  Modern shape design and capture techniques often lead to the geometric data
presented in the form of serial rows of data points. In general, the number of
data points varies from row to row. Lofted or skinned B-spline surface
interpolation is a technique that generates a B-spline surface that passes
through these data points precisely. The traditional process often causes a
large increase in the number of control points of the resulting B-spline
surface. Much of the work to date in mitigating the effects of this increase
has been restricted to open section-curves. The lofting of sequential closed
contours using the interpolation technique has not been addressed in the
existing literature. In this paper, we present two novel conjectures relating
to closed B-spline curve interpolation. We derive the equivalent closed
B-spline interpolation condition of the well-established Schoenberg-Whitney
condition for open B-spline interpolation, a condition that the parameter
values and the domain knots should satisfy to guarantee the system matrix is
always invertible or full-rank. We then apply the interpolation condition to
the problem of lofted B-spline surface interpolation to serial closed contours.
The correctness of these conjectures is validated via numerical results and
several practical experiments. Github repository
https://github.com/ShutaoTang/LBSI-Project
