Practical Algorithms for 3D Computer Graphics, 2nd Edition

6.4. Inverse kinematics 227

Arrows and dots show how

the end point moves as each

rotation is applied.

P

1

P

1

P

4

n

2

n

1

P

1

(c)

(b)

(a)

P

1

P

1

P

1

n

3

P

4

˝

Figure 6.24: Accumulating the small rotations occurring at each link of a three-link

articulation leads to an accumulated change in the position of the end point of the

linkage P

4

. In (a) the linkage is slightly repositioned by a small rotation round

ˆ

n

1

. For

(b) and (c) the small rotations only apply to links lying between the point of rotation

and the end of the articulation at P

4

.

In section 2.12.3 matrices were given which would r otate a vector by a spec-

ified angle around either the x, y or z coordinate axis. If