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Spiral transitions

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Abstract

Spiral curves are free from singularities and curvature extrema. These are used in path smoothing applications to overcome the abrupt change in curvature and super-elevation of moving object that occurs between tangent and circular curve. Line to circle spiral transition is made of straight line segment and curvature continuous spiral curve. It is extendible to other important types of transitions like line to line and circle to circle. Although the problem of line to circle transition has been addressed by many researchers, there is no comprehensive literature review available. This paper presents state-of-the-art of line to circle spiral transition, applications in different fields, limitations of existing approaches, and recommendations to meet the challenges of compatibility with today’s CAD/CAM soft wares, satisfaction of Hermite end conditions, approximation of discrete data for image processing, 3D path smoothness for an unmanned aerial vehicle (UAV), and arc-length parametrization. Whole discussion is concluded with future research directions in various areas of applications.

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Acknowledgements

This research is supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under the Visiting Scientist Programme; and PDE-GIR project which has received funding from the European Unions Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No 778035

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Authors and Affiliations

  1. Faculty of Science, Inonu University, Malatya, Turkey

    Akin Levent

  2. Faculty of Science, Ege University, Izmir, Turkey

    Bayram Sahin

  3. Department of Computer Science, COMSATS University Islamabad, Lahore Campus, Pakistan

    Zulfiqar Habib

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  1. Akin Levent
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  2. Bayram Sahin
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Levent, A., Sahin, B. & Habib, Z. Spiral transitions. Appl. Math. J. Chin. Univ. 33, 468–490 (2018). https://doi.org/10.1007/s11766-018-3554-4

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