Interpolating Values - Computer Animation: Algorithms and Techniques - page 105

y

x

FIGURE 3.43
Step function defined by data points of original curve.

1/10

1/20

20

10

Wide box Box

1/10

20

1

e ( x b ) 2 (2 a 2 )

Tent Gaussian

a 2 π

FIGURE 3.44
Sample smoothing kernels.

it (i.e., convolution ). Figure 3.45 shows a simple tent-shaped kernel applied to a step function.
In the continuous case, this becomes the integral, as shown in Equation 3.39 , where [

s , , s ]is

...

the extent of the support of the kernel function.

Z s

P ðxÞ¼ f ðx þ uÞgðuÞdu (3.39)

s

The integral can be analytically computed or approximated by discretemeans. This can be done either
with or without averaging down the number of points making up the path. Additional points can also be