Analytical Method for Reflection and Refraction

In computer graphics, ray tracing is very simple and powerful method to present physical phenomena especially light-related things such as reflection and refraction since it traces the ray from the eye to the light source; however, we cannot understand how the result image is generated. Then, this chapter describes the mechanism of reflection and refraction. It is very time-consuming to render the target object considering reflection and refraction. If the object distorted by reflection and refraction is previously obtained, it is very fast to generate the result image since all we have to do is to render the distorted object without considering reflection and refraction. In the proposed method, firstly, a virtual object, which is constructed with vertices translated from original ones by considering reflection and refraction, is generated. Then, the image with reflection and refraction is generated by rendering the virtual object. In the analysis, total reflection and attenuation of light power are also considered. At last, the proposed method is applied to two types of transparent objects: cubed glass and cylindrical glass, and the comparison between the simulation results and the real photos is performed to demonstrate that the generated images are the same as the real ones.