[Octave-bug-tracker] [bug #55642] isosurface is slow

[Guillaume]

URL:
  <https://savannah.gnu.org/bugs/?55642>

                 Summary: isosurface is slow
                 Project: GNU Octave
            Submitted by: gyom
            Submitted on: Mon 04 Feb 2019 01:59:26 PM UTC
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Performance
                  Status: None
             Assigned to: None
         Originator Name: Guillaume
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: dev
        Operating System: Any

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Details:

isosurface becomes very slow when the size of the input data increases:


n = 64;
[x, y, z] = meshgrid (1:n, 1:n, 1:n);
v = (x-n/2).^2 + (y-n/2).^2 + (z-n/2).^2;
tic; fv = isosurface (x, y, z, v, max (v(:))/2); toc


Octave takes 11.34s while Matlab takes 0.04s.

If you increase n to 128, Octave takes 200s and Matlab 0.25s

And for n = 256, Matlab takes 2s while Octave was still running after an
hour.

Most of the time is spent in __unite_shared_vertices__ where the loop over
vertices is known to be slow (see bug #46946 and patch #8912). 

One way would be to move __unite_shared_vertices__ into C++. Otherwise I
wonder if one can implement 'unique with tolerance' from sorting the
vertices:


v = sortrows (fvc.vertices);
d = diff (v, 1, 1);
all (abs (d) < tol)


I also notice that the help text of isosurface still mentions the use of
'unique':


## If given the string input argument @qcode{"noshare"}, vertices may be
## returned multiple times for different faces.  The default behavior is to
## eliminate vertices shared by adjacent faces with @code{unique} which may
be
## time consuming.





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