Dissemination of 3D Visualizations of Complex Function Data for the NIST Digital Library of Mathematical Functions

Qiming Wang, NIST, USA

Authors: Qiming Wang, Sandy Ressler, Bonita Saunders, National Institute of Standards and Technology, USA

The National Institute of Standards and Technology (NIST) is in the midst of developing a digital library to replace the widely used National Bureau of Standards Handbook of Mathematical Functions published in 1964. The NIST Digital Library of Mathematical Functions (DLMF) will include formulas, methods of computation, references, and links to software for over forty functions. It will be published in hardcopy format and as a website featuring interactive navigation, a mathematical equation search, 2D graphics, and dynamic interactive 3D visualizations. Dissemination of 3D visualizations is problematic and an opportunity.

Precise 3D visualizations will provide mathematicians and physical scientists with the tools to explore important attributes such as poles, zeros, and branch cuts of high level mathematical functions that solve complex physical problems. The development of such visualizations requires the accurate computation of function data and the determination of the best methods for rendering and disseminating the visualizations in an environment accessible to users on various platforms.

We have created several prototypes to explore various technologies for disseminating the visualizations. We used the Virtual Reality Modeling Language (VRML) to create web based interactive visualizations. In addition to the navigation tools provided by VRML browsers, we designed special controls that allow users to move a cutting plane through the function surface, select the surface color mapping method, choose the axis style, or transform the surface plot into a density plot.

Other visualization technologies and techniques prototyped include QuickTime, for simple animations, QuickTime VR, for interactive pseudo-3D images, and Acrobat 3D for interactive 3D images that can be embedded into PDF documents that provide a faithful representation of the printed document. We will discuss the advantages and disadvantages of each of these technologies particularly when considering issues concerning platform portability and the dissemination of the information to as wide as possible of an audience.


Keywords: visualization, VRML, digital library, document dissemination