Determine When a Parametric Surface is a Surface of Revolution

Year 2022, Volume: 15 Issue: 2, 313 - 320, 31.10.2022

Haohao Wang Jerzy Wojdylo

https://doi.org/10.36890/iejg.1064089

Abstract

A surface of revolution is a surface that can be generated by rotating a planar curve (the directrix)
around a straight line (the axis) in the same plane. Using the mathematics of quaternions, we provide a parametric
equation of a surface of revolution generated by rotating a directrix about an axis by quaternion multiplication
of the parametric representations of the directrix curve and the line of axis. Then, we describe an algorithm
to determine whether a parametric surface is a surface of revolution, and identify the axis and the directrix.
Examples are provided to illustrate our algorithm.

Keywords

Surface of revolution, quaternion multiplication, rotation axis, directrix

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