The method by which the detail surfaces are constructed is fairly fast, but it produces details whose boundaries are less-than-perfect approximations of the base surface. Thus, the composite surface often contains gaps between the base and detail surfaces.
We will describe a technique called "quasi-interpolation" which may be used to approximate functions. We will then explain how this method may be used to produce pasted surfaces that are "more nearly continuous", with improved position and first derivative properties. Moreover, we will examine the impact that using quasi-interpolation will have on the cost of computing pasted surfaces.