Finite Element Method Worthy Trisurf Recipe

[ChrisRackauckas]

This gets mentioned quite a bit. Starting point:

https://github.com/JuliaPlots/Plots.jl/issues/392

I want to make sure it got on the issue list itself.

[SimonDanisch]

Does this work for you: http://makie.juliaplots.org/stable/functions.html#Mesh-1

[ChrisRackauckas]

Maybe? I don't understand the format. I'm used to see the indices as an 3xN matrix where each column denotes the indices for the ith triangle. How is this interpreted?

[SimonDanisch]

We can have a simple recipe for this :) e.g. just overload to_indices to do the conversion... Do you happen to have a nice notebook or something, that I can port and make sure it works?

[ChrisRackauckas]

https://github.com/JuliaPlots/Plots.jl/issues/392#issuecomment-342238881

That was a good example. That JLD is on an old version of DiffEqProblemLibrary though: we might want to move that example over to here since I want to delete that sooner rather than later. Pin to v0.11.0.

[SimonDanisch]

Ah, so I already demonstrated how to do it... we might want to have a recipe, that adds the additional wireframe call to mesh as an attribute!

[SimonDanisch]

https://github.com/JuliaPlots/Plots.jl/issues/392#issuecomment-342238881

[ChrisRackauckas]

I still don't get how the format is defined though.

[SimonDanisch]

What part? The mesh is just vertices = Vector{Point{N, Float32} && triangles = Vector{GLTriangle} where GLTriangle == Face{3, UInt32}, where Points and Faces are static arrays... The face type has a lot of convenience defined for indexing, even if it's 0 indexed etc.

[ChrisRackauckas]

Your example code doesn't show Point or GLTriangle stuff though, just:

using Makie
using GLVisualize: loadasset, assetpath

scene = Scene(resolution = (500, 500))
x = [0, 1, 2, 0]
y = [0, 0, 1, 2]
z = [0, 2, 0, 1]
color = [:red, :green, :blue, :yellow]
i = [0, 0, 0, 1]
j = [1, 2, 3, 2]
k = [2, 3, 1, 3]

indices = [1, 2, 3, 1, 3, 4, 1, 4, 2, 2, 3, 4]
mesh(x, y, z, indices, color = color)

I'm not sure how indices is interpreted. Is that reshaped to a 3xN?

[SimonDanisch]

No, that's converted to vertices = Vector{Point{N, Float32} && triangles = Vector{GLTriangle}

[ChrisRackauckas]

How does the second one take place? Is every 3 a triangle?

[SimonDanisch]

Ah yeah, it is ;)

[SimonDanisch]

I mean, it's just reinterpret(Face{3, Int}, indices)

[ChrisRackauckas]

So then it is the same as thinking of it as the 3xN indices. This should be more explicit in the docs. So what's shown is actually a tetrahedron then? That angle doesn't show it.

[ChrisRackauckas]

I think the example should be reworked a little bit. I'll see if I can do that sometime sooner rather than later.

As far as a recipe, here's the two things a finite element recipe would need:

1) A 2D mesh. The values are (x,y) that are a triangular mesh of a space. But then there's a z value which is the value of the PDE at the triangular nodes. So this naturally is viewed as a trisurf plot like seen here:

https://scicomp.stackexchange.com/questions/10203/visualizing-finite-element-solutions-in-matlab

or just in a projection to show via only color.

2) A 3D mesh. In many cases the mesh might use 3D elements like tetrahedrons. In that case, it's (x,y,z,w), where w is the PDE solution that denotes color. This is commonly denoted as a tetramesh plot, like:

https://www.mathworks.com/help/matlab/ref/tetramesh.html https://andreweib.wordpress.com/2010/12/14/element-aspect-ratio/

From this discussion it seems that the mesh function is enough to build these tools. When the recipe system is created I can give this a go.