Veltkamp, Remco C.2014-10-212014-10-2119921467-8659https://doi.org/10.1111/1467-8659.1120093This survey presents an overview to various types of continuity of curves and surfaces, in particular parametric (Cn), visual or geometric (Cn, Gn), Frenet frame (Fn), and tangent surface continuity (Tn), and discusses the relation with curve and surface modeling, visibility of (dis) continuities, and graphics rendering algorithms. It is the purpose of this paper to provide an overview of types of continuity, and to put many terms and definitions on a common footing in order to give an understanding of the subject.1991 Computing Reviews Classification:I.3.5 [Computer Graphics] Computational geometry and object modeling.I.3.7 [Computer Graphics] Three-Dimensional Graphics and Realism.10.1111/1467-8659.112009393-112