An Angle-Based Approach to Two-Dimensional Mesh Smoothing
An Angle-Based Approach to Two-Dimensional Mesh Smoothing
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发表时间：
2000
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通讯作者：
Tianxiao Zhou;K. Shimada
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作者：
Tianxiao Zhou;K. Shimada
本文提出了一种有效的、易于实现的三角形、四边形和三角形混合网格的基于角度的光顺方法。对于每个网格节点，我们的算法比较所有对相邻的角度入射到节点，并调整这些角度，使它们成为平等的情况下，三角形网格和四边形网格，或者他们形成理想的比例的情况下，一个三-四混合网格。经过该算法的网格尺寸和形状质量都比经过拉普拉斯平滑后的网格有很大的提高。所提出的方法是上级拉普拉斯平滑，通过减少的风险，产生倒置的元素和增加的元素大小的均匀性。我们的平滑方法的计算成本远低于基于优化的平滑。为了证明该算法的有效性，我们比较了一组双线性补丁对应于一个网格与Laplacian平滑和网格与建议的平滑方法逼近一个给定的分析曲面的误差。实验表明，用我们的方法平滑的网格近似误差约减少20%。
We present an effective and easy-to-implement angle-based smoothing scheme for triangular, quadrilateral and tri-quad mixed meshes. For each mesh node our algorithm compares all the pairs of adjacent angles incident to the node and adjusts these angles so that they become equal in the case of a triangular mesh and a quadrilateral mesh, or they form the ideal ratio in the case of a tri-quad mixed mesh. The size and shape quality of the mesh after this smoothing algorithm is much better than that after Laplacian smoothing. The proposed method is superior to Laplacian smoothing by reducing the risk of generating inverted elements and increasing the uniformity of element sizes. The computational cost of our smoothing method is yet much lower than optimization-based smoothing. To prove the effectiveness of this algorithm, we compared errors in approximating a given analytical surface by a set of bi-linear patches corresponding to a mesh with Laplacian smoothing and a mesh with the proposed smoothing method. The experiments show that a mesh smoothed with our method has roughly 20% less approximation error.