Issues on Displaying 3D Data for Scientific Visualization Thomas Theußl theussl@cg.tuwien.ac.at Institute of Computer Graphics Vienna University of Technology Vienna, Austria

Opacity-modulating Triangular Textures

Rheingans [13] suggested a straightforward approach which uses conventional texture mapping techniques to apply a pre-computed two-dimensional texture to a surface in 3D. These surfaces are assumed to be composed entirely of triangles, for arbitrary polygon meshes can easily be transformed into triangle meshes.
The texture should have certain characteristics in order to give strong shape cues on surfaces:

• It must be able to be tiled without seams, since such seams might draw the observers attention without providing useful information.
• It must have both enough transparent parts for the objects behind to be seen clearly and enough opaque parts for the surface on which it lies to be clearly perceived. For these are directly at odds with one another, the right balance must carefully be achieved as the case arises.
• It should be easy to generate and quick to render. Therefore, it should be a precomputed image stored in texture memory rather than defined by a procedure evaluated during the shading calculations.

Since the polygons the texture is to be applied to are all triangles, it is obvious to define an equilateral triangular texture element which is easily mapped to the triangles. Furthermore, if the sequence of texture values along each side is identical, and consequently the values at the texture extreme points are the same, any side of the texture element will match seamlessly with any other side.
If the texture element is defined on an equilateral triangle, the textured surface will appear most regular when the triangles on the surface are also equilateral. Unfortunately, surface extraction methods like the marching cubes algorithm [11] normally do not produce equilateral triangles. So texture pattern regularity must be improved by a preprocessing step which regularizes the polygonal tessellation producing triangles more uniformly sized and closer to equilateral, to avoid disruption of the texture regularity. Rheingans used a re-tiling algorithm developed by Turk [15]. Figure 4 compares multiple transparent surfaces to multiple opacity-modulating surfaces.

  
Figure 4: Multiple transparent surfaces on the left and multiple opacity-modulating surfaces on the right