一种基于G^1拼接技术的曲面造型新方法

A New Method for Surface Modeling Based on the G^1 Continuity

C-B样条曲线不能精确表示半圆弧和半椭圆弧。本文讨论了C-B样条曲线和有理三次Bézier曲线的端点性质,在对C-B样条曲线和有理三次Bézier曲线端点特性分析的基础上,通过增加控制顶点使C-B样条曲线通过控制多边形的首末顶点并与首末边相切,给出了C-B样条曲线和有理三次Bzier曲线间G1拼接条件,利用有理三次Bézier曲线能够精确表示半圆弧的特点,与C-B样条曲线进行G1拼接,从而较好地解决了C-B样条曲面造型中圆弧和半圆弧的表示问题,有效地增强了C-B样条方法控制及表达曲线的能力。

Based on an analysis of the C-B-spline and the Cubic Bezier terminal properties, we increase the control points to make the C-B-spline curves pass the boundary vertex and the tangent direction parallel to the boundary edge. This paper presents the G^1 condition of the C B-spline curves and the Cubic Bezier curves, uses the Cubic Bezier curves to represent the circle and semicircle and continues G^1 with the C B-spline curves to resolve the representation of circles and semicircles in the C B-spline surface modeling. Then, it is useful for the C-B-spline in the shape modification and representation of curves.