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

Next Article

Contents of this Issue

Other Issues


ELibM Journals

ELibM Home

EMIS Home


Pick a mirror

 

Reflections on Refractions

Georg Glaeser, Hans-Peter Schröcker

Institute for Architecture, University of Applied Arts Vienna
Oskar Kokoschka-Platz 2, A 1010 Wien, Austria
email: georg.glaeser@uni-ak.ac.at

Abstract: 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.

Keywords: Refraction, reflection, curved perspectives, fish-eye perspectives, diacaustic, catacaustic, normal congruence, real-time 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.

© 2002 Heldermann Verlag
© 2002–2013 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition