Abstract: There has been many ways of computing or approximating geodesic distance and path on triangle meshes, but none of them works on simplifying the intrinsic of an embedding. Here a new idea about simplification of the intrinsic distance of a mesh via conformal factor is given. First fundamental form and conformal factor plays important role in the approximating algorithm. After the simplification, an application of approximating the geodesic distance and path by minimizing the distance function on the surface of a mesh will be introduced.

Key words: intrinsic distance, geodesic, first fundamental form, conformal factor, clustering

摘要： 测地距是曲面上两点之间最短的距离，它在几何分析和运算中起非常重要的作用。目前精确计算测地距方法的时间复杂度非常大，为了加快测地距的估算，提出了通过分析网格模型的本征距离来快速估算任意两点间测地距的算法。首先根据网格模型的第一基本式对其进行聚类分块，然后通过调整其参数化方式将每块的共形参数模型简化为二次曲面模型，最后通过共形参数对测地距进行快速估算。实验结果表明，该方法可以极大地减少计算时间，快速地估算出网格模型上位于不同块上的任意两点间测地距。

关键词: 本征距离, 测地距, 第一基本式, 共形参数, 聚类