Section: Overall Objectives

Geometry

In Computer Aided Systems, the mathematical representation of curves and surfaces are based on parametric surfaces. This representation is very practical for the designer. The designer can create curves and surfaces very easily with control points and basis functions that influence the domain of control points. However, there are a lot of theoretical and practical computational problems with these surfaces. From 2004, our overall objective in CAD is based on new Differential Geometry contributions. We have found find original ways to address these problems: continuity, geometric operators (see Section 2). In the next two years, we want to improve our contributions in geometry for CAD, but also to extend our contributions and address related Engineering and Manufacturing problems.