This paper introduces and develops an interval geometric representation for curved objects. The representation is based on rounded interval arithmetic and addresses robustness problems in current boundary representation solid modelers operating in floating point arithmetic. These problems include topology violation (such as gaps and inappropriate intersections), incidence asymmetry, and incidence intransitivity. The concepts of interval polynomial spline curves and surface patches are employed in this context. A graph-based data structure incorporating the special features of interval geometries is developed and extended to represent nonmanifold objects. Copyright