Curve and surface construction with moving B-splines

Abstract

This paper proposes a simple technique of curve and surface construction with B-splines. Given a control polygon or a control mesh together with node ordinates corresponding to all control points, a rational curve or surface is obtained by least squares fitting of a moving constant to the control points with weights given by uniform B-splines centered at the prescribed nodes. This kind of curves and surfaces are natural generalizations of uniform B-spline curves and surfaces. By choosing proper nodes, the obtained curves can have sharp or rounded corners, partial or full straight edges while the obtained surfaces can have sharp or rounded vertices, sharp or smoothed edges, feature lines, etc. Except at sharp corners or sharp edges, the curves or surfaces have the same continuity orders as the moving B-splines. Practical examples have been given to demonstrate the effectiveness of the proposed technique for curve and surface modeling.