Practical Algorithms for 3D Computer Graphics, 2nd Edition

222 6. Computer animation

Start with the linkage configuration defined by the set of angles:

θ

1

, θ

2

, θ

3

...θ

n

(which we will write as Θ),

and end point located at P i.e. at coordinate (x, y)

Apply the steps below to move the end point towards its goal at P

g

(i.e. at :(x

g

, y

g

))

Step 1 :

Calculate the in c r emental step ∆X = P

g

− P

Step 2

Calculate J(θ

1

, θ

2

, θ

3

, ...θ

n

) (use the current valu es of θ

1

etc.)

Step 3 :

Find the inverse of J which we will call J

−

then:J

−

= J

T

(JJ

T

)

−1

(if J is a 2 × n ma tr ix J

−

is a n × 2 matrix)

Step 4 :

Test for a valid convergence of the iteration:

i f ( k(I − JJ

−

)∆Xk > ǫ ) the s tep towards the goal

the ∆X) is too large, so set ∆X =

∆X ...