Add TriMesh element

[philippjfr]

Triangle meshes are a common form of data when working with complex polygons and are frequently employed in environmental modeling. The most common way to compute such a mesh is using Delaunay triangulation and the data is usually represented as two data structures:

1. The simplices representing each triangle, usually these are node indices.
2. The nodes or points representing each corner of a triangle.

This representation is in fact simply a specific type of graph and closely follow the data structures we already use for graphs, where the simplices represent the abstract connectivity of the mesh and the nodes represent the positions. It was therefore trivial to write a TriMesh element which simply reuses the same data structures, organization, and plotting code as existing graph elements.

Here is a simple example:

import param
import numpy as np
import holoviews as hv
from scipy.spatial import Delaunay

from holoviews.element.graphs import Graph, EdgePaths

hv.extension('bokeh')

n_verts = 1000
pts = np.random.randint(1, n_verts, (n_verts, 2))
tris = Delaunay(pts)

hv.TriMesh((tris.simplices, tris.points))

This approach is reasonably fast for small meshes (~1 second/5000 triangles) and once you start plotting more than ~10k triangles you will want to use datashader anyway. It is also flexible enough to associate additional values both with the simplices and with the nodes.

Once holoviz/datashader#525 is merged I will get on with allowing datashader operation such as aggregate to operate on the TriMesh element.

• Reference gallery entries
• Unit tests

[philippjfr]

If you enable WebGL rendering in bokeh you can actually scale up to some pretty large meshes, here is an example of selecting on 40485 triangles:

[philippjfr]

I've now allowed filling the triangles by a value, so here's the example above this time with filled triangles:

I'd now consider this PR ready for review, I've added unit tests and reference notebooks. The datashading portion will follow in another PR once it's been merged into datashader.

[philippjfr]

Yay, we even gained coverage.

[basnijholt]

I am trying this out since I work a lot with triangulations, currently, I create plots like:

(an Overlay of Polygon and Image)

Using this branch I am trying to get something similar, but it's not getting better:

%%output size=200
%%opts TriMesh (node_size=0 edge_line_width=0.1 edge_nonselection_alpha=0.01)
plot * hv.TriMesh((tris.simplices, points))

I am unable to set the alpha and linewidth, am I not understanding it, or is this a bug?

[basnijholt]

Another question, the hv.Image I used in the Overlays above are created from an interpolation that uses the scipy.spatial.Delaunay object, but looking at your example plot it seems to be possible to fill the triangles directly with the values at the vertices, but I can't see how exactly. Could you please give a simple example?

[philippjfr]

Looks like you're using the matplotlib backend but specifying bokeh options, try changing that to edge_linewidth and edge_alpha.

but looking at your example plot it seems to be possible to fill the triangles directly with the values at the vertices, but I can't see how exactly.

Have a look at the example notebook, the last example demonstrates it. Going to be pushing a small fix for that shortly.

[philippjfr]

@jlstevens @jbednar Requesting review.

[jbednar]

Looks great!

[jbednar]

What are hImage and .Image ?

[jbednar]

How can rasterize be derived from trimesh_rasterize? That seems like a broken type hierarchy, as it does not satisfy "is a" ("rasterize" is not a kind of "trimesh_rasterize").

[philippjfr]

True, it was easiest to inherit all the methods and parameters but a cleaner class hierarchy is worth the extra handling.

[jbednar]

Does this not yet handle regridding?

[philippjfr]

I was going to handle that in another PR once datashader has made the API more consistent.

[jbednar]

Ok. And that's on my plate, but after this conference prep...

[basnijholt]

Great work! 👍

How can I use the interpolation here?

How do I go from:

%%opts TriMesh [filled=True edge_color_index='z'] (cmap='viridis' node_alpha=0 edge_line_alpha=0.4)
def plot_TriMesh(learner):
    ip = learner.ip()
    simplices = ip.tri.simplices
    nodes = ip.tri.points
    z = ip.values[simplices].mean(axis=1)
    return hv.TriMesh((np.column_stack([simplices, z]), nodes), vdims='z')
plot_TriMesh(learner)

to

%%opts Image (cmap='viridis')
%%opts Contours (color='k')
learner.plot(triangles_alpha=0.4)

I would like to know because:

%timeit plot_TriMesh(learner)
2.71 ms ± 309 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

%timeit learner.plot(triangles_alpha=0.4)
216 ms ± 13.9 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

EDIT
the timing is not such an issue anymore, implemented an overlay of an Image and TriMesh

# new
%timeit learner.plot(triangles_alpha=0.4)
11.7 ms ± 803 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

# old
%timeit learner.plot(triangles_alpha=0.4)
317 ms ± 17.3 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

however learner.plot() now fails when there is no data yet.

[basnijholt]

For the same reason hv.Image([]) is useful, the same would go for hv.TriMesh.

Would it be easy to make this work with hv.TriMesh(([], []))or something?

My data is calculated and plotted live, and in be beginning there might not be data to plot yet.

Then I could write beautiful things like:

if self.data:
    x = y = np.linspace(-0.5, 0.5, n)
    ip = self.ip()
    z = ip(x[:, None], y[None, :])
    image = hv.Image(z, bounds=lbrt)
    tris = hv.TriMesh((ip.tri.simplices, self.unscale(ip.tri.points)))
    tris = tris.opts(style=dict(edge_line_alpha=triangles_alpha))
    plot = image * (tris if triangles_alpha else hv.TriMesh(([], [])))
else:
    plot = hv.Image([]) * hv.TriMesh(([], []))

[philippjfr]

@basnijholt Both hv.TriMesh(([], [])) and hv.TriMesh([]) now work.

[basnijholt]

How can I change the colors of the edges?

(I think) I've tried all style parameters with *_color* but I am not able to get it to work.

[philippjfr]

@basnijholt Are your values on the vertices or simplexes? Currently it only allows coloring by values on the simplexes.

[philippjfr]

@jlstevens Requesting review again.

[basnijholt]

Are your values on the vertices or simplexes

The values are at the vertices.

[philippjfr]

Need to fix this docstring.

[philippjfr]

Will add a comment about this. By default edgepaths are not computed but .select expects it to be.

[jlstevens]

Yes, a comment next to this line explaining it would be a good idea.

[philippjfr]

Addressed the comments, added vertex averaging and updated the reference notebooks. Ready for a final review.

[jlstevens]

New changes look good and tests have passed. Merging!