质心坐标变换及其在纹理映射均匀化中的应用

在现有质心坐标变换方法基础上，提出一种改进方法——均匀面积质心变换方法：在某一顶点邻域中，采用相应点所对应的边高比之和作为质心坐标进行分析推导，并将其应用到复杂三维形体的纹理映射均匀化中．首先通过面积权重质心坐标变换将复杂三维网格映射到平面上；在此基础上进行均匀面积质心坐标变换，就可使平面网格较均匀地分布．求解其纹理坐标可实现采用单幅图像的纹理映射均匀化．通过典型三维模型的实验和比较可以看到：采用文中方法所获得的纹理映射均匀化效果较现有的保角变换、保面积变换方法有显著改善，而且算法简单、稳定、快速．

Barycentric Coordinate Mapping and Its Application in Uniform Texture Mapping

Based on available barycentric coordinate mappings, a so-called UAM (uniform area mapping) barycentric coordinate mapping method is proposed. It uses such a weight as the barycentric coordinate, which is the sum of two ratios of the edge and the height of a neighboring vertex corresponding to a given inner vertex in a triangle mesh. Analyses and derivation of UAM are given. The UAM is used in uniform texture mapping of complex 3D meshes through two steps: firstly an area barycentric coordinate mapping is used to map a 3D mesh into a square, then the UAM is used to map the non-uniform mesh square to a uniform mesh square. After calculating the texture coordinates in the uniform mesh, a fairly uniform texture mapping can then be realized for complex 3D meshes that only use one texture image. Experiments and comparisons are taken with representative 3D meshes, which reveals that our method has obvious improvement in uniform texture mapping than available conformal mapping methods and authalic mapping methods. The algorithm is simple, stable and fast.