Practical Algorithms for 3D Computer Graphics, 2nd Edition

6.2. Animating rigid motion 197

Function B i s ect ( d) {

B i s ect ( d ) returns a τ in the interval [0, 1] which wh en substituted in

P(τ) will return a p o int at a distance d from P

0

. Start by settings

upper and lower bounds for the interval in which τ

d

lies: τ

1

= 0 and τ

2

= 1.0

LOOP:

Test whether the interval in which τ

d

lies is small enough so that

the iteration ca n be terminated: ǫ < 10

−3

i f ( τ

2

− τ

1

< ǫ) jump on to DONE:

Call the function given in listing 6.4 to calculate the dist a n c e along

the spline up to the point determined by τ

d

=

1

2

(τ

1

+ τ

2

)

d

m

= SegLength(τ

d

)

i f (d

m

< d) {

Reduce the interval size by lowering th e upper bound: Set τ

2

= τ

d

}

e