by kakaroto, published
This is a customizable pendant of the rhodonea curve and other curves.
This is taken from my curve generator and made into a pendant : http://www.thingiverse.com/thing:50249
UPDATE: Now supports up to 5 different types of curves. See updated instructions below for more information.
This script will generate a pendant with an artistic rendering of a mathematical curve inside.
It was originally a generator for the Rhodonea curve (Rose).
Here are the equations used for each one of those curves :
Rhodonea curve : x=cos(a/bt)sin(t); y=cos(a/bt)cos(t)
Epicycloid : x=(a+b)cos(t)-bcos(((a/b)+1)t); y=(a+b)sin(t)-bsin(((a/b)+1)t)
Epitrochoid : x=(a+b)cos(t)-ccos(((a/b)+1)t); y=(a+b)sin(t)-csin(((a/b)+1)t)
Hypocycloid : x=(a-b)cos(t)+bcos(((a/b)-1)t); y=(a-b)sin(t)-bsin(((a/b)-1)t)
Hypotrochoid: x=(a-b)cos(t)+ccos(((a/b)-1)t); y=(a-b)sin(t)-csin(((a/b)-1)t)
(See also http://en.wikipedia.org/wiki/Rose_%28mathematics%29 )
You can set the 'a, 'b', and 'c' parameters to affect the look of the pattern (see http://en.wikipedia.org/wiki/File:Rose-rhodonea-curve-7x9-chart-improved.svg for example) and chose which pattern type to generate.
The patterns can vary a lot depending on the parameters, even for the same type of curve, so experiment and see what you like. I've created a few remixes that show some of the possibilities.
You can define the thickness of the pattern and outer wall as well as the height of pendant The rose radius will set the radius of the pendant.
The epitrochoid, epicycloid, hypotrochoid and hypocycloid patterns may not fit entirely in the outer circle of the pendant, so you can adjust the "Ring Adjustment" property to make them fit completely, or even to make them go beyond the borders if you think it's nicer that way.
Experiment, create and enjoy!
Note: This is my second attempt at using openscad (the first being http://www.thingiverse.com/thing:49590).
This was a lot of work since openscad wasn't made for drawing curves, and it seems I'm the first one to achieve somehting like that.
Thanks for all those who liked the design!