Civil Engineering Reference
In-Depth Information
// Output: Elements connected to node k: {Pi,
i
, i = {Pi,
k
+ 1, P
k+1
}
Set zero to array P: {P
k
= 0, k = 1,N
p
+ 1}
Loop: i = 1,Ne
Loop: j = 1,4
k=V
j
; P
k
= P
k
+ 1
End loop j
End loop i
P
1
= P
1
+ Np + 1
Loop: k = 1,Np
P
k+1
= P
k+1
+ P
k
End loop k
Loop: i = 1,Ne
Loop: j = 1,4
k=V
j
; m = P
k
; P
m
= i; P
k
= m - 1
End loop j
End loop i
2.5.4 Find the edges (unique line segments) of a triangular mesh
This simple algorithm is based on the idea that edge j1 - j2 shared by two elements follow-
ing the orientation of the triangles will be that j1 < j2 in one element and vice versa, j2 < j1,
in the other element, as shown in Figure 2.29. As j1 ≠ j2, the edge will only be counted
once. To complete the set, all the boundary edges still have to be included, which are con-
nected to only one element, and hence, the boundary condition
T
i
j
= 0
is also included in
the
If
test.
Algorithm Edges_T3 (Np, Ne, V, T, E)
// Find the edges (unique line segments) of a triangular mesh
// Np and Ne are respectively the number of nodes and elements in the
// mesh.
// Input: V = Vertices of the elements, Neighbours of triangles T
// Output: Edges E: {
E
j
, i = 1,n; j = 1,2}
n = 0
Loop: i = 1,Ne
Loop: j = 1,3
j1=V
i
mod(j,3)+1
;
j2=V
i
mod(j+1,3)+1
j
If (j1 < j2 or
T=0
i
) then
1
2
n = n + 1;
E=j1; E=j2
n
n
End if
End loop j
End loop i
j
1
Include
Exclude
j
2
Figure 2.29
Finding the edges of a triangular mesh.
