细分曲面求交裁剪算法研究

基于细分曲面的参数化表示，研究了细分曲面的精确求交、裁剪算法。首先对控制网格建立局部坐标系，将细分曲面表示为一系列小的面片，并对每个控制顶点赋予参数值。然后用改进的轮廓删除法细分控制网格，在关联曲面间进行相交性检测，得到近似交点及其参数值，再用迭代法求得精确解。根据用户指定的裁剪区域确定交线的走向，将被裁剪曲面的控制网格面分为保留面、裁剪面和删除面，设置每个裁剪面的裁剪域，从而实现细分曲面的精确裁剪。算例表明，该文的方法简单、有效。

Research on intersection and trimming algorithms for subdivision surfaces

Based on parametrization representation of subdivision surfaces，precise intersection and trimming algorithms are put forward.A series of local coordinate systems are set up and the surface is divided into many small patches.Each control vertex relates to a series of local parameter coordinates in the coordinate system it belongs to.The meshes are splitting with revised skirt-removed subdivision approach and intersecting faces are found among related faces.Then initial intersections and their parameters are gotten based on the Divide-Conquer idea and precise results can be obtained with iteration method.According to the trimming region required，the direction of each intersect line is reset.The control mesh facets of the trimmed surface are classified into three types：reserved facets，trimmed facets and discarded facets.Trimming domain of the trimmed facets are set automatically.Examples indicate simpleness and efficiency of this method.