用三维局切面族逼近法实现逆向精确造型

在某点邻域构造初始三维局切面，以黎曼图表示局切面间的邻接关系，用欧几里德最小生成树实现局切面的法矢一致化，再用步进立方体法进行轮廓追踪，最后用能量函数法优化初始网格。该逆向造型方法除点的三维坐标外无需任何附加信息即可确定离散点蕴涵的拓扑信息，适于精确地反求具有任意拓扑结构的原型体。

The Method of Accurate Shape Reverse based on 3D Local Tangent Planes

The 3D initial tangent planes were estimated by the neighborhoods of the point, and their proximities were encoded by Rieman-Graph. The EMST is adopted to adjust the normal vector direction of the tangent plane. Marching cubes method was used to track the contour. Then, the initial meshes were optimized by energy function. The method requires only the coordinates of the points, no additional information is provided, and can reconstruct manifold surfaces of arbitrary topological type.