Computer Graphics in Use
The use of and relevance of computer graphics has blossomed in many areas in the past 20 years, ranging from the studio arts to new mathematical disciplines such as computational geometry. The areas in which graphics have arguably had the most impact—and certainly the most visibility—can loosely be categorized as entertainment and advertising, scientific visualization, and industrial design.
Entertainment and AdvertisingNo doubt the most stylish deployment of computer graphics today is in Hollywood and on Madison Avenue. Special effects, photographic manipulations, computer animation, and other digital trickery routinely spice up (often otherwise dull) movies and ad spots. Students are aware that many of these effects—based as they are on generating shapes and transforming shapes over time—are inherently geometric in nature. From the perspective of classroom geometry, these graphics applications can be great motivators. As Walter Whiteley once pointed out to me, if Pixar can win Academy Awards for Tin Toy and Toy Story, then the lesson to students is clear: you can get an Oscar for being a geometer!
Scientific VisualizationThough slightly less glamorous than Hollywood, scientific visualization forms a second important focus of computational modeling and graphics efforts. Here, computer-generated illustrations and simulations are used to depict the structure of objects that cannot otherwise be inspected because they are too small (e.g., chemical compounds and crystal structures), too large (global weather patterns), too remote (topography of distant planets), too abstract (such as multi-dimensional mathematical manifolds), or too dangerous (such as atmospheric conditions in the eye of a hurricane and in deep ocean trenches). In fact, most computer graphics technologies are originally developed to provide some new tools to the scientific visualization community, and then later reappear in less expensive applications within other domains. The visualization technologies that this past summer allowed engineers at Pasadena's Jet Propulsion Labs to "pre-drive" a simulated robot rover across a three-dimensional, virtual reconstruction of the Martian landscape (before uploading the day's driving route, by slow satellite signal, to the actual Sojourner rover on Mars) will no doubt reappear in driving simulators in next summer's video arcades.
Industrial DesignComputer-aided design (CAD; and computer-aided manufacture, CAM) form computer graphics' third major bailiwick. Designers today routinely employ computerized visualizations and structural models to test industrial artifacts (mass-produced consumer goods, airplanes, vehicles, buildings, bridges, etc.) for safety, cost, utility, and efficiency before manufacturing a first physical prototype.
Geometry often plays a novel role in resolving a central tension faced by industrial designers. On the one hand, it's essential to have a precise mathematical model and symbolic representation of a new design, so that it can be exhaustively analyzed for the previously mentioned viability factors (safety, efficiency, and so forth). But on the other, if one is designing a new automobile, one can't test-drive an equation from the blackboard! Geometry mediates between these conflicting desires—for a precise symbolic representation of the engineered object, and for a fluid, artistic visualization of it—by defining the intersection of analytic and aesthetic characteristics of shape.