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中文摘要：
逼近型细分方法生成的细分曲面其品质要优于插值型细分方法生成的细分曲面．然而，逼近型细分方法生成的细分曲面不能插值于初始控制网格顶点．为使逼近型细分曲面具有插值能力，一般通过求解全局线性方程组，使其插值于网格顶点．当网格顶点较多时，求解线性方程组的计算量很大，因此，难以处理稠密网格．与此不同，在不直接求解线性方程组的情况下，渐进插值方法通过迭代调整控制网格顶点，最终达到插值的效果．渐进插值方法可以处理稠密的任意拓扑网格，生成插值于初始网格顶点的光滑细分曲面．并且经证明，逼近型细分曲面渐进插值具有局部性质，也就是迭代调整初始网格的若干控制顶点，且保持剩余顶点不变，最终生成的极限细分曲面仍插值于初始网格中被调整的那些顶点．这种局部渐进插值性质给形状控制带来了更多的灵活性，并且使得自适应拟合成为可能．实验结果验证了局部渐进插值的形状控制以及自适应拟合能力．
英文摘要：
The quality of subdivision surface generated by the approximating scheme is usually better than that by the interpolating scheme, while the approximating subdivision surface is unable to interpolate the vertices of the initial control mesh. Traditional methods that make the approximating subdivision surface interpolate the initial mesh need to solve a global linear system. It is computation- intensive, and hard to deal with dense meshes. Without solving a linear system, the progressive interpolation calculates the approximating subdivision surface that interpolates the initial mesh by adjusting the vertices of the control mesh iteratively. It can handle control meshes of any size and any topology while generating smooth subdivision surfaces that faithfully resemble the shape of the initial meshes. In this paper, we show the local property of the progressive interpolation for approximating subdivision schemes. That is, if only a subset of the vertices of the control mesh are adjusted, and others remain unchanged, the limit of the subdivision surface generated in the progressive interpolation procedure still interpolates the corresponding subset of the vertices in the initial mesh. The local property of the progressive interpolation brings more flexibility for shape controlling, and makes the adaptive fitting possible. Lots of experimental examples illustrate the shape controlling and adaptive fitting capabilities of the local progressive interpolation, ss
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An efficient joint implementation of three stages for fast computation of color space conversation i
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