Conclusions

The use of grid generation appears to be an effective tool in facilitating the plotting of 3D surfaces, but the complex nature of many special functions makes it difficult to design tools that work for all types of domains. The development of clear and informative visualizations for the NIST DLMF project will provide continued opportunities and motivation for exploring this problem. For the functions examined to date, somewhat simple structured grids have sufficed, but more advanced techniques will be needed for domains containing more numerous poles, zeros and other singularities. Some testing of unstructured grids has been done, but the authors have found that when the resulting data is translated to VRML, the surface shading is not as smooth. This problem might be diminished with the use of block structured grids.

After looking at off-the-shelf packages, it appears that commercial developers of 3D graphics packages might be interested in this work, especially as it relates to the use of contour meshes to efficiently clip a function.

Currently, we are exploring ways to feed the grid generation algorithm information about the special function so that it concentrates grid points in areas of high curvature. This will help the grid capture zeros of functions more accurately. Much work remains to be done on the visualization aspects of the DLMF project, but the hope is that what has been learned so far will make the development of visualizations for more complicated functions somewhat easier.