[OpenSCAD] Improve rendering speed

Parkinbot rudolf at parkinbot.com
Fri Jun 10 14:51:10 EDT 2016


Ronaldo, 

thanks again, for showing how mighty your approach is. I tried to dig out my
code on that, but found only my first approach, which I did in OpenSCAD. I
think I changed to Matlab after that. I remember there was a point, I got
frustrated on calculating the skin part - in which your approach seems to be
very good. 
<http://forum.openscad.org/file/n17639/SchwarzP.png> 

its better here 
http://www.indiana.edu/~minimal/archive/Triply/genus3/PLines/web/

For the R²->R part: You can resolve the skin equation
0 = cos(x) + cos(y) + cos(z)
for z
z = acos(-cos(x) - cos(y))

and then solve this system for any (feasible) z-discretrization, while
restricting x and y (out of R²) to the symmetry region (shown by the lines
in linked picture). Not such a big deal.


> So, the inside surface was obtained just by doing an "offset" of the
> original function value and the min() is equivalent to an intersection.
> That
> is one of the marvelous things of the implicit representation of f-reps.

yes, this is indeed marvelous. I'll have to dig into that one day. 

Hermann Schwarz was a German mathematican. Can't help you with Costa ...
Surface math is not my world by the way.



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