Smoothly blended articulated models are often difficult to construct using current techniques. Our solution in this paper is to extend the surfaces introduced by Blinn [Blinn 1982] by using three-dimensional convolution with skeletons composed of polygons or curves. The resulting convolution surfaces permit fluid topology changes, seamless part joins, and efficient implementation. CR Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling - curve, surface, solid, and object representations. Additional Keywords and Phrases: Implicit Surface, Parametric Surface, Convolution, Solid Modeling, Blends.