A new approach for lofted B-spline surface approximation to scanned data

Abstract

This paper addresses the problem of B-spline surface approximation to rows of points by B-spline surface lofting. Lofting is a well known surface create technique and has been used in CAD and CAGD. However, the traditional lofting approach tends to result in an astonishing number of control points in the process of merging the different knot vectors. This paper presents a new approach fixing this problem. The approach includes a novel process of creating a set of compact B-spline curves from the given points. The process is based on the binary search and the least-squares method, determining a set of local common knot vectors of most of rows of points, which meet the given conditions. Then, fully common knot vectors have been determined by the method of merging different knot vectors. The proposed approach is efficient in computation and can realize more efficient data reduction than previous approach without losing the shape of the lofted surface. Several experimental results demonstrate the usefulness and quality of the proposed approach.