Civil Engineering Reference
In-Depth Information
Figure 4.30
Domain boundary.
Figure 4.31
Dividing boundary segments.
q
=
q
(
p
, M,
u
)
such that ‖
pq
‖
M
= 1
Given metric M, starting at point
p
along direction
u
, unit length function
q
( ) will
locate point
q
such that the metric distance between points
p
and
q
is equal to unity.
This unit-length function
q
is one of the most important operations in anisotropic
meshing as unit-length measure from a point is often required throughout the mesh
generation process. From a corner point of the domain, apply function
q
repeatedly to
generate nodes of unit spacing along a boundary edge, as shown in Figure 4.31, such
that
p
k+1
=
q
(
p
k
, M,
u
)
such that ‖
p
k
p
k+1
‖
M
= 1,
k = 1,n
where
p
1
is the starting point, and
p
n+1
is the ending point. The unit distance between
two points A and B measured with respect to metric field M is given by
1
∫
AB
=
AB MA tABABdt
T
(
+
)
=
1
M
0
