International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 21, Pages 1121-1132
doi:10.1155/S0161171204211012
Reflection curves—new computation and rendering techniques
Mathematical Institute, University of Applied Sciences, Esslingen 73728, Germany
Received 1 November 2002
Copyright © 2004 Dan-Eugen Ulmet. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Reflection curves on surfaces are important tools for free-form
surface interrogation. They are essential for industrial 3D
CAD/CAM systems and for rendering purposes. In this note, new
approaches regarding the computation and rendering of reflection
curves on surfaces are introduced. These approaches are designed
to take the advantage of the graphics libraries of recent releases of
commercial systems such as the OpenInventor toolkit (developed by
Silicon Graphics) or Matlab (developed by The Math Works). A new
relation between reflection curves and contour curves is derived;
this theoretical result is used for a straightforward Matlab
implementation of reflection curves. A new type of reflection
curves is also generated using the OpenInventor texture and
environment mapping implementations. This allows the computation,
rendering, and animation of reflection curves at interactive
rates, which makes it particularly useful for industrial
applications.