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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