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Design, Simulation, Manufacturing: The Innovation Exchange

DSMIE 2022: Advances in Design, Simulation and Manufacturing V pp 196–205Cite as

Compositional Interpolation of Spatial Discretely Presented Curves by Harmonizing Pointed Polynomials

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Part of the Lecture Notes in Mechanical Engineering book series (LNME)

Abstract

This study defines the point calculus Balyuba-Naidysh (point BN-calculus). The principle of the geometric interpolation method, which is carried out only based on harmonized point polynomials, is explained. A record of the characteristic function is given in general. The sequence of transition from the characteristic function to BN-coordinates, which are components of harmonized point polynomials, is presented. To solve the problem of global interpolation of spatial discrete represented curves (DPC), the definition of the metric operator of three points (MOTP), the geometric scheme of its calculation, and one of its properties, which is the basis for calculating the length of segments in space, is provided. An interpretation of the terms composition and geometric composition is given. They define how they should be understood and applied in this study. Using the MOTP, a generalized record for determining the length of the section is shown, a record of the length of the section is shown in point form, and calculation formulas are given in the coordinate form, using which its length is calculated. It is indicated that the interpolation nodes are the vertices of the accompanying broken line (ABL), which is built on the basic points of the DPC through which the interpolation curve will pass in the form of a point polynomial. The CF harmonization method for forming a harmonized point polynomial continuously interpolates the spatial DPC.

Keywords

  • Point BN-calculus
  • Geometric composition
  • Characteristic functions
  • Curve
  • Industrial growth

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Authors and Affiliations

  1. Bogdan Khmelnitsky Melitopol State Pedagogical University, 20, Hetmanska St., Melitopol, 72300, Ukraine

    Victor Vereshchaga, Andrii Naydish, Oleksandr Pavlenko & Kseniia Lysenko

  2. Zaporizhzhia National University, 160-a, Heroiv Ukrainy St., Melitopol, 72319, Ukraine

    Yevhen Adoniev

Authors
  1. Victor Vereshchaga
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  2. Andrii Naydish
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  3. Yevhen Adoniev
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  4. Oleksandr Pavlenko
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  5. Kseniia Lysenko
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Corresponding author

Correspondence to Oleksandr Pavlenko .

Editor information

Editors and Affiliations

  1. Sumy State University, Sumy, Ukraine

    Prof. Vitalii Ivanov

  2. Poznan University of Technology, Poznan, Poland

    Dr. Justyna Trojanowska

  3. Sumy State University, Sumy, Ukraine

    Prof. Ivan Pavlenko

  4. Free University of Bozen-Bolzano, Bolzano, Bolzano, Italy

    Dr. Erwin Rauch

  5. University of Zagreb, Zagreb, Croatia

    Prof. Dragan Peraković

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Vereshchaga, V., Naydish, A., Adoniev, Y., Pavlenko, O., Lysenko, K. (2022). Compositional Interpolation of Spatial Discretely Presented Curves by Harmonizing Pointed Polynomials. In: Ivanov, V., Trojanowska, J., Pavlenko, I., Rauch, E., Peraković, D. (eds) Advances in Design, Simulation and Manufacturing V. DSMIE 2022. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-06025-0_20

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  • DOI: https://doi.org/10.1007/978-3-031-06025-0_20

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