可展曲面的焦散曲线

Miklós HOFFMANN; Imre JUHÁSZ; Ede TROLL

doi:10.1631/FITEE.2000613

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可展曲面的焦散曲线

常规文章 | Updated：2022-03-28

- 可展曲面的焦散曲线
  Enhanced Publication
- Caustics of developable surfaces
- 信息与电子工程前沿（英文） 2022年23卷第3期页码：479-487
- Affiliations：
  
  1.Institute of Mathematics and Computer Science, Eszterházy Károly University, Eger3300, Hungary
  2.Department of Computer Graphics and Image Processing, University of Debrecen, Debrecen4010, Hungary
  3.Department of Descriptive Geometry, University of Miskolc, Miskolc3515, Hungary
- Author bio：
  
  ‡Corresponding author
  E-mail: imre.juhasz@uni-miskolc.hu;
  E-mail: troll.ede@uni-eszterhazy.hu
- Funds：
  
  European Union and the European Social Fund(EFOP-3.6.3-VEKOP-16-2017-00002);European Union and the European Social Fund
- DOI：10.1631/FITEE.2000613
  中图分类号： O43
- 收稿：2020-11-06，
  
  录用：2021-03-17，
  
  网络出版：2022-01-29，
  
  纸质出版：2022-03-0
- Accepted：
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Miklós HOFFMANN, Imre JUHÁSZ, Ede TROLL. 可展曲面的焦散曲线[J]. 信息与电子工程前沿（英文）, 2022,23(3):479-487.

Miklós HOFFMANN, Imre JUHÁSZ, Ede TROLL. Caustics of developable surfaces[J]. Frontiers of Information Technology & Electronic Engineering, 2022, 23(3): 479-487.
Miklós HOFFMANN, Imre JUHÁSZ, Ede TROLL. 可展曲面的焦散曲线[J]. 信息与电子工程前沿（英文）, 2022,23(3):479-487. DOI： 10.1631/FITEE.2000613.

Miklós HOFFMANN, Imre JUHÁSZ, Ede TROLL. Caustics of developable surfaces[J]. Frontiers of Information Technology & Electronic Engineering, 2022, 23(3): 479-487. DOI： 10.1631/FITEE.2000613.

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。

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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references

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