A new approach for lofted B-spline surface interpolation to serial contours

Abstract

This paper addresses the problem of B-spline surface interpolation to serial contours, where the number of points varies from contour to contour. A traditional approach to the problem creates a set of B-spline curves via B-spline curve interpolation to each contour, makes them compatible via degree elevation and knot insertion and performs B-spline surface lofting to get a B-spline surface that interpolates them. The approach tends to result in an astonishing number of control points in the lofted B-spline surface. This situation arises mainly from the inevitable process of progressively merging different knot vectors to make the B-spline curves compatible. This paper presents a new approach for fixing this problem. The approach includes a novel process of obtaining a set of compatible B-spline curves from the given contours. The process is based on universal parameterisation [1, 2], allowing the knots to be selected freely but leading to a more stable linear system for B-spline curve interpolation. Since the number of control points in each compatible B-spline curve is equal to the highest number of contour points, the proposed approach can realise efficient data reduction and provide a compact representation of a lofted B-spline surface while keeping the desired surface shape. Some experimental results demonstrate its usefulness and quality.