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Given a family of curves, we will construct a strip between two consecutive curves that consists of conical panels i.e. panels that lie on general cones, see sec. 3.3.

As outlined in sec. 3.2, the construction of a connecting developable surface between two curves is solved, but the angle between the ruling and the curves’ tangents can behave wildly, especially if curves have small perturbations.

On the other extreme, one could choose one of the two curves – call it the base curve b – and, if an underlying surface S is given, construct the tangent developable surface G as in sec. 3.1. The rulings of G are by definition the conjugate directions for the points of b, so this is the method of (Wallner et al 2010). In general, the second or target curve will not lie on G.