Page 203 - Basic Structured Grid Generation

192 Basic Structured Grid Generation

N 5 N 4

N 7
N 6 N 3

N 8

N
N 1 2

Fig. 8.2 Delaunay triangulation.

N 5
N 4

N 7
N 6 N 3

N 8

N 1 N 2

Fig. 8.3 Circumcircle for N 5 , N 6 , N 7 .

B

C
A

D

Fig. 8.4 Circumcircle property.

do represent a Delaunay triangulation. (This procedure is called, naturally, diagonal
swapping.) Of the two possible choices of diagonal, it can be shown that the one
corresponding to the Delaunay triangulation maximizes the minimum of the six angles
in the resulting two triangles, and thus can be said to make the triangles as close to
equilateral as possible. This choice can also be shown to be the one for which the sum
of opposite interior angles ABC and ADC is less than 180 degrees (as opposed to the