**
Generation of All-Quadrilateral Meshes**

Using a Triangular Mesh Generator

**
Daniel Rypl, Zdeněk Bittnar
**

Department of Structural Mechanics

Faculty of Civil Engineering

Czech Technical University in Prague

Thákurova 7, 166 29 Prague, Czech Republic

### Abstract:

This paper deals with discretization of 3D surfaces into all-quadrilateral
meshes. The focus is laid on using an existing
triangular mesh generator based on the Advancing Front Technique
subjected to some minor modifications instead of developing a complex
strategy for a new quadrilateral mesh generator. The actual
discretization is split into three phases. In the first phase, a mixed
mesh is created using the augmented triangular mesh generator. This
initial mesh could generally contain a large percentage of triangular
elements. In the second phase, the initial mesh is subjected to
optimization in terms of Laplacian smoothing and topological cleanup.
After the second phase, only very low percentage of the triangular
elements is present in the mesh. In the third phase, the remaining triangles
are eliminated by a one-level refinement applied to the optimized
initial mesh. The final mesh is then once more optimized using the
Laplacian smoothing. The proposed strategy is capable to produce
uniform and graded all-quadrilateral meshes of high quality. The performance of
the adopted approach is demonstrated on several examples.