
Show HN: Delaunay Triangulating Robert Delaunay's Eiffel Tower Paintings - modalduality
https://modalduality.org/posts/delaunay-triangulating-delaunays-eiffel-tower/
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phireal
If you're using Python anyway, you can use scipy's triangulation module to
avoid having to compile triangle:

[https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/...](https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.spatial.Delaunay.html)

The triangulation can then be plotted fairly straightforwardly with
matplotlib's triangulation routines: matplotlib.pyplot.triplot and
matplotlib.pyplot.tripcolor
([https://matplotlib.org/examples/pylab_examples/tripcolor_dem...](https://matplotlib.org/examples/pylab_examples/tripcolor_demo.html)).

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arketyp
I did some work [1] on constrained Delaunay triangulations similar to this
where visually important, and constrained, edges were automatically determined
by Laplace-like filters.

[1] [https://femtondev.wordpress.com/](https://femtondev.wordpress.com/)

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knolan
It seems to me that the Voronoi diagram [0], the counterpart of Delaunay
triangulation, is probably more useful as a general approach to this idea.

The cellular nature is great for lots of applications.

[0]
[https://en.m.wikipedia.org/wiki/Voronoi_diagram](https://en.m.wikipedia.org/wiki/Voronoi_diagram)

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amitp
If your goal is to make it "cellular" you can get an even more cellular
appearance by using the Delaunay triangle _centroids_ instead of the
circumcenters like Voronoi diagrams use. Side by side comparisons
[https://www.redblobgames.com/x/1721-voronoi-
alternative/](https://www.redblobgames.com/x/1721-voronoi-alternative/)
(scroll halfway down). The polygons end up looking rounder. I also made a
little toy where you can drag an image onto the page to fill a cellular
polygon diagram [https://www.redblobgames.com/x/1722-delaunay-map-
import/](https://www.redblobgames.com/x/1722-delaunay-map-import/) (cartoon
images work pretty well but fine detail is lost)

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jgtrosh
As suggested in the discussion points, thin lines/stripes get muddled up with
wider adjacent surfaces. Is this a problem with the goal of the exercise ?
Maybe it needs to be more clearly defined. I suppose the idea is that the
method and the style fit together nicely, and as a result the paintings are
representable quite efficiently with low resolution triangulations. It already
mostly fits the bill, except for some exceptions to the main shapes
represented. Does the author suggest further work should be devoted to
improving the efficiency of the depiction? I guess the thin lines are quite
important in keeping the paintings structured but I'm not sure what's to gain
from that exercise if straying too far from the original triangulation — I
think you'd lose the amusing coincidence of these concepts applying nicely
together.

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modalduality
The main idea is to explore the concept of skinny triangles being unaesthetic
(and thus undesirable for triangulations). This is true for many tasks in
computational geometry, but not so true in art. Bringing these two together
shows jarring conflict where the Delaunay Triangulation and your brain's sense
of aesthetics disagree.

It's not really supposed to be useful, just exploration in reduction of an
already reduced art style: what is lost when we enforce that all shapes are
triangles that tend to be more large-angle? For one, I think this destroys the
perspective since one common trope is to make objects narrower as they are
farther away.

Although the entire thing is mostly a joke based on their shared last names.

~~~
jgtrosh
Thanks for your answer.

For what it's worth I think the result is incredibly adapted to the art style;
I think you overestimate your conclusions and I don't think that is fair to
extrapolate claims over the importance of skinny triangles in art in general.

This representation conveys most of what the originals had to offer, and has
the added benefit of being a light content in a meaningful format. It's a good
sign that your questions pulled me into the subject but I don't think there's
much more to extrapolate from the experiment.

Now how about trying delaunay triangulation on animated content with the added
constraint of optimising for fluidity? (Like the works on incorporating art
styles to pictures and videos from last year that you may have noticed, and
that were published in siggraph.)

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liminal
The other day I was looking at this coding challenge to automatically select
points and create a Voronoi of an image:
[https://codegolf.stackexchange.com/questions/50299/draw-
an-i...](https://codegolf.stackexchange.com/questions/50299/draw-an-image-as-
a-voronoi-map)

Of course half the fun here is the coincidence of the last names :)

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davidwitt415
Interesting experiment! Per the talking points, I think a good color strategy
would be to sample the lightest and darkest points from each region, and then
use them as endpoints in a gradient fill.

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mysticalfair
Super cool! Why does the Delaunay triangulation avoid skinny triangles?

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vinchuco
[https://en.wikipedia.org/wiki/Delaunay_triangulation](https://en.wikipedia.org/wiki/Delaunay_triangulation)

Delaunay triangulations maximize the minimum angle of all the angles of the
triangles in the triangulation

