均匀准保角球面参数化

Uniform Quasi-Conformal Spherical Parameterization

针对闭的或者单边界亏格为0的三角网格,提出一种球面参数化方法.通过立体投影将现有的平面参数化方法推广到球面上,得到一个初始的球面参数化;为了减小变形,引入质心坐标进行全局优化;最后用Moebius变换均匀化最终的球面网格.该方法能够避免立体投影出现三角形折叠的情况,保证最后的映射是双射.通过大量典型的三维模型实验和比较可以看出:文中的参数化方法变形小,在复杂网格的纹理映射中的均匀化效果较现有的保角、保面积变换有明显的改善.

This paper presents a novel spherical parameterization method for closed genus-zero triangular mesh or single boundary genus-zero triangular mesh. An initial spherical parameterization is firstly constructed by lifting planar parameterization to the sphere through the stereographic projection. Then we introduce an efficient approach based on bary centric coordinate to improve the initial spherical parameterization. At last, a uniform spherical parameterization is generated by a Moebius transformation. Our method can avoid fold-overs by the stereographic projection and always yields bijective mappings. Experiments and comparisons are taken with representative 3D meshes, which reveals that our approach has low distortion, and it has also obvious improvement in uniform texture mapping for complicated meshes than available conformal mapping methods and authalic mapping methods.