International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 21, Pages 1121-1132

Reflection curves—new computation and rendering techniques

Dan-Eugen Ulmet

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.


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.