Approximation of doubly curved surfaces by analysis-suitable piecewise surfaces with high developability

A doubly curved surface can be approximated with a piecewise developable surface by constructing the envelope of the family of the tangent planes along given curves on the input surface. In this paper, we utilize this fact to approximate a doubly curved input surface by a piecewise ruled B-spline surface with high developability. This brings advantages to downstream applications such as ease of fabrication and ease of covering the surfaces with non-extendable materials such as film-based perovskite solar modules. We also present a method for transforming the thereby defined piecewise developable surface into a watertight B-spline geometry that can be used for numerically solving partial differential equations using isogeometric analysis. In our approach, we compute the intersection points of neighboring developable surfaces starting from the first pair and propagate the parameterization of the first intersection curve to all other pairs, thereby maintaining accuracy and developability when approximating the points with a ruled B-spline surface.