Ray Tracing in Non-Constant Media


This is joint work with Eric Languenou from IRIN at the University of Nantes, France. Back when I was a PhD student and Eric was doing his post-doc at the University of Toronto we decided to model the shimmering effects due to heat. The following research is the fruit of this collaboration which started in Toronto and was polished up in the suburbs of Paris.

Following is the abstract of the paper which we presented at the 7th EUROGRAPHICS Workshop on Rendering which was held in Porto, Portugal, June 17-19, 1996. The paper will be published in a Springer-Verlag monograph.

In this paper, we explore the theory of optical deformations due to continuous variations of the refractive index of the air, and present several efficient implementations. We introduce the basic equations from geometrical optics, outlining a general method of solution. Further, we model the fluctuations of the index of refraction both as a superposition of blobs and as a stochastic function. Using a well known perturbation technique from geometrical optics, we compute linear approximations to the deformed rays. We employ this approximation and the blob representation to efficiently ray trace non linear rays through multiple environments. In addition we present a stochastic model for the ray deviations derived from an empirical model of air turbulence. We use this stochastic model to precompute deformation maps.


I will try to put some mpegs of the video that we showed at the Workshop since the following still images do not do justice to the method.

Three frames from an animation using the "stochastic rendering" algorithm. The deformations are modelled as a random process and generated directly. The turbulence is adevcted by the heat field and travels upwards. Notice the "eddie-like" structures which would be hard to fake using standard texture mapping techniques.

Three frames from an animation of a camera flying around a particularly hot "hot dog". The heat field is modelled as a superposition of blobs which are advected in a turbulence. This sequence demonstrates that our model is truly three-dimensional and coherent from frame to frame. In fact there are no restrictions on the scene to be deformed, e.g., notice that the "hot dog" is deformed as well. Here is a bigger picture of the "hot dog":