[tuhopuu-devel] /* A (half baked) attempt at a Relax UV tool.

[Bjornmose]

Hi Blendix and all

was looking at your relaxing approach
if i did understand it correctly, it is attempting get the objective
function
sum_over_ all_ faces (| dist(UVnodes)-dist(Meah_vertices)|) to zero.
this is mathematicaly prooven impossible if the mesh is not already
flat. ( think of a tetraeder )
So best you can hope for is get stuck in some local minimum of the
objective function.
The visible result i'd expect is some more or less relaxed domians
surrounded by wildy flipped seams.

This is why all the papers handle a minimization task. (did a little
homework on the papers)
e.g.
Angle based flattening : sum (|angles(uv)-angles(faces)|) = min with
additional flattness constraint
which has a unique global minimum in the angles space, yet leaving a
linear degree of freedom.

the least sqaure conform mapping algo
states an square objective function avioding the scaling (linear
problem)
i am working an a geometric interpretation. sigh... says i have an idea
how it works, but did not understand completly.
they say the redefine the optimization with consrtaints to a nonlinear
problem without and i don't get the leap yet.
hmm.. i'v got a masters degree in physics some years ago. may be i
should give it back.

your realxing framework is in a mathematical sense aequivalent to the
proposal in the papers solving sparse matrix equations and i think it is
a good start.
hmm.. may be not that efficient though.
just a hint : use synchronus dynamics = do not alter the input values in
the loop.
says newvalues = function(oldvalues) and not newvalues=function(mix of
new and old values depending on alredy calculated)

hope to come up with some new ideas soon

ole (bjornmose)