An Angle-Based Approach to Two-Dimensional Mesh Smoothing

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.