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N-dimensional surfaces are defined by the tensor product of B-spline basis functions. To estimate the unknown control points of these B-spline surfaces, the lofting method also called skinning method by cross-sectional curve fits is applied. It is shown by an analytical proof and numerically confirmed by the example of a four-dimensional surface that the results of the lofting method agree with the ones of the simultaneous estimation of the unknown control points. The numerical complexity for estimating  v n   control points by the lofting method is  O(v n+1  ) while it results in  O(v 3n  ) for the simultaneous estimation. It is also shown that a B-spline surface estimated by a simultaneous estimation can be extended to higher dimensions by the lofting method, thus saving computer time.

N-dimensional B-spline surface estimated by lofting for locally improving IRI