Robustness in CAD geometric constructions

Many authors have so far studied the problem of geometric construction in CAD from a combinatorial point of view. The derived algorithms are efficient but not general enough. Moreover the problem of robustness is seldom mentioned. We expose a logical framework of geometric construction which points out the difficulties to overcome in order to implement a correct geometric universe. We think that this precise study of the particularities of geometry is necessary to obtain a robust geometric solver