ADAPTIVE COMPOSITE B-SPLINE GRID GENERATION FOR INTERACTIVE 3D VISUALIZATIONS

We describe an adaptive grid generation technique based on the composition of tensor product B-spline mappings, T and phi , where phi maps a unit square domain onto itself and  T maps the square onto the desired physical domain. The technique allows us to reparameterize mesh boundary curves without disturbing the accuracy of the spline boundary approximation. We apply the technique to the generation of computational meshes for interactive surface visualizations in the NIST Digital Library of Mathematical Functions (DLMF). The structured, or curvilinear coordinate, based technique allows us to write efficient codes to handle our customized visualization requirements, including user specified color maps and interactive movement of surface cutting planes in various coordinate directions.  Adapting the computational meshes to curvature and gradient information extracted from the function improves the surface color map and enhances the performance of some visualizations due to the reduction in file size.  The NIST DLMF contains over 200 interactive 3D visualizations. The project team is committed to maintaining  and improving the state-of-the-art visualizations that have helped the project win several awards in the past year:  U.S. Department of Commerce Gold Medal,  U.S. Government Computer News Information Technology Project of the Year,  plus a cover article in the Notices of the American Mathematical Society ( August 2011).  The effectiveness of our grid generation technique will be demonstrated by showing several DLMF visualizations.