Random caustics
Jos Stam · 1996
Subtle variations in intensity such as caustics can either be simulated directly using optical simulations or can be faked using textures. The method that I propose in this sketch lies somewhere in between. In general it is easier to generate textures of surfaces than to generate textures of the illumination field reflected or refracted from such surfaces. Indeed, it is very difficult to fake moving caustics using standard texture synthesis tools. The basic idea behind my method is to construct a texture synthesis algorithm for the intensity field which is consistent with both the texture of the surface and the laws of optics. This idea is not new in computer graphics and can be traced back to Blinn’s bump maps. Ten years later, Krueger formalized this idea using statistical theories [1]. He modelled both the surface height and the intensity fluctuations as random functions. Statistical models for surfaces are well known and are synthesized for example by convolving a white noise. In order to synthesize textures for the intensity fluctuations, Krueger proposes to derive statistical models for them. He simplified the problem considerably by assuming that the intensity correlation is related to the surface correlation by a perspective transformation. Qualitatively this means that the intensity fluctuations closely resemble those of the surface fluctuations. Caustics, however, are visually very different from the appearance of the water surface. In this sketch I propose an alternative method to synthesize textures of caustics using a wave description of light. Such a description was introduced to computer graphics fifteen years ago by Moravec, who unsuccessfully applied it to the global illumination problem [2]. His algorithm relies on the fact that the propagation of a planar light wave can be modelled by a series of convolutions. I will use precisely these filters defining the convolutions to synthesize textures of caustics.