Game Development Reference

In-Depth Information

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-

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
.