# Would compute the wave function and the backward ray tracing step shader

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Our algorithm works as follows: We start at the bottom of the sea, right after we have painted the ground plane. Then, a second, additive blended pass is used to render the caustic on top of that. To do so, we create a mesh with the same granularity as the wave mesh and one that will be colored per-vertex with the caustic value: zero means no lighting and one means a beam of very focused light hits the sea bottom. To construct this lighting, backward ray tracing is used. For each vertex of the mesh, we project it vertically until we reach the wave point located right on top of it. Then, we compute the normal of the wave at that point using finite differences. With the vector and the normal, and using Snell's Law (remember the IOR for water is 1.33333), we can create secondary rays that travel from the wave into the air. Now, all we have to do is check which rays actually hit the sun after leaving the water. To do so, we compute the angle between the ray and a vertical ray using the dot product. We know the sun is 0.53° across, but its halo can be considered as a secondary light source, most days covering an arc 10 times larger. Then, we use the angle to index a texture map, which encodes the luminosity of the caustic depending on the angle (see

Figure 20.9).

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This technique can also be implemented using classic graphics programming. But it was designed from day one to be coded using pixel shaders for increased efficiency. To do so, we would compute the wave function and the backward ray tracing step in a shader, which also computes the derivative of the wave function. More details and a demo of this implementation can be found in the Gamasutra paper by Juan Guardado of NVIDIA and me, and is available on the Gamasutra web site."