Explicit Superconic Curves

TL;DR

This paper introduces a new class of explicit superconic curves that extend conics, Cartesian ovals, and aspheric curves, with potential applications in optics and a representation in explicit form.

Contribution

It presents a novel explicit form of superconic curves extending previous models to include aspheric curves based on conics.

Findings

New explicit form of superconic curves

Extensions include conics, Cartesian ovals, and aspheric curves

Potential applications in optical design

Abstract

Conics and Cartesian ovals are very important curves in various fields of science. Also aspheric curves based on conics are useful in optics. Superconic curves recently suggested by A. Greynolds are extensions of both conics and Cartesian ovals and have been applied to optics while they are not extensions of aspheric curves based on conics. In this work, we investigate another kind of superconic curves that are extensions of not only conics and Cartesian ovals but also aspheric curves based on conics. Moreover, the superconic curves are represented in explicit form while Greynolds' superconic curves are in implicit form.