Graphics Programs Reference
In-Depth Information
function [xNode,yNode] = map(x,y,s,t)
% Computes x and y-coordinates of nodes.
N = zeros(4,1);
N(1)=(1-s)*(1-t)/4;
N(2)=(1+s)*(1-t)/4;
N(3)=(1+s)*(1+t)/4;
N(4)=(1-s)*(1+t)/4;
xNode = dot(N,x); yNode = dot(N,y);
EXAMPLE 6.13
3
y
4
3
2
x
2
1
2
Evaluate the integral
x
2
y
dx dy
I
=
+
A
over the quadrilateral shown.
Solution
The corner coordinates of the quadrilateral are
0 220
0032
x
T
y
T
=
=
The mapping is
4
x
(
ξ,η
)
=
N
k
(
ξ,η
)
x
k
k
=
1
(1
+
ξ
)(1
−
η
)
(1
+
ξ
)(1
+
η
)
=
0
+
(2)
+
(2)
+
0
4
4
=
1
+
ξ
4
y
(
ξ,η
)
=
N
k
(
ξ,η
)
y
k
k
=
1
(1
+
ξ
)(1
+
η
)
(1
−
ξ
)(1
+
η
)
=
0
+
0
+
(3)
+
(2)
4
4
(5
+
ξ
)(1
+
η
)
=
4
Search WWH ::
Custom Search