Re: [CAD_CAM_EDM_DRO] Math for constant speed ellipse

At 11:34 PM 1/6/03 -0500, you wrote:

>> - If you are milling around the outside of the ellipse, then you
>> will be chewing up a higher volume per time of material
>
>Interesting; can you explain why this is so? Better yet, do you know of an
>approach that will chew the same volume of material per unit time? This
>would be much better.

Because the curvature increases the difference between the toolpath and the
actual curve, which means due to sharper curvature at ends, it travels
farther along ends per unit time.

>> At any rate, since whatever calculus and DE brain cells I may have
>> had have mostly died, I would look for a less math-intensive
>> approach to the problem: pick an approximate step size for theta,
>> calculate the new x,y position that you are headed for, calculate
>> the distance from where you are now to over there,

You'd be better off to pick an x or y incremental distance to feed to the
formula and then calc the corresponding other coord with the rectilinear
form of equation, then make the move from present to next location based on
that. I could write an algorithm to do this myself.

>> BETTER YET!! Look up Breshenham's Algorithm on the net or in a computer
>> graphics book. It's how graphics hardware draws straight lines into

Right on!

>Do you know off-hand how much variation in speed Breshenham's approach will
>produce when applied to circles?

It should produce relatively constant velocity for any equation.

Regards, Hoyt McKagen

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