I'm doing some work on geometric tiling (the 15 shades of pentagon) and need
to numerically solve 2 variable functions. Fortunately they are
well-behaved:

http://forum.openscad.org/file/t229/2dfunction.jpg

Broyden's method (and refinements) seems to be the thing to use but I wonder
if anyone has an implementation already  - or a different approach to
function optimisation

Chris

--
Sent from: http://forum.openscad.org/

Indeed so although its performance is not so good. There are a range of
algorithms implemented in other languages like scipy for Python and the gnu
C libraries. Code for any of these optimisation algorithms would be useful.

Looking around a bit more it looks like the downhill Simplex
https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method looks quite good
and not too difficult to implement .  For a 2D function it needs 3 initial
points -  I'll give that a go.

Of course the problem with using such functions as you well know is the
inability to pass functions as parameters- I must checkout Curv!

--
Sent from: http://forum.openscad.org/

I implemented the simplex method as per

https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method

It's been tested on the Rosenbrock function (for degree 2 at least) and on
my own problem in geometry and convergence looks good.

https://github.com/KitWallace/openscad/blob/master/simplex-method.scad

--
Sent from: http://forum.openscad.org/