Anti-pedals and Primitives of Curves in Minkowski Plane

Abstract

The orthogonal projection of a fixed point on the tangent lines of a given curve yields a pedal curve of that curve. The aim of this study is to examine some special curves, such as pedal curves, which have singular points even for regular curves, in the Minkowski plane. For this, we investigate an anti-pedal and a primitive of curve, which is closely related to the pedal curve. The primitive of a curve is a curve that is provided by the inverse construction to make pedal. Using the envelope of a family of functions, we obtain the notion of primitive for the curves in the Minkowski plane. Then, we show that an anti-pedal of the original curve is equal to the inversion image of the pedal curve. Moreover, we analyze the relationships between primitive and anti-pedal of the curve using the inversion. We also present examples that provide our results.