Cubic B样条旋转曲面的自由绘制技术

Rotation Surface Modeling Technique by Cubic B-spline Free Drawing

随着基于样条曲线的模型逐渐成为CAGD的主要研究对象,进一步带动了高度自由曲面建模技术的发展.本文描述一个新颖、直观的旋转曲面绘制技术,它支持三次B样条的自由输入作为轮廓线,并通过提取的样点矢量以及最小方差逼近方法形成旋转轴,利用轴上测量点的切线方向确定各个圆平面,从而建立了平面上旋转坐标矩阵,最终插值空间球面样点生成双三次B样条曲面.实验结果有效地验证了此技术的高效性.

The increasing adoption of Spline-based models in CAGD field has accelerated the development of free-form surface modeling technique. This paper proposed a novel and intuitive method for rotation surface construction; it supported cubic Bspline free drawing as profiles, and it thus computed the rotation axis by extracting sampling points and adopting Least Square Distance Approximation method （LSDA）. Furthermore, it defined the circle planes through calculating the tangent vectors of the sampling points on the rotation axis. A series of circles are finally used to interpolate a cubic B spline surface. The experiments illustrated the efficiency of this approach.