应用可变形模型进行曲线曲面光顺

Fairing 3D Curves and Surfaces Using Deformable Models

根据物理模型的造型技术可以从另一个角度研究曲线曲面的光顺问题．基于能量的可变形曲线曲面可用于光顺一批有误差的散乱数据点．该方法不必要求数据点有序的条件，通过在数据点与曲线和曲面之间连接假想弹簧，可以克服“光顺”和“插值”的矛盾，得到所需形状．文章采用三次Ｂ样条几何表达形式，建立了光顺模型，分析了光顺机理。

The problem of curve and surface fairness is studied from the point of view of physics based modeling techniques. Energy based deformable models are used to fit a set of unorganized data points. This method needs no connectivity information about data points. The contradictory of “smooth” and “fit” can be mediated by anchoring an imaginary spring between each data point and deformable curve or surface. The cubic B spline is adopted as the basis for the deformable curve and surface. The fairing model is established. The principle is analyzed and the algorithm is presented. Some examples are presented.