On Fri, Mar 4, 2011 at 4:41 PM, Gerald K. Dobiasovsky <gerald.dob@aon.at> wrote:

Yes, but that doesn't solve the case of, say, your epicycloids in general.
I shudder at the thought of converting the formula (for a fixed number of cusps)
to cartesian and/or polar form even with the aid of Mathematica/Maple/Maxima.

The epicycloid formula seems to be fairly close even with driving the parametric form with the angle. I had no luck finding or deriving the other forms. It makes a good curve the way it is even if it isn't exactly correct.
 
Oh? I checked it with DOS Fractint before pasting it into the mail.
Any format munging by the mail service, perhaps?
Or fracton not liking "passes=t" (I forgot to set this back to "passes=1").
Anyway, sorry for the inconvenience.


I figured out what happened to the formula. There was a small clickable line in the middle of the formula in my Gmail mail reader that said "Show quoted text". When I clicked that, the missing part of the formula came back. It still didn't run though because the place that said "Show quoted text" changed to "Hide quoted text". Deleting the Hide quoted text from the pasted formula made it work just fine. I don't know if that quoted thing is unique to my mail reader but I have never seen it in formulas before. Fracton ignores the passes= parameter so that is no problem. The Deltoid_Mset formula looks like it will be a good one because  of the 3 sided symmetry.

The cartesian form method you mentioned worked great. I used it to make a curve with a loop. See my other post for today. Thanks again for the great suggestion.

--
Mike Frazier
www.fracton.org