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One of the major problems in the generation of skinning B-spline surfaces is the incompatibility of the cross-sectional curves. This occurs when the cross sections are defined by control polygons having different number of control devices. Traditionally, this incompatibility is overcome by knot insertion that makes all control polygons have equal number of vertices. The drawback of this solution is that it can very quickly lead to an explosion in the number of vertices of the control mesh defining the skinning surface. In this paper, we show that this problem can be rectified through the use of subdivision surfaces. We describe an approach to generate a skinning Catmull-Clark subdivision surface through incompatible cross-sections of cubic B-spline curves. The resulting surface has all the properties of subdivision surfaces while requiring a smaller number of control points than those obtained through the more conventional techniques.