Abstract：Aiming at the low efficiency and serious mapping distortion of current mesh parameterization, a mesh parameterization method with limiting distortion was proposed. Firstly, the original mesh model was pre-processed. After inputting the original 3D mesh model, the Half-Edge data structure was used to reorganize the mesh and the corresponding seams were generated by cutting the mesh model. The Tutte mapping was constructed to map the 3D mesh to a 2D convex polygon domain, that is to construct the 2D mesh model. Then, the mesh parameterization calculation with limiting distortion was performed. The Tutte-mapped 2D mesh model was used as the initial data for limiting distortion calculation, and the distortion metric function relative to the original 3D model mesh was established. The minimum value points of the metric function were obtained, which form the mapped mesh coordinate set. The mapped mesh was used as the input mesh to limit the distortion mapping, and the iteration termination condition was set. The iteration was performed cyclically until the termination condition was satisfied, and the convergent optimal mesh coordinates were obtained. In calculating the mapping distortion, the Dirichlet energy function was used to measure the isometric mapping distortion, and the Most Isometric Parameterizations (MIPS) energy function was used for the conformal mapping distortion. The minimum of the mapping distortion energy function was solved by proxy function combining assembly-Newton method. Finally, this method was implemented and a prototype system was developed. In the prototype system, mesh parameterization experiments for limiting isometric distortion and limiting conformal distortion were designed respectively, statistics and comparisons of program execution time and distortion energy falling were performed, and the corresponding texture mapping effects were displayed. Experimental results show that the proposed method has high execution efficiency, fast falling speed of mapping distortion energy and stable quality of optimal value convergence. When texture mapping is performed, the texture is evenly colored, close laid and uniformly lined, which meets the practical application standards.
蔡兴泉, 孙辰, 葛亚坤. 限制失真的网格参数化方法[J]. 计算机应用, 2019, 39(10): 3034-3039.
CAI Xingquan, SUN Chen, GE Yakun. Mesh parameterization method based on limiting distortion. Journal of Computer Applications, 2019, 39(10): 3034-3039.
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2019, Vol. 39 
