Interpolation-Based Animation - Computer Animation: Algorithms and Techniques - page 127

2 0

4

2

4

4

2

0

2

4

4

2

0

2

4

FIGURE 4.18
Global bend operation.

The deformations are specified by moving the control points from their initial positions. The func-
tion that effects the deformation is a trivariate Bezier interpolating function. The deformed position of a
point P stu is determined by using its ( s , t , u ) local coordinates, as defined by Equations 4.3-4.5 , in the
Bezier interpolating function shown in Equation 4.8 . In Equation 4.8 , P ( s , t , u ) represents the global
coordinates of the deformed point, and P ijk represents the global coordinates of the control points.

m
j

n
k

1

X l m X n

l
i

li

s i 1

mj

t j 1

nk

u k Pðs; t; uÞ¼ ð s Þ ð t Þ ð u Þ (4.8)

i¼ 0 j¼ 0 k¼ 0