Geomnet's Layered Client- Server Architecture Lets Users Perform Distributed Geometric Computing over the Geomnet: Geometric Computing over the Internet

Consider two real-life problems. First, suppose you have a collection of nails hammered into a board. If you were to stretch a rubber band around the outside of the nails and let it snap, what shape would the rubber band take? Second, imagine two planes whose trajectories and flight patterns show that they must, at one instance in time, fly dangerously close to one another—will they collide? In geometric terminology, the shape sought in the first problem is called the convex hull of a set of points in the plane (nails on the board). This is the smallest convex polygon containing all the points. The solution sought in the second problem is an efficient algorithm for detecting potential collisions between objects. Geometric computing emerged from algorithms developed to solve such problems. It has become a central building block in fields like computer graphics, artificial intelligence, CAD, and GIS databases. Although many representational formats for geometric data exist, only a few fully implement the combinatorial connectivity information that makes geometric data so interesting. Typically, each geometric software package is designed for a unique, incompatible data format. Designing a standard language for describing geometric data would necessitate the encoding of all possible relationships between the numerical and combinatorial components of geometric data—a Herculean task that doesn’t seem likely. In spite of difficulties, there are a number of robust implementations of geometric algorithms. Many of these are available on the Internet (see the sidebar “Geometric Software on the Web”). Our group at the Center for Geometric Computing developed the GeomNet system to provide easy Internet access to geometric implementations via a plug-and-play environment, forming a link between software