Graphics Reference
In-Depth Information
2r
=
d
+
r
0
+
r
1
d
C
0
C
C
1
r
1
r
0
Figure 6.5
Merging spheres
S
0
and
S
1
.
distance between the sphere surfaces; thus:
r
1
)
2.
r
=
(
d
+
r
0
+
The sphere center
C
is computed by adjusting
C
0
by
r
0
units away from
C
1
and then
back toward
C
1
by
r
units:
C
0
)
C
0
)
C
=
C
0
−
r
0
(
C
1
−
C
1
−
C
0
+
r
(
C
1
−
C
1
−
C
0
C
0
)
=
C
0
+
(
r
−
r
0
)(
C
1
−
C
1
−
C
0
.
The code for this follows.
// Computes the bounding sphere s of spheres s0 and s1
void SphereEnclosingSpheres(Sphere &s, Sphere s0, Sphere s1)
{
// Compute the squared distance between the sphere centers
Vector d = s1.c - s0.c;
float dist2 = Dot(d, d);
if (Sqr(s1.r - s0.r) >= dist2) {
// The sphere with the larger radius encloses the other;
// just set s to be the larger of the two spheres
