采用两次局部映射法简化三角网格

Simplify Triangles with Two Local Mapping

在计算可视化领域 ,通常采用三角网格来表示三维物体 ,但是 ,由于大量的三角网格会影响实时交互的效果 ,因而 ,三角网格的简化越来越引起人们的重视。为了有效地进行网格简化 ,在传统的边压缩方法的基础上 ,提出了一种采用两次局部映射的三角网格简化方法 ,即首先利用高斯球 ,将三角网格投影到二维平面上 ,然后在二维平面上简化后 ,再投影回三维空间 ,以达到简化目的。实践证明 ,该方法不仅误差小 ,简化效率高 ,而且不会产生自相交 ,同时具有运行稳定和适用性强等优点。

In the field of computer visualization, three-dimensional object is usually rendered by triangle meshes,but too many triangle meshes can affect the result of real-time operation, such as shifting, rotation and zooming, most of users can't bear the slowness. So how to simplify the triangle meshes is regarded more and more important. To simplify triangles effectively while not influence the vision effect, based on the traditional method of edge contraction, a new method is presented, which named Two Times of Local Mapping. First, it maps the three-dimensional triangle meshes from three-dimensional space to two-dimensional plane by using Gaussian sphere which can determine the direction of projection. Then on two-dimensional plane, using the traditional edge contraction method, a new contracted point is found in the kernel of a polygon. With the new point, the number of triangles is reduced greatly. After simplification, when mapping the simplified triangles back to three-dimensional space, the error is checked. Two kinds of error are defined to ensure the minimum error. It is proved that the given method is little-error, efficient and without self-intersected, and also it is stable and applicable.