Digital Library of Mathematical Functions
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Viewing DLMF Interactive 3D Graphics

In the DLMF, we provide facilities for the interactive display of special functions of two independent variables. Users can render a 3D scene and interactively rotate, scale, and otherwise explore a function surface. Below we provide some notes and links to online material which might be helpful in viewing our visualizations, but please see our Disclaimer. We have strived to provide the most current information available, but if any details appear to be out of date or confusing, please notify us.

§ WebGL

We offer WebGL as the default format for viewing our displays. WebGL is a JavaScript API (application programming interface) for rendering 3D graphics in a web browser without the use of a plugin. Our WebGL code is based on the X3DOM framework which allows the building of the WebGL application around X3D, an XML based graphics code. WebGL is supported in the current versions of most common web browsers.

While WebGL reportedly works with Internet Explorer 11 in Windows 8.1, some advanced features of X3DOM are currently not fully supported (see Until these issues are resolved we cannot guarantee that the DLMF WebGL visualizations can be viewed in Internet Explorer. For that reason we will continue to offer VRML/X3D options as indicated under Additional Options. If you have trouble viewing the WebGL visualizations in your web browser, see or for information on WebGL browser support.

§ Additional Options

If you prefer to use a web browser that is not WebGL-enabled, we currently also provide VRML and X3D versions of the DLMF visualizations that may be viewed with a special VRML/X3D browser or plugin. You must select Customize DLMF on the DLMF Menu bar and choose either VRML or X3D under “Visualization Format.” VRML (Virtual Reality Modeling Language) is a standard file format for viewing 3D graphics on the web and X3D is its successor. Both are expected to be superseded by WebGL. The VRML Plugin and Browser Detector lists VRML and X3D browsers available for your machine and detects any browser already installed. Any installed browser should be removed before installing a new one.

Note that some VRML/X3D browsers are not capable of handling the complex files necessary for our visualizations. In fact, we have not found a VRML/X3D browser or plugin that works consistently with our VRML/X3D visualization files in Linux. Linux users must view the visualizations in a WebGL-enabled browser. Please see or for information on WebGL browser support.