基于高斯曲率的三角网格模型简化的研究

摘要

The paper studies the issues regarding triangular mesh simplification and designs a corresponding algorithm. The process of triangle mesh simplification contains two phases: removing the grid and rebuilding the grid. During the phase of removing the grid, the triangle's vertexes are classified according to their Gauss curvature. If the triangle's three vertexes belong to the same class, the triangle and its adjacent triangles are to be deleted. In the process of rebuilding the grid, it is important to position the new vertex. The paper adopts the gravity center of the triangle to position the new vertex. Finally, using two examples, the paper compares the original grid model and the simplified grid model to demonstrate that the proposed algorithm can not only effectively simplify the triangular grid model but also maintain the basic features of the original triangular grid model.%针对三角网格模型简化中的相关问题进行了研究并设计出了相应的算法.三角网格的简化过程包括网格删除和网格重建两个过程.在网格的删除中,通过顶点的高斯曲率对其分类,如果三角形的三个顶点属于同一类,则对该三角形及其邻接三角形进行删除.在网格重建中,重点是新顶点的定位.首先,将新顶点定位在该三角形的重心上,然后,通过它的邻接点对其定位进行优化,最后,以两个实例进行探讨,实现对不同三角网格的验证,并以原始网格模型与简化后的网格模型进行对比说明本研究所得的简化网格模型即有效地实现了三角网格模型的简化,又保持了原有三角网格模型的基本特征,达到了令人满意的结果.