Pseudo-evolute curves and caustic surfaces 伪渐屈线与焦散面

DALKILIÇ H. N., YAYLI Y.

Frontiers of Information Technology and Electronic Engineering, vol.26, no.9, pp.1733-1741, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 9
  • Publication Date: 2025
  • Doi Number: 10.1631/fitee.2400930
  • Journal Name: Frontiers of Information Technology and Electronic Engineering
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC
  • Page Numbers: pp.1733-1741
  • Keywords: Caustic surfaces, Developable surfaces, Normal caustic developable surfaces, O182, O435, Osculating caustic developable surfaces, Pseudo-evolute curves, Rectifying caustic developable surfaces
  • Ankara University Affiliated: Yes

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.