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Mesh Refinement

To eliminate the triangles remaining in the mesh after the mesh
optimization step, a one-level refinement is applied. It consists in
introducing a midnode at the center of each edge, triangle,
quadrilateral, and pentagon (optionally formed by a remaining triangle
and a neighbouring quadrilateral) and consequent splitting each triangle,
quadrilateral, and pentagon to three, four, and five quadrilaterals,
respectively. This yields the final all-quadrilateral mesh which is
optimized by the standard Laplacian smoothing. Note that the newly
introduced nodes must satisfy the surface or, if relevant, boundary
curve constraint.

Since the refinement procedure
actually halves the size of all elements, it is important to generate
the initial mixed mesh with the doubled target element size. However, this
might not be always possible, especially if the element size is
controlled by the surface curvature. In this case, meshes of higher
density than desirable are produced. Note also that splitting the quadrilaterals and
pentagons with two neighbouring sides at the surface boundary might
result in quadrilaterals of poor quality with dihedral
angle close to . In such a case it is better to split the
quadrilateral to two triangles before the refinement step is performed.

** Next:** Examples
**Up:** Generation of Quad-dominant Meshes
** Previous:** Topological Cleanup
*Daniel Rypl *

2005-12-07