4.1 Static and Dynamic Visualizations of Special Functions

The author of the chapter on Airy functions[7] specified which Airy functions should be displayed and suggested the ranges for the plots. To obtain reliable data we used a double precision Fortran routine for the calculation of Airy functions written by D.E. Amos [2]. In general, all of the authors of the DLMF should be knowledgeable about the latest computational techniques being used for the functions in their chapter and should therefore be able to point us to the best means for obtaining reliable data.

For both the still images and dynamic visualizations we began by using available packages such as MATLAB and MATHEMATICA to plot the data so that we could examine the graphical representation and adjust the scaling to bring out interesting features. Also, considerable effort was spent determining the most informative views for the still images. The still images were stored in GIF or POSTSCRIPT format. To obtain dynamic visualizations, we wrote a C program to convert the data to VRML (Virtual Reality Modeling Language; http://www.vrml.org/) format. VRML is a standard 3D file format for describing the geometry and movement of a 3D virtual world. We chose VRML because of its accessibility on the Web and its interactive capabilities. Also, VRML browsers for a variety of platforms can be freely downloaded. However, it is not a foregone conclusion that the completed version of the DLMF will use VRML. We have to address such issues as whether VRML browsers will continue to be readily available and what to do if a browser is not available for a specific platform. We will also examine the feasibility of using alternatives to VRML such as JAVA 3D which would not require the user to download a browser. Currently the user is given the option of viewing a still 3D image if a VRML browser is not available. Figure 3 shows a VRML display of the real part of Airy function Ai$(z)$. The browser controls allow the user to rotate the figure, zoom in and out, and move the figure in an arbitrary direction.

Figure 3: VRML display on CosmoPlayer.