Full Text:   <3843>

Summary:  <603>

CLC number: O43

On-line Access: 2024-08-27

Received: 2023-10-17

Revision Accepted: 2024-05-08

Crosschecked: 2021-03-17

Cited: 0

Clicked: 6882

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Miklós HOFFMANN

https://orcid.org/0000-0001-8846-232X

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

http://doi.org/10.1631/FITEE.2000613


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



Abstract: 
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.

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