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Modern shape design and capture techniques often lead to the geometric datapresented in the form of serial rows of data points. In general, the number ofdata points varies from row to row. Lofted or skinned B-spline surfaceinterpolation is a technique that generates a B-spline surface that passesthrough these data points precisely. The traditional process often causes alarge increase in the number of control points of the resulting B-splinesurface. Much of the work to date in mitigating the effects of this increasehas been restricted to open section-curves. The lofting of sequential closedcontours using the interpolation technique has not been addressed in theexisting literature. In this paper, we present two novel conjectures relatingto closed B-spline curve interpolation. We derive the equivalent closedB-spline interpolation condition of the well-established Schoenberg-Whitneycondition for open B-spline interpolation, a condition that the parametervalues and the domain knots should satisfy to guarantee the system matrix isalways invertible or full-rank. We then apply the interpolation condition tothe problem of lofted B-spline surface interpolation to serial closed contours.The correctness of these conjectures is validated via numerical results andseveral practical experiments. Github repositoryhttps://github.com/ShutaoTang/LBSI-Project

Optimal lofted B-spline surface interpolation based on serial closed contours