基于边界法线插值的两步法细分曲面造型

针对曲面造型中光滑边界曲线的插值要求（位置和法线），提出了两步法插值边界法线细分方法：首先按边界位置插值细分规则对控制网格进行一次迭代细分，分别计算其细分后的V点、E点、F点；然后调整边界点相邻顶点的位置来满足边界法线要求。该方法将插值边界法线先转化为邻城顶点的调整，后转变为单参数的求解问题，并通过实例验证了该方法能有效地控制细分曲面造型的边界形状。该方法对丰富细分曲面造型技术和推广其应用起到一定作用。

Two stepped method for the modeling of subdivided curved surface based on boundary normal interpolation

Aimed at interpolation requirements(positions and normal) on smooth boundary curves in the modeling of curved surfaces,this paper put forward a two stepped subdivision method to interpolate boundary normal.First of all to carry out an iterative subdivision on the controlling net in accordance with the subdivision rule of boundary position interpolation and calculate its V-point,E-point and F-point respectively after subdivision,and then adjust the position of apex adjacent to boundary point so as to satisfy the requirement of boundary normal.This method let the interpolation of boundary normal be firstly converted to the adjustment of apex of neighbor region,and then transformed to problems of making solution of singlar parameter,and proved through a living example that this method could effectively control the boundary shape of subdivided surface model.This method could play a certain role for enriching the modeling technology of subdivided curved surface and spreading its application.