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Case
Candidate MTD Direction s min
FV 5
s = n ( f A )
VF
s = n ( f B )
EE
s = ± norm ||·|| ( e A × e B )
VE 6
s = norm ||·|| ( v A proj ( v A ,e B ))
EV
s = norm ||·|| ( proj ( v B ,e A ) v B )
VV 7
s = norm ||·|| ( v A v B )
Ta b l e 4 . 3 . Candidate support directions in nondegenerate feature pair cases. Every unde-
fined case is degenerate (see Table 4.2 ).
Equation (4.4):
( s min ,d min )=max
d
{
( s ,d ): s
FV
VF
EE
}
.
(4.4)
P A,i ( s i ) and
P B,i (
For each potential direction s i , we can find support planes
s i )
and signed distance d i = d A,i + d B,i . Computing every d i , we compute the
Figure 4.5. SAT cases.
5 The face must lie in the support plane P , n ⊥ f P⊥ s min s min n .
6 If the vertex and the edge are the supporting features, the vertex will always project into the
interior of the edge, so no bound checking is necessary.
7 Vertices must project into each other along s : v A v B s .
 
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