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Displaying graphics with computers offers more possibilities for interaction than almost any other display technology can provide. For example, the viewer/user can zoom into an image or manipulate its colors. With appropriately specified graphics, the user can also change the viewpoint within a three-dimensional scene, choose a point in time in animated graphics, specify input points for geometrically constructed graphics, or query points within data visualization applications.
Many of these interaction techniques are examples of parameter manipulations, for example, the selection of a time parameter in an animation. Unfortunately, the specification of parametrized graphics requires the algorithmic specification of dependencies on parameters; thus, some kind of programming language is necessary in order to formally describe parametrized graphics.
In this work, we exploit the semantic power of Mathematica expressions, particularly those representing Mathematica graphics, to specify parametrized graphics, and we use the applet LiveGraphics3D to display them and interactively manipulate their parameters. Using Mathematica expressions allows us to generate, manipulate, and process these graphics within Mathematica; that is, Mathematica becomes our generic tool to handle these parametrized graphics. With the help of several examples from various fields, we demonstrate how to use Mathematica efficiently for this purpose.
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