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CLC number: O182;O435
On-line Access: 2025-10-13
Received: 2024-10-20
Revision Accepted: 2025-01-24
Crosschecked: 2025-10-13
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Pseudo-evolute curves and caustic surfaces
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Hande Nur DALKILI, Yusuf YAYLI. Pseudo-evolute curves and caustic surfaces[J]. Frontiers of Information Technology & Electronic Engineering, 2025, 26(9): 1733-1741.
@article{title="Pseudo-evolute curves and caustic surfaces",
author="Hande Nur DALKILI, Yusuf YAYLI",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="26",
number="9",
pages="1733-1741",
year="2025",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.2400930"
}
%0 Journal Article
%T Pseudo-evolute curves and caustic surfaces
%A Hande Nur DALKILI
%A Yusuf YAYLI
%J Frontiers of Information Technology & Electronic Engineering
%V 26
%N 9
%P 1733-1741
%@ 2095-9184
%D 2025
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.2400930
TY - JOUR
T1 - Pseudo-evolute curves and caustic surfaces
A1 - Hande Nur DALKILI
A1 - Yusuf YAYLI
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 26
IS - 9
SP - 1733
EP - 1741
%@ 2095-9184
Y1 - 2025
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.2400930
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.
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