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If one wants to approximate a given surface with developable surfaces or planar quads via an optimization, principal curvature networks are a good starting point, see (Liu et al 2011) and (Pottmann et al 2008).

To approximate a given surface with almost rectangular panels, see (Wallner et al. 2010), which relies on finding geodesic lines of almost constant distance, see (Kahlert et al 2011).

A completely different approach is to start with two curves and construct a developable surface between them, see (Pottmann et al 2007), by connecting points with coplanar tangents with a line l, i.e. the tangents and l lie in the same plane E. These planes E envelope a surface, the connecting developable surface, and the lines l are its rulings. Note that this surface is not unique for given input curves. The angle between the ruling l and the curves’ tangents varies. This approach has been followed by (Subag and Elber 2006) for the approximation with NURBS surfaces.

If one curve is given and the other one is to be approximated, this approach leads to nonlinear equations and has been done for B-spline curves and a developable B-spline by (Aumann 2004) and (Chu and Séquin 2002).