Math for constant speed ellipse (Again)

Todd F:
My approach to making an ellipse was:
1. Generate a circle with diameter = ellipse major diameter
2. Since data is in X and Y registers, Multiply the Y register by
a number < 1. This will now be the data for the "new" Y for the
ellipse.
3. Output the New Y data as required
4. We will use theta form the circle in later calculations

Now the tangential velocity is V tang = SQR( Vx^2 + Vy^2)
Since Vy is propoprtional to the new Y, (smaller than Vx), we can
calculate V tang from theta above. It will need to be increased by
the ratio of _____________Vo________________
SQR((COS theta)^2 + (SIN theta/R)^2)
where R is the ratio Majordiam/Minordiam.

Since the velocity is proportional to the Clock frequency, it will be
necessary to increase the clock freq as a function of theta for a
constant tangential speed. This should be fairly easy to implement
with an interpolator.

R will tell us hoow much the clock needs to be increased. Your
processing speed may limit the actual machine speed since for a ratio
of 10 (major D vs minor D), the frequency in will need to go to 10x
the usual speed.

I talked to Fred Smith, I M Service, asking about his CAD/CAM
capabilities and he said:
1. You can use straight line approximations to generate the ellipse
2. You can use arc approximations
3. Either form may be cutter compensated . Thus you may accommodate
the cutter diameter speed effect for sharp radii also. Either of
these seems like a workable solution.
Regards,
Jack C. Cain