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Frontiers of Information Technology & Electronic Engineering

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Pseudo-evolute curves and caustic surfaces

Author(s): Hande Nur DALKILIÇ^‡¹ , Yusuf YAYLI²
Affiliation(s): ¹Department of Mathematics, Graduate School of Natural And Applied Sciences, Ankara University, Ankara, 06000, Türkiye; more
Corresponding email(s): hncetin@ankara.edu.tr, yayli@science.ankara.edu.tr
Key Words: Pseudo-evolute curves; Caustic surfaces; Developable surfaces; Rectifying caustic developable surfaces; Osculating caustic developable surfaces; Normal caustic developable surfaces

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Hande Nur DALKILIÇ^‡¹ , Yusuf YAYLI². Pseudo-evolute curves and caustic surfaces[J]. Frontiers of Information Technology & Electronic Engineering,in press.https://doi.org/10.1631/FITEE.2400930

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author="Hande Nur DALKILIÇ^‡¹ , Yusuf YAYLI²",
journal="Frontiers of Information Technology & Electronic Engineering",
year="in press",
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doi="https://doi.org/10.1631/FITEE.2400930"
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doi="https://doi.org/10.1631/FITEE.2400930"

Abstract
Chinese Summary
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Reviewer Comment

Abstract: In this study, osculating caustic developable and rectifying caustic developable surfaces were obtained by considering space curves and curves on the surface as base curves and changing the direction of the light source reflected by the mirror surface. It was proved that the pseudo-evolute curves represent the striction curves (regression edges) of these surfaces. In the case of developable surfaces based on curves on the surface, it was observed that osculating caustic developable surfaces are equivalent to rectifying caustic developable surfaces if the curve is geodesic. In addition, 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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