In geometric modeling, exact symbolic data is used to represent topological information whereas the corresponding geometry is only approximated. The approximations within geometry creation algorithms must balance data volume, degree of the surface and curve representations, and performance expectations, in the context of floating point arithmetic. Today, informal use of tolerance values often leads to unexpected results, particularly for distributed geometric design.
Progress requires both new mathematics and improved implementations.
The speakers in this session will illustrate how new uses of topology, numerical analysis, and logic are leading to improved software prototypes for geometric modeling.