NURBS曲面求交及变半径过渡曲面生成

INTERSECTION BETWEEM TWO NURBS SURFACES AND CONSTRUCTING A VARIABLE RADIUS TRANSITION SURFACE

本文探索NURBS曲面求交及构造过渡曲面的方法。基于交线跟踪算法求出NURBS曲面间的交线,算法比较稳定、可靠;采用参数化平面与等距面求交找出两曲面空间等距点,具有自然与变半径过渡曲面的定义相呼应、找点快、准确、稳定的特点;过渡曲面表示为2×3次NURBS曲面,自然、充分地利用了NURBS曲线可精确表示圆弧段的特性,过渡曲面具有表达简单、比较准确、便于采用统一的NURBS曲面处理算法对其进行各种几何处理的优点;实验证明这些方法可行,效果令人满意。

Based on an improved tracing way to find the intersection between tow NURBS surfaces,a method for constrcuting a variable radius transition NURBS defined surface is proposed. By using 2×3 NURBS form expression,the advantages of NURBS method is naturally and fully utilized and the transition surface is more accurate and its fullness can be controled easily. Besides,unified way can be adopted to process this transition surface. To get necessary information for constructing transition surface,an algorithm for finding offset point around intersection curve between two surfaces is proposed.The algorithm has the advantage over the traditional approach in that offset point can be found more quickly and acuu- rately.Any rectangular parametric surfaces can be transited as long as their offset surfaces are smooth so that intersection between a parametrically defined plane and one of surface offset can be well defined.