A new paradigm for designing smooth surfaces is described. A finite set of points with weights specifies a closed surface in space referred to as skin . It consists of one or more components, each tangent continuous and free of self-intersections and intersections with other components. The skin varies continuously with the weights and locations of the points, and the variation includes the possibility of a topology change facilitated by the violation of tangent continuity at a single point in space and time. Applications of the skin to molecular modeling and to geometric deformation are discussed.