Figure 1. Guaranteed-quality quad mesh of Lake Superior. Angle rangle is [45˚-ε, 135˚+ε].
There are mainly three advantages for this algorithm:
-Generate guaranteed-quality all-quadrilateral mesh for given smooth curves;
-Preserving local geometric features and narrow regions.
-Guaranteed-quality: all the angles in the mesh ∈ [45˚-ε, 135˚+ε] (ε ≤ 5˚);
The flowchart of this algorithm consists of six steps:
Figure 2. Flowchart of the quadtree based meshing algorithm.
An example using this algorithm:
Figure 3. Quad mesh of the air foil.
Figure 4. Guaranteed-quality quad mesh of Lake Superior. Angle rangle is [60˚-ε, 120˚+ε].
Enlightened by the geometry of hexagon, the quadtree-based algorithm can be further developed such that a wider angle range can be guaranteed, which is [45˚-ε, 135˚+ε] (ε ≤ 5˚), The main change in this new algorithm is that when doing the domain decomposition, the quadtree is replaced by a hexagon-based tree structure. Moreover, the idea for template implementation is improved so that much less templates are needed. Steps 5 & 6 are also adjusted corresponding to the hexagon-based tree.
Likewise, the flowchart of this algorithm consists of six steps:
Figure 5. Flowchart of the hexagon-based meshing algorithm.
Matching interior and exterior meshes:
Figure 6. Flowchart of the matching algorithm.
Likewise, the flowchart of the sharp feature preservation:
Figure 7. Flowchart of the sharp feature preservation algorithm.
