Civil Engineering Reference
In-Depth Information
(b)
(a)
(c)
Figure 6.44
Elimination of a short edge: (a) delete segment; (b) triangulation; (c) merging.
Shrink to a point
Conversion
Triangulation
Figure 6.45
Elimination of a small quadrilateral.
or
Figure 6.46
Swap of diagonal between two quadrilaterals.
neighbours are identified, which are eliminated (a) by deleting all the edges connected to the
short edge; (b) the resulting empty polygon is triangulated; and (c) triangles are merged to
form quadrilaterals, as shown in Figure 6.44. This process can also be applied to eliminate a
small quadrilateral by first shrinking it to a point, followed by the triangulation of the asso-
ciated polygon and the conversion of triangles into quadrilaterals, as shown in Figure 6.45.
Diagonal swap between two quadrilaterals is also an effective means in improving the quality
of a mesh. Within the hexagon formed by two adjacent quadrilaterals, there are altogether
three ways in dividing it into two quadrilaterals. Apart from the original configuration, an
edge swap for the other two alternatives can be carried out if the overall quality of the result-
ing quadrilaterals is superior to that before transformation, as shown in Figure 6.46.
6.4.3 Tetrahedral meshes
In a tetrahedral mesh, a node on the average is surrounded by some 27 tetrahedra, and a
node can be deleted if it is surrounded by only a few tetrahedra, as shown in Figure 6.47. In
Figure 6.47
Elimination of nodes surrounded by four tetrahedral elements.
