Geodesic
Reflections on Refractions
Journal for geometry and graphics, Tome 4 (2000) no. 1, pp. 001-018.

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In computer graphics, it is often an advantage to calculate refractions directly, especially when the application is time-critical or when line graphics have to be displayed. We specify efficient formulas and parametric equations for the refraction on straight lines and planes. Furthermore, we develop a general theory of refractions, with reflections as a special case. In the plane case, all refracted rays are normal to a characteristic conic section. We investigate the relation of this conic section and the diacaustic curve. Using this, we can deduce properties of reciprocal refraction and a virtual object transformation that makes it possible to produce 2D-refraction images with additional depth information. In the three-dimensional case, we investigate the counter image of a straight line. It is a very special ruled surface of order four. This yields results on the order of the refrax of algebraic curves and on the shading of refracted polygons. Finally, we provide a formula for the diacaustic of a circle. 
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     author = {G. Glaeser and H.-P. Schr�cker},
     title = {Reflections on {Refractions}},
     journal = {Journal for geometry and graphics},
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     year = {2000},
     url = {http://geodesic.mathdoc.fr/item/JGG_2000_4_1_a0/}
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G. Glaeser; H.-P. Schr�cker. Reflections on Refractions. Journal for geometry and graphics, Tome 4 (2000) no. 1, pp. 001-018. http://geodesic.mathdoc.fr/item/JGG_2000_4_1_a0/