Civil Engineering Reference
In-Depth Information
Boundary edges
Ellipsoid
Torus
Closed surface: no boundary edge
Open surface
Figure 8.6
Open and closed surfaces.
Side 1
Side 2
(a)
Normal
θ
(b)
Edge L
Surfaces
connected
Common edges
between surfaces
Figure 8.7
Couple with neighbouring surface: (a) surface orientations; (b) surfaces connected by the least
dihedral angle.
θ
Figure 8.8
Trace a region in 2D.
be traced out consistently following the smallest internal angles going in either clock-
wise or counter-clockwise direction.
3. In merging two surfaces, the region boundary is updated. All the common edges will
cancel each other, and the unclosed surface grows in size, as shown in Figure 8.9. Go
to step 2 if there are still free boundary edges.
4. No more free edges imply that a closed region has been formed. Each side of a sur-
face can be a wall of only one single region; hence, the region formation process fin-
ishes if both sides of the surfaces have been used in the construction of regions. A
