CoCalc -- generate_elements

GitHub Repository: trixi-framework/Trixi.jl
Path: blob/main/docs/literate/src/files/behind_the_scenes_simulation_setup_plots/src/generate_elements_figure.jl
²⁰⁷⁸ views
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using Plots
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function min(coordinates::Vector{Tuple{Float64, Float64}}, i)
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    min = coordinates[1][i]
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    for j in coordinates
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        if min > j[i]
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            min = j[i]
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        end
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    end
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    return min
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end
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function max(coordinates::Vector{Tuple{Float64, Float64}}, i)
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    max = coordinates[1][i]
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    for j in coordinates
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        if max < j[i]
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            max = j[i]
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        end
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    end
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    return max
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end
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function nodes_project_four(coordinates::Vector{Tuple{Float64, Float64}})
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    nodes_1d = [-1.0, -0.4472135954999579, 0.4472135954999579, 1.0]
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    nodes_2d = Array{Float64, 2}(undef, 16, 2)
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    for i in range(1, length(nodes_1d))
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        for j in range(1, length(nodes_1d))
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            nodes_2d[(i - 1) * 4 + j, :] = [nodes_1d[i], nodes_1d[j]]
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        end
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    end
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    k_x = (max(coordinates, 1) - min(coordinates, 1)) / 2
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    k_y = (max(coordinates, 2) - min(coordinates, 2)) / 2
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    b_x = min(coordinates, 1)
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    b_y = min(coordinates, 2)
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    for i in range(1, Int(length(nodes_2d) / 2))
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        nodes_2d[i, 1] = k_x * (nodes_2d[i, 1] + 1) + b_x
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        nodes_2d[i, 2] = k_y * (nodes_2d[i, 2] + 1) + b_y
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    end
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    return nodes_2d
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end
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import Base.+
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+(a::Tuple, b::Tuple) = a .+ b
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# level 1
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plot(Shape([(2, 0), (2, -2), (0, -2), (0, 0)] .+
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           [(0.5, -0.75), (0.5, -0.75), (0.5, -0.75), (0.5, -0.75)]), linecolor = "black",
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     fillcolor = "white", label = "elements", legend_position = :right, linewidth = 2,
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     size = (800, 600), showaxis = false, grid = false, x_lims = (-3, 5.5),
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     ylims = (-3.5, 3))
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nodes_2d = nodes_project_four([(2, 0), (2, -2), (0, -2), (0, 0)] .+
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                              [(0.5, -0.75), (0.5, -0.75), (0.5, -0.75), (0.5, -0.75)])
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scatter!(nodes_2d[:, 1], nodes_2d[:, 2], color = "red", label = "Gauss-Lobatto nodes",
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         markersize = 5)
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# level 2
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# upper right
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plot!(Shape([(2, 2), (2, 1), (1, 1), (1, 2)] .+
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            [(0.75, 0.5), (0.75, 0.5), (0.75, 0.5), (0.75, 0.5)]), linecolor = "black",
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      fillcolor = "white", label = false, linewidth = 2)
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nodes_2d = nodes_project_four([(2, 2), (2, 1), (1, 1), (1, 2)] .+
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                              [(0.75, 0.5), (0.75, 0.5), (0.75, 0.5), (0.75, 0.5)])
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scatter!(nodes_2d[:, 1], nodes_2d[:, 2], color = "red", label = false, markersize = 5)
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plot!(Shape([(0, 2), (1, 2), (1, 1), (0, 1)] .+
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            [(0.25, 0.5), (0.25, 0.5), (0.25, 0.5), (0.25, 0.5)]), linecolor = "black",
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      fillcolor = "white", label = false, linewidth = 2)
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nodes_2d = nodes_project_four([(0, 2), (1, 2), (1, 1), (0, 1)] .+
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                              [(0.25, 0.5), (0.25, 0.5), (0.25, 0.5), (0.25, 0.5)])
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scatter!(nodes_2d[:, 1], nodes_2d[:, 2], color = "red", label = false, markersize = 5)
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plot!(Shape([(0, 0), (0, 1), (1, 1), (1, 0)] .+
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            [(0.25, 0.0), (0.25, 0.0), (0.25, 0.0), (0.25, 0.0)]), linecolor = "black",
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      fillcolor = "white", label = false, linewidth = 2)
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nodes_2d = nodes_project_four([(0, 0), (0, 1), (1, 1), (1, 0)] .+
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                              [(0.25, 0.0), (0.25, 0.0), (0.25, 0.0), (0.25, 0.0)])
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scatter!(nodes_2d[:, 1], nodes_2d[:, 2], color = "red", label = false, markersize = 5)
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plot!(Shape([(2, 0), (2, 1), (1, 1), (1, 0)] .+
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            [(0.75, 0.0), (0.75, 0.0), (0.75, 0.0), (0.75, 0.0)]), linecolor = "black",
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      fillcolor = "white", label = false, linewidth = 2)
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nodes_2d = nodes_project_four([(2, 0), (2, 1), (1, 1), (1, 0)] .+
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                              [(0.75, 0.0), (0.75, 0.0), (0.75, 0.0), (0.75, 0.0)])
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scatter!(nodes_2d[:, 1], nodes_2d[:, 2], color = "red", label = false, markersize = 5)
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# upper left
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plot!(Shape([(-0, 2), (-0, 1), (-1, 1), (-1, 2)] .+
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            [(-0.25, 0.5), (-0.25, 0.5), (-0.25, 0.5), (-0.25, 0.5)]), linecolor = "black",
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      fillcolor = "white", label = false, linewidth = 2)
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nodes_2d = nodes_project_four([(-0, 2), (-0, 1), (-1, 1), (-1, 2)] .+
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                              [(-0.25, 0.5), (-0.25, 0.5), (-0.25, 0.5), (-0.25, 0.5)])
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scatter!(nodes_2d[:, 1], nodes_2d[:, 2], color = "red", label = false, markersize = 5)
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plot!(Shape([(-2, 2), (-1, 2), (-1, 1), (-2, 1)] .+
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            [(-0.75, 0.5), (-0.75, 0.5), (-0.75, 0.5), (-0.75, 0.5)]), linecolor = "black",
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      fillcolor = "white", label = false, linewidth = 2)
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nodes_2d = nodes_project_four([(-2, 2), (-1, 2), (-1, 1), (-2, 1)] .+
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                              [(-0.75, 0.5), (-0.75, 0.5), (-0.75, 0.5), (-0.75, 0.5)])
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scatter!(nodes_2d[:, 1], nodes_2d[:, 2], color = "red", label = false, markersize = 5)
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plot!(Shape([(-2, 0), (-2, 1), (-1, 1), (-1, 0)] .+
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            [(-0.75, 0.0), (-0.75, 0.0), (-0.75, 0.0), (-0.75, 0.0)]), linecolor = "black",
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      fillcolor = "white", label = false, linewidth = 2)
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nodes_2d = nodes_project_four([(-2, 0), (-2, 1), (-1, 1), (-1, 0)] .+
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                              [(-0.75, 0.0), (-0.75, 0.0), (-0.75, 0.0), (-0.75, 0.0)])
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scatter!(nodes_2d[:, 1], nodes_2d[:, 2], color = "red", label = false, markersize = 5)
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plot!(Shape([(-0, 0), (-1, 0), (-1, 1), (-0, 1)] .+
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            [(-0.25, 0.0), (-0.25, 0.0), (-0.25, 0.0), (-0.25, 0.0)]), linecolor = "black",
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      fillcolor = "white", label = false, linewidth = 2)
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nodes_2d = nodes_project_four([(-0, 0), (-1, 0), (-1, 1), (-0, 1)] .+
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                              [(-0.25, 0.0), (-0.25, 0.0), (-0.25, 0.0), (-0.25, 0.0)])
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scatter!(nodes_2d[:, 1], nodes_2d[:, 2], color = "red", label = false, markersize = 5)
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# lower left
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plot!(Shape([(-0, -0), (-0, -1), (-1, -1), (-1, -0)] .+
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            [(-0.25, -0.5), (-0.25, -0.5), (-0.25, -0.5), (-0.25, -0.5)]),
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      linecolor = "black", fillcolor = "white", label = false, linewidth = 2)
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nodes_2d = nodes_project_four([(-0, -0), (-0, -1), (-1, -1), (-1, -0)] .+
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                              [(-0.25, -0.5), (-0.25, -0.5), (-0.25, -0.5), (-0.25, -0.5)])
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scatter!(nodes_2d[:, 1], nodes_2d[:, 2], color = "red", label = false, markersize = 5)
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plot!(Shape([(-2, -1), (-2, 0), (-1, -0), (-1, -1)] .+
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            [(-0.75, -0.5), (-0.75, -0.5), (-0.75, -0.5), (-0.75, -0.5)]),
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      linecolor = "black", fillcolor = "white", label = false, linewidth = 2)
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nodes_2d = nodes_project_four([(-2, -1), (-2, 0), (-1, -0), (-1, -1)] .+
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                              [(-0.75, -0.5), (-0.75, -0.5), (-0.75, -0.5), (-0.75, -0.5)])
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scatter!(nodes_2d[:, 1], nodes_2d[:, 2], color = "red", label = false, markersize = 5)
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plot!(Shape([(-2, -2), (-2, -1), (-1, -1), (-1, -2)] .+
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            [(-0.75, -1), (-0.75, -1), (-0.75, -1), (-0.75, -1)]), linecolor = "black",
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      fillcolor = "white", label = false, linewidth = 2)
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nodes_2d = nodes_project_four([(-2.0, -2.0), (-2.0, -1.0), (-1.0, -1.0), (-1.0, -2.0)] .+
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                              [(-0.75, -1), (-0.75, -1), (-0.75, -1), (-0.75, -1)])
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scatter!(nodes_2d[:, 1], nodes_2d[:, 2], color = "red", label = false, markersize = 5)
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plot!(Shape([(-1, -2), (-1, -1), (-0, -1), (-0, -2)] .+
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            [(-0.25, -1), (-0.25, -1), (-0.25, -1), (-0.25, -1)]), linecolor = "black",
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      fillcolor = "white", label = false, linewidth = 2)
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nodes_2d = nodes_project_four([(-1.0, -2.0), (-1.0, -1.0), (-0.0, -1.0), (-0.0, -2.0)] .+
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                              [(-0.25, -1), (-0.25, -1), (-0.25, -1), (-0.25, -1)])
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scatter!(nodes_2d[:, 1], nodes_2d[:, 2], color = "red", label = false, markersize = 5)
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savefig("./elements")
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