ARTICLE | doi:10.20944/preprints202301.0032.v1
Subject: Computer Science And Mathematics, Computer Vision And Graphics Keywords: Minkowski Pythagorean Hodograph Curve; Rational Rotation Minimizing Frame; Euler-Rodrigues Frame; Split Quaternion Polynomial; Minkowski-Hopf Map; Type (n, m) Curve
Online: 3 January 2023 (11:36:33 CET)
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.