T-Base: A Triangle-Based Iterative Algorithm for Smoothing Quadrilateral Meshes

TL;DR

TBase is an innovative iterative algorithm that smooths quadrilateral meshes by optimizing the shape of triangles within each quad, outperforming traditional Laplacian smoothing in various scenarios.

Contribution

The paper introduces TBase, a novel triangle-based iterative method for quadrilateral mesh smoothing, with three variants and demonstrated superior performance over Laplacian smoothing.

Findings

Vari.2 of TBase outperforms Laplacian smoothing for planar quad meshes.

Vari.2 and Vari.1 are most effective on parametric and interpolation surfaces, respectively.

TBase effectively improves mesh quality by optimizing triangle shapes within quadrilaterals.

Abstract

We present a novel approach named TBase for smoothing planar and surface quadrilateral meshes. Our motivation is that the best shape of quadrilateral element (square) can be virtually divided into a pair of equilateral right triangles by any of its diagonals. When move a node to smooth a quadrilateral, it is optimal to make a pair of triangles divided by a diagonal be equilateral right triangles separately. The finally smoothed position is obtained by weighting all individual optimal positions. Three variants are produced according to the determination of weights. Tests by the TBase are given and compared with Laplacian smoothing: The Vari.1 of TBase is effectively identical to Laplacian smoothing for planar quad meshes, while Vari.2 is the best. For the quad mesh on underlying parametric surface and interpolation surface, Vari.2 and Vari.1 are best, respectively.