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Perlin noise for character animation

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Trying to understand how animation works from Ken Perlin's "[url="http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=468392&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel1%2F2945%2F9858%2F00468392.pdf%3Farnumber%3D468392"]Real time responsive animation with personality[/url]" (sorry, article is behind pay wall), so this is probably for folks who are still in school or have access to IEEE journals.

For a given joint, a range of motion is given for angle values of rotation about each axis {x,y,z}, e.g. start: {5 5 5} finish {-5 -5 -5} would mean the joint starts at 5 degrees of rotation about each axis and ends at -5 degrees of rotation about each access... I think.

But a third 3-tuple is given that specifies how to go about interpolating between the limits/ ranges of motion. I think I get the "raised sine" part. For some time t, use the angle within the interval along the graph of raised sine.

But more confusing is the use of the noise functions. I take it that this is supposed to interpolate between values, in our case between 5 and -5 for any axis (since they're all the same). But the functions generally take the form: .5 * (1 + noise(t)). I'm assuming t to be some time, though the paper does not specify this.


What I definitely do not understand is how the noise functions actually interpolate between the extremes.

Can anyone explain this?

Also, I really don't understand the use of bias and gain. I graphed out Perlin's bias and gain functions, but I don't see how they relate to character animation nor the notation used in the paper.

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