Pedal curves and surfaces

Authors:
Kenji Ueda
Affiliations:
Ricoh Co., Ltd., Tokyo, Japan
Venue:
Mathematical Methods for Curves and Surfaces
Year:
2001

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Abstract

The positive pedal curve of a given curve is the locus of the feet of perpendiculars from a fixed point to all the tangent lines to the curve. Higher pedals are defined by induction. In this paper, it is shown that complex numbers are suitable for representing pedal curves. Pedal surfaces are defined in a similar manner to pedal curves, and quarternions are suitable for expression pedal surfaces.