Approximate TT-spline surface skinning

This paper considers the problem of constructing a smooth surface to fit rows of data points. A special class of TT-spline surfaces is examined, which is characterized to have a global knot vector in one parameter direction and individual knot vectors from row to row in the other parameter direction. These TT-spline surfaces are suitable for lofted surface interpolation or approximation. A skinning algorithm using these TT-spline surfaces is proposed, which does not require the knot compatibility of sectional curves. The algorithm consists of three main steps: generating sectional curves by interpolating data points of each row by a BB-spline curve; computing the control curves of a skinning surface that interpolates the sectional curves; and approximating each control curve by a BB-spline curve with fewer knots, which results in a TT-spline surface. Compared with conventional BB-spline surface skinning, the proposed TT-spline surface skinning has two advantages. First, the sectional curves and the control curves of a TT-spline surface can be constructed independently. Second, the generated TT-spline skinning surface usually has much fewer control points than a lofted BB-spline surface that fits the data points with the same error bound. Experimental examples have demonstrated the effectiveness of the proposed algorithm.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► An efficient algorithm for approximate TT-spline surface skinning is proposed. ►TT-spline surface skinning suffers no knot compatibility problem. ► A lofted TT-spline surface usually has fewer control points than a BB-spline surface.