by Ron K. Lussier
MiniTutorial #1
v0.8
Not being much of a mathematician, this this a 'novice' tutorial of how I currently do rotations of wheels and balls in Max animation. This tutorial uses Expression controllers, I've found the use of a MaxScript controller to be better for advanced control.
Set up:
Create a Sphere and a Dummy helper object. Align them and link the Sphere to the Dummy. Assign a Checker map to the Sphere, maybe 2x3, for visual reference.
The right number:
In this case, pi. It is the ratio of a circles
circumference to it's diameter. (pi = 3.14159~) It can be called in Max expressions
by name.
We can get the radius of a procedural object from Max, multiply it by 2, there's
diameter. Now multiply by pi, there's circumference, that's the distance in which the circle
should turn one full revolution. (If you are not using a procedural object, you can
measure the diameter easily with a Tape helper.)
So..
radius * 2 * pi = 1 full rotation (360 degrees)
or.. (in an Euler controller axis, Expression controller)
The expression:
degToRad ( posit.x * 360 / (radius*2*pi) )
 where "posit" is assigned to the parent dummy's position and
"radius" to the sphere primitives Radius value (you'll have to assign a Bezier
controller to the latter)
Expression explained:
1. Use Degrees to Radians (degToRad  radians are Max's way of looking at rotation)
2. Make distance traveled comparable to degrees to rotate (x360)
3. divide by the circumference (1 full rot. or (radius * 2 * pi) )
4. use the value
That's the one dimensional version anyway. (That is, it will only work when the object is
moved along the axis used on the expression. [x] )
The inverse:
Also, the reverse of that, for getting rotation from
movement ...but it fails at 90 degrees from Euler flipping. (I used this in the
"balbounc.max" file that is in the Scenes\Samples\Animation directory on the
Max2.5 CD.)
(Radius*2*pi) / 360 * radToDeg(roll)
 where "roll" is assigned to a single axis of an Euler controller and Radius is
either assigned to the radius track of a primitive or replaced by a number that
corresponds to the radius of the geometry.
MaxScript version?:
Pros and Cons: MaxScript can do this extremely well because
it can calculate direction as well as distance, thus allowing the math to work on a wheel
rolling any direction. The disadvantage is that it only works when the animation is run
forward through every frame. (Moving the Time Slider, or playing the animation with
RealTime set can make the wheel(s) rotate incorrectly, but it will reset at frame zero
correctly.)

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