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.
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.
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Miklós HOFFMANN, Imre JUHÁSZ, and Ede TROLL contributed equally, on a shared basis to the research, jointly developing the mathematical computations and creating the experimental figures.
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Miklós HOFFMANN, Imre JUHÁSZ, and Ede TROLL declare that they have no conflict of interest.
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Project supported by the European Union and the European Social Fund (No. EFOP-3.6.3-VEKOP-16-2017-00002). Open Access funding provided by European Union and the European Social Fund
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Hoffmann, M., Juhász, I. & Troll, E. Caustics of developable surfaces. Front Inform Technol Electron Eng 23, 479–487 (2022). https://doi.org/10.1631/FITEE.2000613
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DOI: https://doi.org/10.1631/FITEE.2000613