Lofting Curve Networks using Subdivision Surfaces

Lofting is a traditional technique for creating a curved shape by first specifying a network of curves that approximates the desired shape and then interpolating these curves with a smooth surface. This paper addresses the problem of lofting from the viewpoint of subdivision. First, we develop a subdivision scheme for an arbitrary network of cubic B-splines capable of being interpolated by a smooth surface. Second, we provide a quadrangulation algorithm to construct the topology of the surface control mesh. Finally, we extend the Catmull-Clark scheme to produce surfaces that interpolate the given curve network. Near the curve network, these lofted subdivision surfaces are C² bicubic splines, except for those points where three or more curves meet. We prove that the surface is C¹ with bounded curvature at these points in the most common cases; empirical results suggest that the surface is also C¹ in the general case