基于空间多边形三角剖分的曲面分割求交算法

针对传统曲面分割求交方法存在的平面片的选取、遗漏部分交线段以及交线间断 的问题，提出一种基于空间多边形三角剖分的曲面分割求交算法。以等深度分割方法为基础， 避免了交线不连续的问题，当分割达到一定层次时以空间多边形近似曲面片，并对空间多边形 进行三角剖分，以三角形对的交线近似空间多边形之间的交线，进而以空间多边形的交线近似 曲面片的交线，最终得到相交曲面之间的交线。利用曲面片轮廓构造出的空间多边形更加接近 曲面片的真实形状，提高了逼近精度，同时对空间多边形进行三角剖分，提高了求交精度，进 而降低了丢失交线的可能性。实验验证了该算法比传统的分割法更加精确。

Surface Segmentation Algorithm Based on Spatial Polygon Triangulation

The problems with the traditional surface segmentation intersection lie in the choice of plane, loss of intersection line and discontinuous intersection line. In view of these problems, this paper proposes a surface segmentation intersection algorithm based on spatial polygon triangulation. The algorithm based on equal depth segmentation avoids the problem of discontinuous intersection line. When the segmentation reaches a certain level, the spatial polygon is used to approximate the surface patch, and the spatial polygon is triangulated. The intersection of the triangular pair is similar to the intersection between the spatial polygons, then the intersection of the spatial polygons is approximated to the intersection of the patches. Finally we get intersection lines between the intersection surfaces. The spatial polygons constructed by the contours of the surface patch are closer to the true shape of the patch, and the approximation accuracy is improved. The triangulation of the spatial polygons improves the accuracy of the intersection, thus reducing the possibility of losing the intersection line. In theory, this algorithm is more accurate than the traditional segmentation method, and the experiment also verifies this conclusion.