Dynamic 3D visualizations of complex function surfaces using X3DOM and WebGL

In 1997 the National Institute of Standards and Technology (NIST) embarked on a huge project to replace one of the most cited resources for mathematical, physical and engineering scientists, the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables [Abramowitz and Stegun 1964], originally released by the National Bureau of Standards (NBS) in 1964. The 1997 project, designed to update and modernize the handbook, culminated in May 2010 with the launch of a freely available website, the NIST Digital Library of Mathematical Functions [DLMF] (http://dlmf.nist.gov/), and its print companion, the NIST Handbook of Mathematical Functions [Olver et al. 2010]. While the presence of graphics was sparse in the original handbook, the new resource contains more than 600 illustrations of high level mathematical functions, including close to 200 interactive 3D visualizations on the website. We provide the motivation for the visualization work through the context of the project and discuss our current implementation using X3DOM and WebGL.