From 2D to 3D: Numerical Grid Generation and the Visualization of Complex Surfaces

The widespread use of high level mathematical functions to solve problems in the mathematical and physical sciences has led the National Institute of Standards and Technology to engage in a massive project to update and expand the National Bureau of Standards Handbook of Mathematical Functions [1]. The handbook, which discusses the definition and computations of “special functions”, will be disseminated on the World Wide Web as the NIST Digital Library of Mathematical Functions. A key feature of the digital library will be 3D visualization capabilities that allow a user to interactively examine the unique features of complicated mathematical functions. The complex nature of these functions makes the visualization task quite difficult. Many contain singularities and poles which make the computational domains irregular, discontinuous, or multi-connected. This paper discusses the use of grid generation techniques to facilitate the plotting of the complicated 3D surfaces that represent these higher mathematical functions.