Mike Frazier wrote:
Another great tip. Thanks for sharing it. This one looks like it would work for curves with loops.
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. Another way would be - for each orbit point - to step (with a sufficiently small stepsize) along the curve and record the smallest distance to the orbit point. Although the formula parser has no user loop construct, changing the formula to do both in the main loop can be done (and has been done for other purposes). But think of the slowdown!
For folks trying this on their own, some of the formula is missing. To get the Deltoid_Example to work, I pasted the xx,yy,a, and distance equations into the formula for Astroid_Mset_v2.
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. Regards, Gerald P.S. I had to send this a second time, because xmission refused to accept the first post. Seems Jim Muth is not the only person "spamming" the list.