Applying Numerical Grid Generation to the Visualization of Complex Function Data

Friday, April 9, 2010 - 1:25pm - 2:25pm
Vincent 570
Bonita Saunders (National Institute of Standards and Technology)
Numerical grid generation, that is, structured grid generation, is the development of a generalized curvilinear coordinate system. Originally designed for solving computational fluid dynamics problems over oddly shaped domains, structured techniques have competed with various unstructured methods such as Voronoi or Delaunay triangulations and quadtree designs. However, the effectiveness of a given grid often depends on how it is used. For complex function visualization problems, the grid generation technique may be less important than how closely the grid lines follow the contours of the function. This talk looks at the use of a tensor product B-spline mapping to generate a boundary/contour fitted mesh that captures significant attributes such as zeros, poles, branch cuts and other singularities when the mesh is used to plot a complex function surface.

This work has been used to create over 200 interactive 3D visualizations of complex function surfaces for the NIST Digital Library of Mathematical Functions (DLMF). The NIST DLMF and its hardcopy version, the NIST Handbook of Mathematical Functions, will replace the well-known NBS Handbook of Mathematical Functions edited by Abramowitz and Stegun and first published in 1964.
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