Add high level methods for sliceplot and lineplot

[pjaap]

This is based on WIAS-PDELib/GridVisualizeTools.jl#20

Implementation of high level methods for line and slice plotting.
The user only has to provide a generic line or plane definition to obtain a plot.

The new coordinate systems are created by isometric rotation and therefore the angles are invariant.

Examples:

grid = simplexgrid(-1.0:0.01:1.0, -1.0:0.01:1.0)
f = map(x -> x[2]*x[1], grid)
line = [1,1,0] # plot along x + y = 0
lineplot(grid, f, line, Plotter=GLMakie)

grid = simplexgrid(-1.0:0.1:1.0, -1.0:0.1:1.0, -1.0:0.1:1.0)
f = map(x -> x[2]*x[1], grid)
plane = [1,1,0,-1.51] # plot along x + y + 0z = 1.51
sliceplot(grid, f, plane, Plotter=GLMakie) 

Note that the intersection is about of size 2 x 0.75 in the new transformed coordinates.

There is a bug in marching_tetrahedra, creating some holes in the plot if the tetrahedra are sliced along the facets:

plane = [1,1,0,-1.5] # plot along x + y + 0z = 1.5

[j-fu]

Ah cool - this seems to work without need to interfere with the plotting backend code.

As for the naming: in fact, these are still scalarplots after all.

An alternative would be to just use the scalarplot method and to add a hyperplane
kwarg. So we could have

scalarplot(grid, f; hyperplane=[1,1,0],Plotter=GLMakie)

[pjaap]

Sorry for the late answer. I somehow missed it.

Thanks for the positive feedback. I like your naming suggestion to keep it as scalarplot.
However, a hyperplane is usually used for more than three dimensions, right?
We already have the planes kwarg, which is too similar to plane.

I think the cleanest solution is slice = Plane(a,b,c,d) for an explicit dummy class Plane. And Line(a,b,c) for the line plot.
Then, we can elegantly document the plane equation coefficients.

[j-fu]

IMHO "hyperplane" is the dimension independent name for an n-1 dimensional affine subspace.
So a line is a hyperplane in 2D, and a plane is a hyperplane in 3D. I am really a fan of dimension independent naming.

[j-fu]

See https://discourse.julialang.org/t/plotting-solution-on-unstructured-mesh-along-a-cartesian-line-in-voronoifvm-jl/126258/2

[j-fu]

As for the naming: we could have a dimension type parameter in HyperPlane and make type aliases for Line and Plane.

[j-fu]

After thinking more about it: slice is really good as a name for the keyword arg.

In principle it might be sufficient to pass a vector or tuple of the right dimension,
we might not need an extra type, so slice=[1,0,2] might be sufficient with proper documentation.

What really would be quite helpful in the API would be the ability to say
slice = :y => 5 or slice = "y" => 5.

We could internally have something like these and call them wherever the slice data are accessed:

function make_slice(spacedim, v::Any)
  if length(v)==spacedim+1
     return v
  else 
   error("hyperplane in dim=$spacedim needs $(spacedim+1) parameters")
end
end

and

function make_slice(spacedim, p::Pair)
   v=zeros(spacedim+1)
   if Symbol(p.first)==:x
       v[1]=1
   elseif Symbol(p.first)==:y
       v[2]=1
    ....
   end
   v[end]=p.second
return v
end

[pjaap]

This also circumvents the problem of exporting the pretty ambiguous types Line and Plane.

I also like the idea to pass pairs, as in slice = :x => 5. I would definitely go with symbols.

Another, maybe really clean approach would be to pass an expression slice = :(x - 5) or slice = :(x + 2y + 4 ) ...
edit: we should not put a = in an expression

What do you think about this one?

[j-fu]

To allow Symbols and strings is easy - the example above should already do this.
As for expressions - well why not... But this IMHO also could be released later if it takes too long
to make it robust. I don't have many experiences with this.

[pjaap]

From my POV, the PR is now feature complete.

We need an downstream change for PlutoVista, like in src/makie.jl.
Therefore, I skipped one test for now, This should be turned on again soon.

[j-fu]

Could you also add line plot and a slice plot example to the docs ? Maybe in examples/plotting.jl ?

[pjaap]

Sure, I added some handy examples. Stupid question: How did you make the SVG files?

[j-fu]

This is via the include("makeplots.jl") in docs/make.jl.
But see #66 ...

[pjaap]

Ah, I see. Still not used to the workflows of this package.

[pjaap]

Ok, I ran into some weird documenter issue with the doc strings of the new slice_plot.jl file.
Now the examples and doc strings should be there.

[pjaap]

Hugh. CI fails due to libpython3 no found. Looks unrelated to me. It didn't fail a few hours ago.
Locally tests are fine.
Force merge or debug the issue?