Section: Scientific Foundations

Robust computation and advanced programming

An implementation of a geometric algorithm is called robust if it produces a valid output for all inputs. Geometric programs are notorious for their non-robustness due to two reasons: (1) geometric algorithms are designed for a model of computation where real numbers are dealt with exactly and, (2) geometric algorithms are frequently only formulated for inputs in general position. As a result, implementations may crash or produce nonsensical outputs. This is observed in all commercial cad -systems.

The importance of robustness in geometric computations has been recognized for a long time, but significant progress was made only in recent years. Geometrica held a central role in this process, including advances regarding the exact computation paradigm . In this paradigm, robustness is achieved by a combination of three methods: exact arithmetic , dedicated arithmetic and controlled rounding .

In addition to pursuing research on robust geometric computation, Geometrica is an active member of a European consortium that develops a large library named cgal . This library makes extensive use of generic programming techniques and is both a unique tool to perform experimental research in Computational Geometry and a comprehensive library for Geometric Computing. The startup company Geometry Factory has been started in January 2003 to commercialize components from cgal and to offer services for geometric applications.