Curve and surface construction with moving B-splines
Xunnian Yang
TL;DR
The paper introduces moving B-splines as a simple generalization of uniform B-splines for constructing rational curves and surfaces from a control polygon or mesh. By fitting a moving constant with weights centered at prescribed nodes, it yields curves P(t) and tensor-product surfaces P(s,t) whose local features (sharp/rounded corners, straight edges, feature lines) are controlled purely through node placement and optional weights. The method preserves key spline properties and typically requires fewer control points than traditional NURBS or MD-splines, offering a straightforward, efficient alternative for free-form modeling. Demonstrations include bottle-like shapes, tunnels, and closed surfaces, highlighting the approach's versatility and potential relevance to CAD, free-form deformation, and isogeometric analysis.
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.