保相似的网格参数化  

As-Similar-As-Possible Planar Parameterization

作　　者：张磊[1,2] 刘利刚[1,2] 王国瑾[1,2] 

机构地区：[1]浙江大学数学系,杭州310027 [2]浙江大学CAD&CG国家重点实验室,杭州310027

出　　处：《中国图象图形学报》2008年第12期2383-2387,共5页Journal of Image and Graphics

基　　金：国家自然科学基金项目(60776799;60503067);浙江省自然科学基金项目(Y105159);国家973计划项目(2002CB312101)

摘　　要：网格参数化是数字几何处理中的重要问题,而三角网格又是典型的一种网格表示形式。为能够快速求解三角网格的平面参数化,同时减少参数化带来的三角形的扭曲,提出了一种保持形状相似的三角网格平面参数化方法—保相似参数化,该方法使得参数化后的网格的相邻两边夹角和长度比例在最小二乘意义下整体上保持不变,从而建立对应三角形的相似性。通过三角形的相邻两条边的夹角和两边的比例值建立线性方程组,在给定初始条件后可以快速地求解该线性方程组,从而得到参数化后的平面网格。该方法也适用于添加任何线性约束条件,而且整个算法是线性的。与现有的一些方法相比,该算法几何意义直观,操作简便。实例表明,该方法可以得到较好的参数化结果,非常适合于纹理映射等计算机图形学的应用。Mesh surface parameterization is an important problem in Digital Geometry Processing, and triangular mesh is the typical form for mesh representation. To solve the problem of planar parameterization for triangular mesh fast, and minimize the distortion of triangles generated in the parameterization simultaneously, a simple as-similar-as-possible planar parameterization method for triangular mesh is presented in this paper. The angles and length ratios between two adjacent edges are globally preserved in a least squares sense after the parameterization, by which the similarity of the corresponding triangles can be satisfied. A linear system is constructed according to the corresponding angle and length ratio of two adjacent edges on the triangular mesh, and the planar parameterization result can be fast obtained by solving the sparse linear system with some initial conditions. Linear constraints can be combined into the linear system in our approach, and the algorithm is of linear complexity. This method has a direct geometric interpretation and can be implemented more easily than other methods. Experimental examples show that good planar parameterization results can be derived from this method, which is a very efficient tool for the applications in Computer Graphics, such as texture mapping.

关 键 词：数字几何处理 网格参数化 保相似 纹理映射 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]