A Class of Variable Degree Trigonometric Polynomial Spline and Its Applications

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• 关键词：Curves and surfaces modeling ; Hermite ; like interpolation ; Variable degree interpolation spline ; Trajectory planning ; Manipulator
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9654
• 期：1
• 页码：148-162
• 全文大小：892 KB
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• 作者单位：Min Sheng (17) (18)
  Benyue Su (18) (19)
  Liping Zou (17)
  
  17. School of Mathematics and Computational Science, Anqing Normal University, Anqing, 246133, China
  18. The University Key Laboratory of Intelligent Perception and Computing of Anhui Province, Anqing Normal University, Anqing, 246133, China
  19. School of Computer and Information, Anqing Normal University, Anqing, 246133, China
  
• 丛书名：E-Learning and Games
• ISBN：978-3-319-40259-8
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349
• 卷排序：9654

文摘

A class of variable degree trigonometric polynomial spline is presented for geometric modeling and industrial design. The corresponding generalized Hermite-like interpolating base functions provide bias and tension control facilities for constructing continuous interpolating curves and surfaces. The constructed curves and surfaces by the new spline can represent some conic and conicoid segments very approximately. The new interpolation spline, which need not solve m-system of equations, provides higher approximation order for data fitting than normal cubic Hermite interpolation spline for proper parameters. The idea is extended to produce Coons-like surfaces. Moreover, the new spline can be used for trajectory planning of manipulators in industrial design, which provides a continuity of position, velocity and acceleration, in order to ensure that the resulting trajectory is smooth enough. The variable degree trigonometric polynomial spline can be used to fit the sequence of joint positions for N joints. This new method approve to be practicable by the experimental results, and can meet the requirements of smooth motion of the manipulator.