形状可调的Loop 细分曲面渐进插值方法

针对Loop 细分无法调整形状与不能插值的问题，提出了一种形状可调的Loop 细分 曲面渐进插值方法。首先给出了一个既能对细分网格顶点统一调整又便于引入权因子实现细分曲 面形状可调的等价Loop 细分模板。其次，通过渐进迭代调整初始控制网格顶点生成新网格，运 用本文的两步Loop 细分方法对新网格进行细分，得到插值于初始控制顶点的形状可调的Loop 细分曲面。最后，证明了该方法的收敛性，并给出实例验证了该方法的有效性。

A Progressive Interpolation Scheme for Loop Subdivision Surfaces with Shape Adjustment

Aming at the problems that Loop subdivision can’t satisfy the shape adjustment and interpolate the given mesh, a progressive interpolation scheme for Loop subdivision surfaces with shape adjustment is presented. Firstly, an equivalent Loop subdivision mask that can adjust the mesh vertices uniformly and facilitate the introduction of weight to adjust the shape of subdivision surfaces is proposed. Secondly, the new grid is generated by the iterative adjustment of the initial control grid, and using the two-phase Loop subdivision scheme presented in this paper to subdivide the new mesh, the shape-adjustable Loop subdivision surface that interpolate the initial control vertices is obtained. Finally, the convergence of the scheme is proved and some typical examples are illustrated to verify its effectiveness.