Lofting with Patchwork B-Splines

Abstract

Lofting—also denoted as surface skinning—is one of the fundamental operations for creating free-form surfaces in Computer Aided Design. This process generates a surface from a given sequence of section curves. It is particularly useful for airfoils and turbine blades, since these shapes are often defined by cross sections with a family of auxiliary surfaces. The use of tensor-product B-splines, which is currently the standard technology, leads to large data volumes if section curves with incompatible knot vectors are used. We adopt the framework of Patchwork B-splines, which supports very flexible refinement strategies, and apply it to the construction of lofting surfaces. This approach not only reduces the resulting data volume but also limits the propagation of derivative discontinuities.