Curve and surface construction with moving B-splines

TL;DR

This paper introduces a method for constructing curves and surfaces using moving B-splines, enabling flexible modeling of sharp features and smooth regions through least squares fitting with weighted B-splines.

Contribution

It presents a novel technique for curve and surface construction that generalizes uniform B-splines by incorporating moving B-splines with adjustable node placement.

Findings

Curves can have sharp or rounded corners and edges.

Surfaces can feature sharp vertices, edges, and feature lines.

The method effectively models complex geometric features.

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.