Spline Overlay Surfaces

We consider the construction of spline features on spline surfaces. 1 The approach taken is a generalization of the hierarchical surface introduced in Forsey88]. Features are regarded as spline-deened vector displacement elds that are overlain on existing surfaces. No assumption is made that the overlays are derived from the base surface. They may be applied with any orientation in a non-hierarchical fashion. In particular, we present a \cheap" version of the concept in which the displacement eld is mapped to the base surface approximately, through the mapping of its control vectors alone. The result is a feature that occupies the appropriate position in space with respect to the base surface. It may be manipulated and rendered as an independent spline, thus avoiding the costs of a true displacement mapping. This approach is useful for prototyping and previewing during design. When a nished product is desired, of course, true displacement mapping is employed.