In this case, we use the refracted beams instead of the reflected beams.
We then project these refracted beams onto a planar map. In this case, we need to see the effect of refraction and so we use a coherently spaced pattern map.

Since we are using a planar map, we have to guarantee that the reflecte vectors hit the map.
The following figure shows the effect of refraction

## Combining the effects of Reflection and Refraction

These effects can be combined by combining the reflection and refraction maps.
The reflectivity is approximated using Fresnel's equation which is approximated by a piecewise function.
Ts'o and Barsky also perturbed the reflected and refracted vectors randomly so that slight blurring occurs.

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Copyright - Sudhir R Kaushik (sudhir@cs.wpi.edu)