using PyPlot
using NtToolBox
using Interpolations

n = 128
V = perform_blurring(randn(n,n,2),[40], "per");

myplot = V-> plot_vf(V[1:6:n,1:6:n, :])

figure(figsize = (7,7))
myplot(V)

Normalize = V -> V ./ repeat( max(1e-9,sqrt.(sum(V.^2, 3))) , outer=(1,1,2));

figure(figsize = (7,7))
myplot(Normalize(V))

Y, X = meshgrid(0:n-1,0:n-1)
mu = sin.(X*pi/n).^2
mu = -4*(mu + mu')
mu[1,1] = 1;

A = V -> real.(ifft(fft(Div(V[:,:,1], V[:,:,2], "per"))./mu))

ProjI = V -> V - Grad(A(V), "per")

U = ProjI(V)

figure(figsize=(7,7))
myplot(U)

figure(figsize=(7,7))
myplot(V-U)

f = load_image("NtToolBox/src/data/lena.png", 2*n)
f = f[n-Base.div(n,2):n+Base.div(n,2)-1, n-Base.div(n,2):n+Base.div(n,2)-1];

U = Normalize(ProjI(V));

periodic = P -> cat(3, mod(P[:,:,1]-1,n)+1, mod(P[:,:,2]-1,n)+1 );

extend1 = f -> [f f[:,1]]
extend = f -> extend1(extend1(f)')';

f1 = extend(f)
itp = interpolate((1:size(f1,1), 1:size(f1,2)), f1, Gridded(Linear()))
size(itp)

function myinterp(P1,f1,Pi)
    itp = interpolate((1:size(f1,1), 1:size(f1,2)), f1, Gridded(Linear()))
    itpd = zeros(size(Pi)[1:2])
    for i in 1:size(Pi,1)
        for j in 1:size(Pi,2)
        itpd[i,j] = itp[Pi[i,j,1], Pi[i,j,2]]
        end
    end
    return itpd
end;

(Y,X) = meshgrid(1:n,1:n)
P = cat(3, X,Y)
(Y1,X1) = meshgrid(1:n+1,1:n+1)
P1 = cat(3, X1,Y1);

W =  (f, U) -> myinterp(P1, extend(f), periodic(P - U));

rho = 2
figure(figsize = (5,5))
imageplot(W(f, rho*U))

include("NtSolutions/graphics_5_fluids/exo1.jl")

## Insert your code here.

include("NtSolutions/graphics_5_fluids/exo2.jl")

## Insert your code here.

nu = 1/10

mu = 2*nu

Wt = (V,U) -> cat(3, W(V[:,:,1],U), W(V[:,:,2],U) );

tau = .5;

V = Normalize(ProjI(V));

g = copy(f);

g = W(g, tau*U)
V = Wt(V, tau*U);

s1 = [2:n; 1]; s2 = [n; 1:n-1];

function Delta(g)
    delta = 1/4.*(g[s1,:,:] + g[s2,:,:] + g[:,s1,:] + g[:,s2,:]) - g
    if size(delta,3)==1
        delta = delta[:,:,1] 
    end
    return delta
end;

V = V + tau*nu*Delta(V)
g = g + tau*mu*Delta(g);

V = ProjI(V);

include("NtSolutions/graphics_5_fluids/exo3.jl")

## Insert your code here.
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