Fine Tuning the Motion

In the last page of the tutorial, we set up the basic motion of a fish swimming. The motion looks good, but notice that the fish really looks more like an eel swimming; its head moves too much. What we want is for the front of the fish not to sway at all and for the tail to sway the most.

To keep the head from moving and to get the tail to sway the furthest, add "* z" to the equation:

Since the points at the head of the fish are modeled at a Z of 0, the distortion amount created by the sine wave will be multiplied by 0 for the points at the head, but will be multiplied by a bigger and bigger number down the length of the fish. At the tail, the distortion amount is multiplied by 2, since the points at the tip of the tail are at Z=2. This makes the amount of distortion 0 at the head which is what we want.
Make a preview and notice that the tail seems to swing too much compared to the head.
To make the tail swing less, divide the z by 3, giving: sin(z - 7*t) * z/3.
Make a preview. This is good, but really the head should move a little bit.
To give the head a small bit of motion, add something small, like 0.7 to the z before it's divided: sin(z - 7*t) * (z + .7)/3.
This makes a nice, natural-looking swimming motion for the fish. Try making previews from some other perspectives on the fish.

Other Ideas

To make the fish swim faster and faster during the scene, try: sin(z - 7*t*t) * (z + .7)/3.
To make the fish sway more and more to the side during the scene, try: sin(z - 7*t) * (z + 2*t)/3.
To make the motion of a sea mammal, like a whale or dolphin, use the same equation in the Point Y channel instead of the X channel.
To make a smooth, corkscrew motion, use sin(z - 7*t) * (z + .7)/3 in the X channel and cos(z - 7*t) * (z + .7)/3 in the Y channel.
To make a random-looking motion, try sin(z - 7*t) * sin(2*z - 20*t) * sin(z/3 + 3*t) * (z + .7)/3 in just the X channel.

Don't be afraid to keep experimenting on your own. It's just math, it won't hurt you.

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