How to plot a 2D rotated array

Specific Domains Visualization
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10

One suggestion using Plots.jl, is to display the data via colored rotated rectangles. The result looks like a rotated heatmap for practical purposes:

Plots_gr_rotated_heatmap
Plots_gr_rotated_heatmap1920×1280 73 KB

Plots.jl gr() code (no bells & whistles) 
using ColorSchemes, Plots; gr(dpi=600)
import ColorSchemes.viridis

rotx(x,y,α) = x*cosd(α) - y*sind(α)
roty(x,y,α) = x*sind(α) + y*cosd(α)

function rectangle(x, y, w, h, α)
    X, Y = [0,w,w,0], [0,0,h,h]
    Shape(x .+ rotx.(X,Y,α), y .+ roty.(X,Y,α))
end

# 1 - INPUT DATA
α        = 45.0
x1, x2   = -150, 150
y1, y2   = -80, 80
w, h     = 4.0, 2.0
xc, yc   = -w/2 .+ range(x1, x2, step=w), -h/2 .+ range(y1, y2, step=h)
cp       = Iterators.product(xc,yc)
Xc, Yc   = first.(cp), last.(cp)
Xr, Yr   = rotx.(Xc,Yc,α), roty.(Xc,Yc,α)
Z        = sin.(hypot.(Xr,Yr)/10)                    # some function of (x,y)


# 2-  PLOT ROTATED HEATMAP
zc       = (Z .- minimum(Z))/(maximum(Z) - minimum(Z))    # normalize extrema to (0,1)
Cz       = get.(Ref(viridis), zc)                         # compute RGB colors
clims    = extrema(Z)
heatmap(xc, yc, NaN*Z, ratio=1, clims=clims, frame=:none, legend=:outerright)
for (x, y, c) in zip(Xr,Yr,Cz)
    plot!(rectangle(x, y, w, h, α), c=c, lw=0.1, lc=c);
end

xaxis    = [-w/2 + x1, w/2 + x2]
yaxis    = [-h/2 + y1, h/2 + y2]
xt, yt   = LinRange(x1, x2, 9), LinRange(y1, y2, 9)
Xxt, Yxt = rotx.(xt, yaxis[1] .+ zero(xt), α), roty.(xt, yaxis[1] .+ zero(xt), α)
Xyt, Yyt = rotx.(xaxis[1] .+ zero(yt), yt, α), roty.(xaxis[1] .+ zero(yt), yt, α)
Xx, Xy   = rotx.(xaxis, yaxis[1] .+ [0,0], α), roty.(xaxis, yaxis[1] .+ [0,0], α)
Yx, Yy   = rotx.(xaxis[1] .+ [0,0], yaxis, α), roty.(xaxis[1] .+ [0,0], yaxis, α)
c        = (y2-y1)/(x2-x1)
dX, dY   = c*[diff(Xx)[], diff(Xy)[]]/10,  [diff(Yx)[], diff(Yy)[]]/10
for (x,y) in zip(Xxt,Yxt)
    plot!([x, x - dY[1]/3], [y, y - dY[2]/3], lc=:black)
end
for (x,y) in zip(Xyt,Yyt)
    plot!([x, x - dX[1]/3], [y, y - dX[2]/3], lc=:black)
end
plot!(Xx, Xy, lc=:black, lw=1)
plot!(Yx, Yy, lc=:black, lw=1)
annotate!(Xxt .- dY[1], Yxt .- dY[2], text.(string.(round.(xt, digits=1)), 5, rotation=α, "Computer Modern"))
annotate!(Xyt .- dX[1], Yyt .- dX[2], text.(string.(round.(yt, digits=1)), :right, 5, rotation=α, "Computer Modern"))
Plots.current()
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