Pseudo-evolute curves and caustic surfaces

Abstract

In this study, osculating caustic developable surfaces and rectifying caustic developable surfaces were obtained by considering space curves and curves on surfaces as base curves and changing the direction of the light source reflected by the mirror surface. It was proved that pseudo-evolute curves represent the striction curves (regression edges) of these surfaces. For developable surfaces based on curves on surfaces, it was observed that osculating caustic developable surfaces are equivalent to rectifying caustic developable surfaces if the curve is geodesic. Additionally, when the base curve was taken over any surface, the caustic surfaces were characterized as flat or normal approximation surfaces, depending on the direction of the light source.

Keywords

Pseudo-evolute curves / Caustic surfaces / Developable surfaces / Rectifying caustic developable surfaces / Osculating caustic developable surfaces / Normal caustic developable surfaces

RIGHTS & PERMISSIONS

Zhejiang University Press