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On-line Access: 2022-03-22

Received: 2020-11-06

Revision Accepted: 2022-04-22

Crosschecked: 2021-03-17

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Citations:  Bibtex RefMan EndNote GB/T7714




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Frontiers of Information Technology & Electronic Engineering  2022 Vol.23 No.3 P.479-487


Caustics of developable surfaces

Author(s):  Miklós HOFFMANN, Imre JUHÁSZ, Ede TROLL

Affiliation(s):  Institute of Mathematics and Computer Science, Eszterházy Károly University, Eger 3300, Hungary; more

Corresponding email(s):   hoffmann.miklos@uni-eszterhazy.hu, imre.juhasz@uni-miskolc.hu, troll.ede@uni-eszterhazy.hu

Key Words:  Caustics, Developable surface, Reflected light rays, Curve of regression

Miklós HOFFMANN, Imre JUHÁSZ, Ede TROLL. Caustics of developable surfaces[J]. Frontiers of Information Technology & Electronic Engineering, 2022, 23(3): 479-487.

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A1 - Miklós HOFFMANN
A1 - Imre JUHÁSZ
A1 - Ede TROLL
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DOI - 10.1631/FITEE.2000613

While considering a mirror and light rays coming either from a point source or from infinity, the reflected light rays may have an envelope, called a caustic curve. In this paper, we study developable surfaces as mirrors. These caustic surfaces, described in a closed form, are also developable surfaces of the same type as the original mirror surface. We provide efficient, algorithmic computation to find the caustic surface of each of the three types of developable surfaces (cone, cylinder, and tangent surface of a spatial curve). We also provide a potential application of the results in contemporary free-form architecture design.


Miklós HOFFMANN1,2, Imre JUHáSZ3, Ede TROLL1


Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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