标题： 使用移动B样条的曲线和曲面构造 显示英文标题

标题： Curve and surface construction with moving B-splines

摘要： 本文提出了一种使用B样条的曲线和曲面构造的简单技术。 给定一个控制多边形或控制网格以及对应所有控制点的节点坐标，通过使用以预定节点为中心的均匀B样条作为权重，对控制点进行最小二乘拟合，得到有理曲线或曲面。 这种曲线和曲面是均匀B样条曲线和曲面的自然推广。 通过选择适当的节点，所得曲线可以具有尖锐或圆角，部分或完全的直线边，而所得曲面可以具有尖锐或圆角顶点、尖锐或平滑的边、特征线等。 除了在尖锐角落或尖锐边缘处，曲线或曲面的连续性阶数与移动B样条相同。 已给出实际例子来展示所提出技术在曲线和曲面建模中的有效性。 显示英文摘要

摘要： 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.