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A Class of Variable Degree Trigonometric Polynomial Spline and Its Applications

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E-Learning and Games (Edutainment 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9654))

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Abstract

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.

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Acknowledgments

Project supported by the National Natural Science Foundation of China (No. 11471093) and in part by the Natural Science Research Funds of Education Department of Anhui Province (No. KJ2014A142).

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Anqing Normal University, Anqing, 246133, China

    Min Sheng & Liping Zou

  2. The University Key Laboratory of Intelligent Perception and Computing of Anhui Province, Anqing Normal University, Anqing, 246133, China

    Min Sheng & Benyue Su

  3. School of Computer and Information, Anqing Normal University, Anqing, 246133, China

    Benyue Su

Authors
  1. Min Sheng
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  2. Benyue Su
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  3. Liping Zou
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Corresponding author

Correspondence to Min Sheng .

Editor information

Editors and Affiliations

  1. Computer Science, John Moores University, Liverpool, United Kingdom

    Abdennour El Rhalibi

  2. Science and Technology, Bournemouth University, Bournemouth, United Kingdom

    Feng Tian

  3. Hangzhou Normal University, Hangzhou, Zhejiang, China

    Zhigeng Pan

  4. Computer Science and Technology, University of Bedfordshire, Luton, United Kingdom

    Baoquan Liu

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Sheng, M., Su, B., Zou, L. (2016). A Class of Variable Degree Trigonometric Polynomial Spline and Its Applications. In: El Rhalibi, A., Tian, F., Pan, Z., Liu, B. (eds) E-Learning and Games. Edutainment 2016. Lecture Notes in Computer Science(), vol 9654. Springer, Cham. https://doi.org/10.1007/978-3-319-40259-8_13

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  • DOI: https://doi.org/10.1007/978-3-319-40259-8_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40258-1

  • Online ISBN: 978-3-319-40259-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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