基于隐式曲面的三角网格模型等距算法

针对三角网格模型，提出了一种基于隐式曲面的等距算法。该算法首先对三角网格模型进行拓扑重建，然后对顶点进行八叉树采样，由采样点及采样点的单位法矢点来构建隐式曲面，将隐式曲面等距，最后将原模型的顶点投影到等距曲面得到投影点，根据先前建立的拓扑关系，将投影点三角网格化得到等距后的三角网格模型。该算法在一定数值范围内避免了等距模型自交问题，而且等距模型三角网格均匀，质量高。

Algorithm of Offset for Triangular Mesh Model Based on Implicit Surface

Based on triangular mesh model, it proposes a novel surface - offset method to deal with implicit surface, which constructs efficiently the topological information of triangular mesh model. Using coordinates of sample points and their normal information, it solves the implicit surface function corresponding to the original triangular mesh model. The implicit surface can be offset by given distance and generate a new implicit surface. At last, the method projects the vertices of the original triangular mesh model onto the new implicit surface by Newton iteration algorithm and gets the final offsetting triangular mesh model with the similar topological information as before. The triangular mesh of the offsetting model is uniform and high quality.