segment at an arbitrary point, not necessarily the vertex, always yields two segments of the same spiral, hence two typical curves.

Quadratic Bezier Curves for Multi-Agent Coordinated Arrival in the Presence of Obstacles

2021 ◽  
Author(s):  
Satyanarayana G. Manyam ◽  
David Casbeer ◽  
Isaac E. Weintraub ◽  
Dzung M. Tran ◽  
Justin M. Bradley ◽  
...  
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Multi Agent

Curves used in highway design and Bezier curves

2021 ◽  
Vol Accepted ◽  
Author(s):  
Bayram Şahin ◽  
Aslı Ayar
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Highway Design

scholarly journals A new method on motion planning for mobile robots using jump point search and Bezier curves

2021 ◽  
Vol 18 (4) ◽  
pp. 172988142110192
Author(s):  
Ben Zhang ◽  
Denglin Zhu
Keyword(s):  
Motion Planning ◽  
Initial Point ◽  
Target Point ◽  
Jump Point ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Front End ◽  
Planning Algorithm ◽  
Point Search ◽  
Path Planning Algorithm

Innovative applications in rapidly evolving domains such as robotic navigation and autonomous (driverless) vehicles rely on motion planning systems that meet the shortest path and obstacle avoidance requirements. This article proposes a novel path planning algorithm based on jump point search and Bezier curves. The proposed algorithm consists of two main steps. In the front end, the improved heuristic function based on distance and direction is used to reduce the cost, and the redundant turning points are trimmed. In the back end, a novel trajectory generation method based on Bezier curves and a straight line is proposed. Our experimental results indicate that the proposed algorithm provides a complete motion planning solution from the front end to the back end, which can realize an optimal trajectory from the initial point to the target point used for robot navigation.

scholarly journals Real-time Trajectory Generation for Multiple Drones using Bézier Curves

2020 ◽  
Vol 53 (2) ◽  
pp. 9276-9281
Author(s):  
Bahareh Sabetghadam ◽  
Rita Cunha ◽  
António Pascoal
Keyword(s):  
Real Time ◽  
Trajectory Generation ◽  
Bezier Curves ◽  
Bézier Curves
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