Graphics Reference
In-Depth Information
(a)
(b)
Figure 12.2
The welding tolerance must be set appropriately. (a) Too small, and some vertices
that should be included in the welding operation could be missed. (b) Too large, and vertices
that should not be part of the welding operation could be erroneously included. Arrows
indicate vertices incorrectly handled during the respective welding operations.
Weld to previous vertex:
12345678
Weld previous vertex to current vertex:
12345678
INPUT:
12345678
Average previous and current vertex:
12345678
tolerance
Average all vertices as a set:
1
2
345678
Figure 12.3
Different outcomes fromalternativemethods for welding a set of points mutually
within the welding tolerance distance.
As shown in Figure 12.3, these alternatives give different results. The first option is
attractive because it limits the
vertex drift
— the distance between a vertex's original
and final position — to be the welding epsilon. Option 2 clearly has a worst-case
vertex drift, proportional to
n
, where
n
is the number of vertices welded. Even though
it is not illustrated here, option 3 also has a worst-case vertex drift proportional to
n
(consider the effects of doubling the welding epsilon given in Figure 12.3). If there
