Re: [Lib2geom-devel] allNearestTimes()

[Nathan H. <nj...@nj...>]

Hi Krzysztof,
I agree with everything you've said.  For the epsilon version you
pretty much just need to call multiroots on the distance polynomial to
get the intervals once you've identified a global minimum, then solve
for each separately:

best = roots(dd);
...
lsqr = dd(best)
sqr = dot(c-p, c-p)-(lsqr+2*eps);  // slightly inaccurate hack to
avoid sqrt of polynomial

portions = roots(sqr) // is there a ranged version of roots?

// minimise inside each portion.

nearest_point(c.portion(portions[i]));


There may be a more efficient way to do this, let's implement a simple
and clean version and reassess if it comes up in profiling.

njh

On Sat, Jul 19, 2014 at 02:40:30AM +0200, Krzysztof Kosiński wrote:
> This method is a little pointless, because it will return more than
> one point only if they are at exactly the same distance. Due to
> limited precision of doubles, this will only happen in very specific
> circumstances - basically only if someone deliberately constructs the
> object and the point with carefully chosen values. It's nearly
> impossible to get more than one result by manipulating shapes on the
> screen. Therefore arbitrarily picking one of the points doesn't change
> much.
> 
> It would be more useful if the method accepted a tolerance parameter
> and returned the local minima of each subset of the shape not further
> than this tolerance from the true nearest time. The attached image
> explains this.
> 
> Regards, Krzysztof


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