Game Development Reference
In-Depth Information
√
9 + 16 + 144 = 13
h = arctan(x/z) = arctan(3/12) = arctan(1/4) = 14.04
o
p = arcsin(−y/r) = arcsin(−4/13) = −17.92
o
so (r, h, p) = (13, 14.04
o
,−17.92
o
)
√
(f) r =
x
2
+ y
2
+ z
2
=
3
2
+ 4
2
+ 12
2
=
11.
(a) A sphere with radius r
0
.
(b) A vertical plane, obtained by rotating the plane x = 0 clockwise about the y axis by
the angle h
0
.
(c) A “right circular conical surface” (two vertical circular cones meeting tip-to-tip at
the origin). The interior angle of the cone is 2p
0
.
12. She was at the north pole, so the bear was white.
1
B.8
Chapter 8
(Page 291.)
1. (a) 5
(b) 3
(c) 6
(d) 1
(e) 2
(f) 4
2.
(a) 3. Yes, they are canonical Euler angles.
(b) 4. Yes, they are canonical Euler angles.
(c) 5. No, this orientation is in Gimbal lock, and in the canonical set, bank should be
zero.
(d) 1. Yes, they are canonical Euler angles.
(e) 2. Yes, they are canonical Euler angles.
(f) 3. No, the pitch angle is outside the legal range.
(g) 5. Yes, they are canonical Euler angles.
(h) 2. No, the pitch angle is outside the legal range.
(i) 6. Yes, they are canonical Euler angles.
2
4
cos(30
o
/2)
3
5
2
4
0.966
3
5
0
@
1
A
0
@
1
A
1sin(30
o
/2)
0sin(30
o
/2)
0sin(30
o
/2)
.259
0.000
0.000
3.
(a)
=
(b) All rotation quaternions have a magnitude of 1!
1
It was polar bear. Get it?! Polar!
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