Version 1
: Received: 30 December 2022 / Approved: 3 January 2023 / Online: 3 January 2023 (11:36:33 CET)
How to cite:
Yazla, A.; Sarıaydın, M.T. Modeling of (n, m) Type Minkowski Pythagorean Hodograph Curves with Hopf Map and Applications. Preprints2023, 2023010032. https://doi.org/10.20944/preprints202301.0032.v1
Yazla, A.; Sarıaydın, M.T. Modeling of (n, m) Type Minkowski Pythagorean Hodograph Curves with Hopf Map and Applications. Preprints 2023, 2023010032. https://doi.org/10.20944/preprints202301.0032.v1
Yazla, A.; Sarıaydın, M.T. Modeling of (n, m) Type Minkowski Pythagorean Hodograph Curves with Hopf Map and Applications. Preprints2023, 2023010032. https://doi.org/10.20944/preprints202301.0032.v1
APA Style
Yazla, A., & Sarıaydın, M.T. (2023). Modeling of (n, m) Type Minkowski Pythagorean Hodograph Curves with Hopf Map and Applications. Preprints. https://doi.org/10.20944/preprints202301.0032.v1
Chicago/Turabian Style
Yazla, A. and Muhammed Talat Sarıaydın. 2023 "Modeling of (n, m) Type Minkowski Pythagorean Hodograph Curves with Hopf Map and Applications" Preprints. https://doi.org/10.20944/preprints202301.0032.v1
Abstract
In present paper, spatial Minkowski Pythagorean Hodograph (MPH) curves are characterized with Rational Rotation Minimizing Frames (RRMFs). We define Euler-Rodrigues Frame (ERF) for MPH curves and by means of this concept, we reach the definition of MPH curves of type (n, m). Expressing the conditions provided by these curves in the form of Minkowski-Hopf map that we define, it is aimed to establish a connection with the Lorentz force which occurs during the process of Computer Numerical Control (CNC) type sinker Electronic Discharge Machines (EDMs). This approach is reinforced by split quaternion polynomials. Finally, we give conditons satisfied by MPH curves of low degree to be type (n, m) and construct illustrative examples.
Keywords
Minkowski Pythagorean Hodograph Curve; Rational Rotation Minimizing Frame; Euler-Rodrigues Frame; Split Quaternion Polynomial; Minkowski-Hopf Map; Type (n, m) Curve
Subject
Computer Science and Mathematics, Computer Vision and Graphics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
