[SciPy-Dev] Qhull Delaunay triangulation "equations" attribute

[Phil Elson]

Great news, thanks Andreas - this will definitely be useful in the future.
In the meantime I'm writing software which has to target v0.10 upwards, so
I've implemented the regular triangulation approach, which I'm reasonably
happy with (good results and reasonable performance, though probably a lot
slower than a direct bilinear interpolation).



On 26 February 2014 11:45, Andreas Hilboll <lists at hilboll.de> wrote:

> Phil,
>
> not directly answering your question, the upcoming 0.14 release will
> include a new class RegularGridInterpolator, which performs efficient
> interpolation on rectangular, possibly unevenly spaced, grids in
> arbitrary dimensions.  The commit is
>
> https://github.com/scipy/scipy/commit/a90dc2804da21ba4c48c2615facd0ac5848ebe59
> .
>
> Cheers, Andreas.
>
>
> On 26.02.2014 12:23, Phil Elson wrote:
> > Thanks Pauli,
> >
> > Based on what you said, I've simply used the Delaunay.lift_points method
> > to take my vertices to the paraboloid. Though I arbitrarily picked a
> > paraboloid of scale 1 and shift of 0.
> >
> > Is it worth submitting a PR to add a static method for the creation of a
> > Delaunay instance from 2 orthogonal 1D coordinates (I've only
> > implemented it for the 2D case) in this way? I've found that for
> > reasonably large regular grids (800, 1200), manually constructing the
> > triangulation can cut ~25s from the ~31s overall execution time.
> >
> > Additionally, I've been using LinearNDInterplator which I would like to
> > be able to construct with an already computed triangulation instance,
> > would there be interest in me submitting a PR for that also?
> >
> > Thanks,
> >
> > Phil
> >
> >
> >
> > On 20 February 2014 17:18, Pauli Virtanen <pav at iki.fi
> > <mailto:pav at iki.fi>> wrote:
> >
> >     20.02.2014 16:00, Phil Elson kirjoitti:
> >     > I'm trying to manually construct a Delaunay triangulation for an
> >     orthogonal
> >     > 2d grid as described in
> >     >
> >     http://stackoverflow.com/questions/21888546<
> http://stackoverflow.com/questions/21888546/regularly-spaced-orthogonal-grid-delaunay-triangulation-computing-the-paraboloi
> >and
> >     > wonder if anybody can help provide some interpretation of the
> >     > "equations" values of a scipy.spatial.Delaunay instance.
> >     > Essentially I'm working off the premise that it is possible to
> >     construct a
> >     > Delaunay triangulation from a regular grid without going through
> the
> >     > expensive triangulation stage, does anybody know if that is true
> >     or not?
> >
> >     Yes, it should be possible to construct the equations manually.
> >
> >     For Delaunay, "equations" contains the hyperplane equation defining
> the
> >     convex hull facets in ndim+1 dimensions corresponding to the
> simplices
> >     of the triangulation.
> >
> >     You get the ndim+1 dim coordinates for each simplex from the ndim
> >     coordinates by adding an additional last coordinate to the vertices
> of
> >     the simplices. The routine Delaunay.lift_points maps points in ndim
> dims
> >     onto the paraboloid in ndim+1.
> >
> >     The hyperplane equations should be constructed for the so transformed
> >     coordinates, in the form
> >
> >             sum([equations[j,k]*x[k] for k in range(ndim+1)])
> >             +
> >             equations[j,ndim+1]
> >             ==
> >             0
> >
> >     Here, x is the coordinate "lifted" to ndim+1 dims.
> >
> >     Geometrically, equations[j,:ndim+1] contains the normal vector of the
> >     facet j, and equations[j,ndim+1] the offset scalar.
> >
> >     --
> >     Pauli Virtanen
> >
> >     _______________________________________________
> >     SciPy-Dev mailing list
> >     SciPy-Dev at scipy.org <mailto:SciPy-Dev at scipy.org>
> >     http://mail.scipy.org/mailman/listinfo/scipy-dev
> >
> >
> >
> >
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> >
>
>
> --
> -- Andreas.
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