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CLC number: O43

On-line Access: 2022-03-22

Received: 2020-11-06

Revision Accepted: 2022-04-22

Crosschecked: 2021-03-17

Cited: 0

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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


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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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.

可展曲面的焦散曲线

Miklós HOFFMANN1,2, Imre JUHáSZ3, Ede TROLL1
1埃斯特尔哈兹大学数学与计算机科学学院,匈牙利埃格尔,3300
2德布勒森大学计算机图形与图像处理系,匈牙利德布勒森,4010
3米什科尔茨大学画法几何系,匈牙利米什科尔茨,3515
摘要:考虑来自点光源或无穷远的光线经过某个镜面曲面反射时,反射光线可产生一个包络,被称为焦散曲线。本文我们研究了镜面曲面为可展曲面的情形。这些具有显式表达的焦散曲面也是可展曲面,并且与初始镜面曲面类型相同。提供了高效的算法以找到3种可展曲面(锥面、柱面和空间曲线的切线面)的焦散面。此外,提供了焦散面在当代自由形式建筑设计中的潜在应用。

关键词:焦散曲线;可展曲面;反射光线;回归曲线

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

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