Boundary/Contour Fitted Grid Generation for Effective Visualizations in a Digital Library of Mathematical Functions

Effective visualizations can help researchers obtain a more complete understanding of high level mathematical functions that arise in mathematics, statistics, physics, fluid dynamics and other fields of the mathematical and physical sciences. Accordingly, dynamic interactive 3D graphs of function surfaces will be a key feature of the National Institute of Standards and Technology Digital Library of Mathematical Functions, a new Web-based compendium of mathematical functions that will replace a popular but dated resource, the National Bureau of Standards Handbook of Mathematical Functions, published by Abramowitz and Stegun in 1964. As developers of commercial packages are well aware, creating software to accurately plot complicated 3D surfaces can be a challenging task. This paper looks at the effectiveness of modifying an algebraic tensor product spline grid generation technique, whose design was originally motivated by problems in aerodynamics and solidification theory, to create computational grids for accurate visualizations of 3D surfaces that capture key function features such as poles, branch cuts and other singularities.