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Geometer’s Workbench Provides Computational Power in a Familiar Environment

Published December 15, 2000

Researchers at Stanford University have developed a prototype of a liveboard interface to Mathematica. Collaboration between the Mathematics and Computer Science departments resulted in the Geometer’s Workbench, a tool for mathematicians exploring or teaching algebraic geometry. The researchers were motivated by the idea of providing familiar human-computer interactions, such as the blackboard experience, while adding the power of a symbolic algebra engine, such as Mathematica, to visualize and control complex geometrical transformations.

The Geometer’s Workbench can be thought of as a graphical front end for Mathematica, projected on the Stanford Interactive Mural–a large (6′ x 2′), high-resolution display screen. In this liveboard environment the mural was fitted with an EFI eBeam to track the movement of the user’s pen on the board, producing a virtual copy of what was written. Although to the user the Workbench appears as one seamless device, it actually consists of a complex system of 10 networked computers (the main computing program, a graphic subsystem of eight PCs driving the mural projectors, and the input server) in addition to the mural and eBeam device.

The Workbench display on the Interactive Mural consists of three areas. The left area, or 2D patch, represents the mapping domain where the user can draw freehand or choose from a menu of simple geometric shapes. In the center liveboard region, called the MultiPoint window, the user selects from a library of mapping functions by picking a parametric family and specifying the values of two parameters. A model of the resulting parametric surface is displayed in the 3D Model region to the right, where it can be manipulated using the eBeam pen as a virtual trackball.

Sha Xin Wei, one of the developers of the Geometer’s Workbench, says the work may be harvested in future projects. The research and knowledge gained from this experiment can be generalized to a large class of technical and scientific applications that use large, high-resolution displays. The Geometer’s Workbench has demonstrated that such devices can be used to advantage to provide interactions that feel natural to users, bridging the gap between casual whiteboard interactions and more syntactically formal analytical engines like Mathematica.