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Web-Based 3D Visualization in a Digital Library of Mathematical Functions



Qiming Wang, Bonita V. Saunders


The National Institute of Standards and Technology (NIST) is developing a digital library of mathematical functions to replace the widely used National Bureau of Standards Handbook of Mathematical Functions published in 1964 [1]. The NIST Digital Library of Mathematical Functions (DLMF) will provide a wide range of information about high-level functions for scientific, technical and educational users in the mathematical and physical sciences. Clear, concise 3D visualizations that allow users to examine poles, zeros, branch cuts and other key features of complicated functions will be an integral part of the DLMF. Specially designed controls will enable users to move a cutting plane through the function surface, select the surface color mapping, choose the axis style, or transform the surface plot into a density plot. To date, Virtual Reality Modeling Language and Extensible 3D (VRML/X3D) standards have been used to implement these capabilities in more than one hundred 3D visualizations for the DLMF. We discuss the development of these visualizations, focusing on the design and implementation of the VRML code, and show several examples.
NIST Interagency/Internal Report (NISTIR) - 7159
Report Number


Wang, Q. and Saunders, B. (2004), Web-Based 3D Visualization in a Digital Library of Mathematical Functions, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online],, (Accessed April 25, 2024)
Created October 31, 2004, Updated October 12, 2021