As-developable-as-possible B-spline surface interpolation to B-spline curves

Abstract

A method is proposed to computing a B-spline surface bounded by two fixed B-spline curves such that the surface achieves as large developability as possible. Existing methods generate discrete developable surfaces from line sequences connecting prespecified points sampled on input curves and need a highly dense sampling to achieve a high degree of developability which largely increases the problem complexity and computational time. Moreover, when generating smooth surfaces from the discrete lines, the parametrization of the sample points has a large impact on the developability of the interpolation surface. To overcome these drawbacks, we propose a variational method to compute a continuous mapping of input curves maximizing the developability of the surface defined by the mapping. The advantages of our method are twofold: by working with a continuous solution space rather than a restricted one composed of sample points, it can find mappings between input curves achieving the maximal developability; the resulting surface is directly a continuous surface and does not depend on any explicit data parametrization. The performance of the proposed method is analyzed from various aspects by experiments and method efficacy is demonstrated with several industrial examples.