Iterative Methods for Improving Mesh Parameterizations
Iterative Methods for Improving Mesh Parameterizations
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DOI：
10.1109/smi.2007.23
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发表时间：
2007-06
期刊：
影响因子：
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通讯作者：
S. Dong;Michael Garland
中科院分区：
文献类型：
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作者：
S. Dong;Michael Garland
我们提出了两种互补的方法来自动改进网格参数化，并证明了它们提供了非常理想的效率和质量的组合。首先，我们描述了构造具有自由边界的拟共形参数的一种新的迭代方法。我们将问题描述为将坐标梯度拟合到两个处处垂直的相等大小的制导向量场。只需一个线性步骤，我们的方法就可以有效地从凸边界生成带有自然边界的参数化。如果重复直到收敛，它将产生狄利克莱特能量的唯一全局极小。接下来，我们介绍了一种新的非线性优化框架，该框架可以在各种度量下快速减少内部失真。通过迭代求解线性方程组，我们的算法在很少的迭代次数内收敛到高质量、低失真的参数化。我们系统的两个组成部分在结合使用或单独使用时都是有效的。
We present two complementary methods for automatically improving mesh parameterizations and demonstrate that they provide a very desirable combination of efficiency and quality. First, we describe a new iterative method for constructing quasi-conformal parameterizations with free boundaries. We formulate the problem as fitting the coordinate gradients to two guidance vector fields of equal magnitude that are everywhere orthogonal. In only one linear step, our method efficiently generates parameterizations with natural boundaries from those with convex boundaries. If repeated until convergence, it produces the unique global minimizer of the Dirichlet energy. Next, we introduce a new non-linear optimization framework that can rapidly reduce interior distortion under a variety of metrics. By iteratively solving linear systems, our algorithm converges to a high quality, low distortion parameterization in very few iterations. The two components of our system are effective both in combination or when used independently.