16 August 2008 - 12:30Caustics from a Sphere

I decided that it was probably time for a release of a graphical demo! Since I did not code up anything in relation to the participating media research I thought that this time I would do the research the other way around! This time I have done some research related to light scattering from large spheres. When considering large spheres, it is vaguely speaking possible to use geometrical optics to describe the physics of the scattering pattern. Geometrical optics is also know as ray tracing in computer graphics.

Although, the use of geometrical optics, instead of the full solution to Maxwell’s equations (known as Mie Theory in this relation), does not provide the classical exact solution to the scattering pattern, it will provide an almost correct one. The scattering pattern will contain the forward scattering known as caustics, the primary rainbow, secondary rainbow and so on.

Having computed the scattering pattern from a sphere and stored in a simple 1D table (say floating point texture), it is pretty straight forward to imagine the use in a real-time application, since the scattering of light in any direction from the sphere is now known from a single look up. Actually it is only a 1D table for a infinite distance light source. In order to handle a nearer point light source correctly, it is necessary to compute a two dimensional table, because the finite distance to the sphere excludes some possibilites of the incoming angles depending on the radius of the sphere. Also to get the entire range of rainbow colors one would have to compute the scattering for different wavelengths.

Demo Info

It is possible to use either the 1D or the 2D apporach in the implementation. Make sure you try both, because there is a pretty rainbow hiding! In the demo the sphere has the same properties as a large water drop and the scattering was only computed for three different wavelengths red, green, and blue. No indirect lighting was taken care of (hey it should be able to run real-time). This means that when the light source (which is modeled as being a point light source) is close to the sphere there will be a large ugly unrealistic shadow on the other side of the sphere. In addition, only light coming directly from the light source will be scattered through the sphere. In principle one could add secondary bounces.

Please, be patient with the loading time, the scattering tables are stored as simple ASCII data. The sphere itself is rendered by a combination of the reflection of light and the first bounce of light coming from the environment. The reflection is computed using the scattering tables ones again, while the light from the environment is estimated by rendering a cube map and looking up in the direction of the double refracted ray through the sphere.

Note that the reference is really enjoyable reading for folks with that sense of humor and is highly recommendable.

Download

Sphere Caustics Demo (2.4MB, Windows only)

References

[1] H.C.Van De Hulst, Light Scattering by Small Particles