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.
Highlights
When light rays are reflected from a curved mirror, the following optical phenomenon may be observed: the reflected light rays may possess an envelope, called a caustic curve or surface
We present the computation of this caustic surface and provide a closed form of it
The caustics of developable surfaces have been studied in this paper
Summary
When light rays are reflected from a curved mirror, the following optical phenomenon may be observed: the reflected light rays may possess an envelope, called a caustic curve or surface. From the computational point of view, this latter type is the most challenging one in engineering applications, but at the same time, this type provides much more freedom in engineering design than the classical cones and cylinders (Seguin et al, 2021) These surfaces are used, among other applications, for creating special developable mechanisms, e.g., for cylindrical (Greenwood et al, 2019) and for conical (Hyatt et al, 2020). The relationship between the focal and caustic surfaces has been established (Pottmann and Wallner, 2000) and it has been proven that the focal surface of a developable surface will be developable of the same type as the original one (Pottmann and Wallner, 2000) This result, in theory, yields the same consequence in terms of caustic surfaces, but these theoretical outcomes do not provide exact, constructive, and algorithmic solutions to compute and display these surfaces in practical applications. These caustic surfaces are of utmost importance in contemporary architecture (Pottmann et al, 2015), where caustics may appear, e.g., as an outcome of the reflected sunshine beams
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
