Approximate T-spline surface skinning

This paper considers the problem of constructing a smooth surface to fit rows of data points. A special class of $T$-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 $T$-spline surfaces are suitable for lofted surface interpolation or approximation. A skinning algorithm using these $T$-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 $B$-spline curve; computing the control curves of a skinning surface that interpolates the sectional curves; and approximating each control curve by a $B$-spline curve with fewer knots, which results in a $T$-spline surface. Compared with conventional $B$-spline surface skinning, the proposed $T$-spline surface skinning has two advantages. First, the sectional curves and the control curves of a $T$-spline surface can be constructed independently. Second, the generated $T$-spline skinning surface usually has much fewer control points than a lofted $B$-spline surface that fits the data points with the same error bound. Experimental examples have demonstrated the effectiveness of the proposed algorithm.