Page 233 - Basic Structured Grid Generation

222 Basic Structured Grid Generation

3
y y
2 1
1 2
Acute-angled 3
x x
3
y y 2 1
2
1 Obtuse-angled 3
x x
3
y y 2 1
1 2 Right-angled 3
x x
3
y y 2 1
1 2
Right-angled 3
x x
3
y y 2 1
1 2 Right-angled 3
x x
Fig. 8.43 Triangles with side 1 parallel to the x-axis.

y 3

P
R 2
a M
1

O x

Fig. 8.44 Locating the circumcentre of a triangle.

the triangle is classified according to whether it is acute-angled, obtuse-angled, or
right-angled.
For example, suppose that side 1 is parallel to the x-axis. Fig. 8.43 shows the
various cases into which the triangle can fall. Subroutine ‘Add-point’ contains six
subroutines of its own, called H 1 , H 2 , H 3 , V 1 , V 2 , V 3 , where, for example, H 1
considers triangles whose side 1 is parallel to the x-axis and V 1 triangles with
side 1 perpendicular to the x-axis. ‘General’ triangles are processed by subroutine
‘Add-point’ itself, and are classified as (a) acute-angled triangles, (b) obtuse-angled
triangles in which the longest side is either side 1 or not side 1, or (c) right-angled
triangles.
The main task of the subroutines is to calculate the position of the circumcentre of
the triangle being processed. When the co-ordinates of the circumcentre have been
calculated, tests are carried out to determine whether the circumcentre lies inside