Many operations within a solid modeling application, notably applying thickness (shelling) or blending edges (filleting), encounter difficulties during topology resolution. In order to create a solid object, certain faces have to be intersected but the geometry is such that no intersection curve can be computed. The solution is to "extend" one or both faces. This means that one has to extrapolate the underlying curves or surfaces. This operation causes instability since extrapolation is inherently an unstable process. An additional difficulty is the selection of a strategy to compute the extension amount. Furthermore, there are additional restrictions relating to continuity across the extension boundary. In this talk I will illustrate by examples some modeling situations where extensions are necessary. I present the methods currently used, and illustrate their advantages and disadvantages. Subsequently, I will demonstrate a solution for primitives such as cylinders, cones, spheres and tori. I will conclude by suggesting approaches which could avoid some of the current pitfalls. 10 Pages
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