Page 235 - Basic Structured Grid Generation

224 Basic Structured Grid Generation

Fig. 8.48 Delaunay triangulation for a circle, amax = 2.2, armax = 5.5.

Fig. 8.49 Delaunay triangulation for an ellipse, amax = 1.4, amax = 5.5.

Fig. 8.50 Delaunay triangulation for a backstep, amax = 0.025, armax = 5.0.

The circumcentre P is located at (x P ,y P ) and the mid-point M of side 1-2 is at
(x M ,y M ),where
1 1
x M = (x 1 + x 2 ), y M = (y 1 + y 2 )
2 2
in terms of the co-ordinates of the vertices 1, 2. We have

2
2 1
PM = R − c ,
2
where c is the length of side 1-2. Then if 1-2 makes an angle α with the x-axis
(positive if anti-clockwise), where
1
sin α = (y 2 − y 1 )
c
1
cos α = (x 2 − x 1 ),
c