高亏格曲面共形参数化方法
发布时间：2018-10-11 12:43
【摘要】：共形映射又称为保角映射,在计算机图形学、几何信息处理和参数化领域扮演着重要角色.调和映射易于计算并且有严密的理论基础,为了计算高亏格曲面的共形映射,提出一种基于调和映射的非线性扩散方法.首先使用贪心算法在高亏格曲面上找到一个同伦群基底;然后通过求解一个线性系统来计算曲面的调和映射,将该映射的结果作为非线性扩散计算的初始条件;再使用拉普拉斯切向法来调节曲面边界的调和能量,调和能量下降的过程即非线性扩散过程;最后最小化调和能量,以获得曲面的共形映射.实验结果表明,文中方法是稳定的,映射结果可以很好地保证曲面三角网格的角度关系;算法对模型网格质量要求不高,具有更高的鲁棒性;与经典的共形映射方法相比,该方法得到的结果更均匀,共形效果更好.该方法可以在参数化、纹理映射、曲面注册等领域得到很好应用.
[Abstract]:Conformal mapping, also called conformal mapping, plays an important role in computer graphics, geometric information processing and parameterization. Harmonic maps are easy to calculate and have a strict theoretical basis. In order to calculate conformal maps of high genus surfaces, a nonlinear diffusion method based on harmonic maps is proposed. Firstly, the greedy algorithm is used to find a homotopy group base on the high genus surface, then the harmonic mapping of the surface is calculated by solving a linear system, and the result of the mapping is regarded as the initial condition of the nonlinear diffusion calculation. Then the Laplacian tangential method is used to adjust the harmonic energy of the surface boundary, the process of harmonic energy decreasing is called nonlinear diffusion process, and the harmonic energy is minimized to obtain the conformal mapping of the surface. The experimental results show that the proposed method is stable, and the mapping results can guarantee the angle relation of triangular mesh of curved surface. The algorithm is less robust to the mesh quality of the model, and compared with the classical conformal mapping method, the proposed algorithm is more robust than the classical conformal mapping method. The results obtained by this method are more uniform and the conformal effect is better. This method can be used in parameterization, texture mapping, surface registration and so on.
【作者单位】： 昆明理工大学建筑工程学院;昆明理工大学理学院;武汉大学计算机学院;
【基金】：国家自然科学基金(11461037,61772379)
【分类号】：TP391.41
本文编号：2264236
[Abstract]:Conformal mapping, also called conformal mapping, plays an important role in computer graphics, geometric information processing and parameterization. Harmonic maps are easy to calculate and have a strict theoretical basis. In order to calculate conformal maps of high genus surfaces, a nonlinear diffusion method based on harmonic maps is proposed. Firstly, the greedy algorithm is used to find a homotopy group base on the high genus surface, then the harmonic mapping of the surface is calculated by solving a linear system, and the result of the mapping is regarded as the initial condition of the nonlinear diffusion calculation. Then the Laplacian tangential method is used to adjust the harmonic energy of the surface boundary, the process of harmonic energy decreasing is called nonlinear diffusion process, and the harmonic energy is minimized to obtain the conformal mapping of the surface. The experimental results show that the proposed method is stable, and the mapping results can guarantee the angle relation of triangular mesh of curved surface. The algorithm is less robust to the mesh quality of the model, and compared with the classical conformal mapping method, the proposed algorithm is more robust than the classical conformal mapping method. The results obtained by this method are more uniform and the conformal effect is better. This method can be used in parameterization, texture mapping, surface registration and so on.
【作者单位】： 昆明理工大学建筑工程学院;昆明理工大学理学院;武汉大学计算机学院;
【基金】：国家自然科学基金(11461037,61772379)
【分类号】：TP391.41
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