A four-sided approach for interpolating B-spline curves by subdivision surfaces

In a recent paper, we proposed an algorithm to interpolate B-spline curves by a recursive subdivision surface. The vertices and edges of a control polygon that defines each curve specify a path on the polyhedron describing the surface. Symmetric topology helps construct strips of panels, that converge to a curve on the surface. We now suggest a new strip construction algorithm that avoids the problem of singular points of the limit surface coinciding with an interpolated curve. The new approach employs a simpler construction procedure than the symmetric scheme. It is based on a four-sided topology and generates smoother surfaces.