Determine When a Parametric Surface is a Surface of Revolution

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International Electronic Journal of Geometry
Volume:15 Issue:2
Determine When a Parametric Surface is a Surface of Revolution

Determine When a Parametric Surface is a Surface of Revolution

Authors : Haohao WANG, Jerzy WOJDYLO

Pages : 313-320

Doi:10.36890/iejg.1064089

View : 52 | Download : 14

Publication Date : 2022-10-31

Article Type : Research Paper

Abstract :A surface of revolution is a surface that can be generated by rotating a planar curve insert ignore into journalissuearticles values(the directrix); around a straight line insert ignore into journalissuearticles values(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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