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Refinement is usually advocated as a means of gaining finer control over a spline curve or surface during editing. For curves, refinement is a local process. It permits the change of control vertices and subsequent editing of fine detail in one reg.'on of the curve while leaving control vertices in other reports unaffected. For tensor-product surfaces, however, refinement is not local in the sense that it causes control vertices far from a region of interest to change as well as changing the control vertices that influence the region. However, with some care and understanding it is possible to restrict the influence of refinement to the locality at which an editing effect is desired. We present a method of localizing the effect of refinement through the use of overlays, which are hierarchically controlled subdivisions. We also introduce two editing techniques that are effective when using overlays: one is direct surface manipulation through the use of edit points and the other is offset referencing of control vertices.

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This paper presents a new method for using cubic interpolating splines in a key frame animation system. Three control parameters allow the animator to change the tension, continuity, and bias of the splines. Each of these three parameters can be used for either local or global control. Our technique produces a very general class of interpolating cubic splines which includes the cardinal splines as a proper subset.

No abstract