Explicit superconic curves.

Conics and Cartesian ovals are extremely important curves in various fields of science. In addition, aspheric curves based on conics are useful in optical design. Superconic curves, recently suggested by Greynolds, are extensions of both conics and Cartesian ovals and have been applied to optical design. However, they are not extensions of aspheric curves based on conics. In this work, we investigate another type of superconic curves. These superconic curves are extensions of not only conics and Cartesian ovals but also aspheric curves based on conics. Moreover, these are represented in explicit form, while Greynolds's superconic curves are in implicit form.