Techniques of refining a model of a complex surface can include refining, upon insertion of a new control point, only those blending functions corresponding to the control points adjacent to the control point being inserted. The resulting curves cannot be considered as B-splines because the relationship between blending functions corresponding to adjacent control points no longer has a fixed relationship. Rather, the resulting blending functions, denoted herein as “S-splines,” sacrifice this fixed relationship in exchange for the ability to specify how many blending functions corresponding to adjacent control points are refined when performing exact local refinement. S-splines do not produce excess control points and have a simple representation. While the resulting functions representing the surface are not B-splines, they allow for exact refinement without affecting the blending functions corresponding to control points not neighboring the new control point. Such a representation uses fewer computing resources and improves the user experience.
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