Journal for Geometry and Graphics Vol. 4, No. 1, pp. 1–18 (2000) 

Reflections on RefractionsGeorg Glaeser, HansPeter SchröckerInstitute for Architecture, University of Applied Arts ViennaOskar KokoschkaPlatz 2, A 1010 Wien, Austria email: georg.glaeser@uniak.ac.at Abstract: In computer graphics, it is often an advantage to calculate refractions directly, especially when the application is timecritical 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 2Drefraction images with additional depth information. In the threedimensional 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. Keywords: Refraction, reflection, curved perspectives, fisheye perspectives, diacaustic, catacaustic, normal congruence, realtime rendering, underwater photography. Classification (MSC2000): 51N05; 51N35, 51N99, 68U05 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 14 Mar 2002. This page was last modified: 10 May 2013.
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