Graphics Reference
In-Depth Information
for(inti=0;i<3;i++) {
// For each axis count any excess distance outside box extents
float v = p[i];
if (v < b.min[i]) sqDist += (b.min[i] - v) * (b.min[i] - v);
if (v > b.max[i]) sqDist += (v - b.max[i]) * (v - b.max[i]);
}
return sqDist;
}
5.1.4
Closest Point on OBB to Point
Let
B
be an OBB given by a center point
C
; three orthogonal unit vectors
u
0
,
u
1
, and
u
2
specifying the orientation of the
x
,
y
, and
z
axes of
B
; and three scalar values
e
0
,
e
1
, and
e
2
specifying the box halfwidths along each axis (Figure 5.4). In this representation,
all points
S
contained by
B
can be written as
S
=
C
+
a
u
0
+
b
u
1
+
c
u
2
, where
|
a
| ≤
e
0
,
b
≤
e
2
.
A point
P
in world space relates to its corresponding point
Q
e
1
, and
|
c
| ≤
=
(
x
,
y
,
z
)in
the coordinate system of the OBB
B
as
P
z
u
2
. Given
P
, the
OBB-space coordinates can be solved for as follows. Only the derivation of the
x
=
C
+
x
u
0
+
y
u
1
+
P
y
x
u
1
u
0
C
e
0
e
1
Figure 5.4
The point
P
, in world space, can be expressed as the point (
x
,
y
) in the coordinate
system of this 2D OBB.
