中文摘要：

三维网格的参数化是数字几何处理中一个基本问题，在纹理映射、重新网格化和几何变形等许多图形处理中都有着非常重要的应用。在现有参数化方法的基础上，根据球面与平面参数化之间的差异，列出了一个关于角度的有效球面三角化的充要条件，使用L—M算法通过对非线性优化问题的求解，得到具有期望目标的球面参数化结果。并介绍算法的应用，给出实例说明了算法有效性。

英文摘要：

Parameterization of triangular meshes is an essential problem of Digital Geometry Processing, especially for texture mapping, remeshing and morphing. In this paper, based on the analysis of the difference between spherical and planar methods,we formulate a set of necessary and sufficient conditions on the spherical angles of the spherical triangles for them to form a spherical parameterization. We get the results with target properties by using the L-M algorithm to solve a non-linear optimization. Applications of the method is introduced, at last some experimental results demonstrate the availability of the method.