using PyPlot
using NtToolBox 
using Interpolations

X, F = read_mesh("NtToolbox/src/data/nefertiti.off")
n = size(X,2);

B = compute_boundary(F);

p = length(B);

figure(figsize=(10,10))
#plot mesh
plot_mesh(X, F, el=80,az=-100, lwdt=.6, dist=6)

#plot boundary
for i in 1:length(B)
    plot(X[1,B], X[2,B], X[3,B], color="red", lw=3)
end

W = spzeros(n,n)

for i in 1:3
    i2 = i%3+1
    i3 = (i+1)%3+1
    u = X[:,F[i2,:]] - X[:,F[i,:]]
    v = X[:,F[i3,:]] - X[:,F[i,:]]
    # normalize the vectors   
    u = u ./ repeat(sqrt(sum(u.^2,1)), outer=(3,1))
    v = v ./ repeat(sqrt(sum(v.^2,1)), outer=(3,1))
    # compute angles
    alpha = 1./tan(acos(sum(u.*v, 1)))
    alpha = vec(max(alpha, 1e-2)') #avoid degeneracy
    W = W + sparse(F[i2,:],F[i3,:], alpha, n,n)
    W = W + sparse(F[i3,:],F[i2,:], alpha, n,n)
end;

d = sum(W,1)
D = spdiagm(vec(d), 0,n,n)
L = D - W;

p = length(B)
t = collect(linspace(0,2*pi,p+1))
deleteat!(t,p+1)
Z = [cos(t)'; sin(t)'];

L1 = copy(L)
L1[B,:] = 0
for i in 1:length(B)
    L1[B[i], B[i]] = 1
    end;

R = zeros(2,n)
R[:,B] = Z;

Y = zeros(2,n)
Y = (L1 \ R')';

figure(figsize=(10,10))
plot_mesh([Y;zeros(1,n)],F, lwdt = 1., c="lightgrey");

include("NtSolutions/meshdeform_1_parameterization/exo1.jl");

## Insert your code here.

include("NtSolutions/meshdeform_1_parameterization/exo2.jl");

include("NtSolutions/meshdeform_1_parameterization/exo3.jl");

## Insert your code here.

n1 = 256
T = load_image("NtToolBox/src/data/lena.png", n1)
T = T[n1:-1:1,:];

C = rand(1000,3)
C = C./repeat(sum(C,2),outer=(1,3))
C=C[:,[3,2,1]]
C= sortcols(C)
lambd=C';

fig = figure(figsize = (10,10))
ax = subplot(111, projection="3d")

x = collect(linspace(0, 1, size(T,1)))
#itp = interpolate(T', BSpline(Cubic(Line())), OnGrid())
itp = interpolate((x,x), T', Gridded(Linear()))

for i in 1:size(F,2)
    px = Y[1,F[:,i]]
    py = Y[2,F[:,i]]
    
    points_x = lambd'*px
    points_y = lambd'*py
    points = [points_x ; points_y]

    col = zeros(size(points_x))
    for ind in 1:size(points_x,1)
        col[ind] = itp[points_x[ind], points_y[ind]]
    end
    col = rescale(col)
    col = repeat(col,outer=(1,3))
    
    Px = X[1,F[:,i]]
    Py = X[2,F[:,i]]
    Pz = X[3,F[:,i]]
    
    Points_x = lambd'*Px
    Points_y = lambd'*Py
    Points_z = lambd'*Pz

    scatter3D(Points_x,Points_y,Points_z,s=5,c=col,lw=0,alpha=1)
    ax[:view_init](80, -100)
    axis("off")
    ax[:dist]=6

end

u1 = [247,266]*n1/512.
u2 = [247,328]*n1/512.
u3 = [161,301]*n1/512.;

figure(figsize=(10,10))
imageplot(T)
plot([u1[2],u2[2],u3[2],u1[2]], [u1[1],u2[1],u3[1],u1[1]], ".-b", ms=10, linewidth=2)
gca()[:invert_yaxis]()

v1 = [310,125]*n1/512.
v2 = [315,350]*n1/512.
v3 = [105,232]*n1/512.;

figure(figsize=(10,10))
axis("off")

Y_big = Y*(n1-1) + 1
beg = findn(W)[1]
last = findn(W)[2]

for i in 1:length(beg)
    plot([Y_big[1, beg[i]], Y_big[1,last[i]]],[Y_big[2,beg[i]], Y_big[2,last[i]]],c="blue",lw=2)
end

plot([v1[2],v2[2],v3[2],v1[2]], [v1[1],v2[1],v3[1],v1[1]], ".-r", ms=10, linewidth=3);

T1 = perform_image_similitude(T,"affine",(u1-1)/n1,(v1-1)/n1,(u2-1)/n1,(v2-1)/n1,(u3-1)/n1,(v3-1)/n1);

figure(figsize=(10,10))
axis("off")

Y_big = Y*(n1-1) + 1
beg = findn(W)[1]
last = findn(W)[2]

for i in 1:length(beg)
    plot([Y_big[1, beg[i]], Y_big[1,last[i]]],[Y_big[2,beg[i]], Y_big[2,last[i]]],c="blue",lw=2)
end

plot([v1[2],v2[2],v3[2],v1[2]], [v1[1],v2[1],v3[1],v1[1]], ".-r", ms=10, linewidth=3)
imageplot(T1)
gca()[:invert_yaxis]()

fig = figure(figsize = (10,10))
ax = subplot(111, projection="3d")

x = collect(linspace(0, 1, size(T,1)))
itp = interpolate((x,x), T1', Gridded(Linear()))

for i in 1:size(F,2)
    px = Y[1,F[:,i]]
    py = Y[2,F[:,i]]
    
    points_x = lambd'*px
    points_y = lambd'*py
    points = [points_x ; points_y]

    col = zeros(size(points_x))
    for ind in 1:size(points_x,1)
        col[ind] = itp[points_x[ind], points_y[ind]]
    end
    col = rescale(col)
    col = repeat(col,outer=(1,3))
    
    Px = X[1,F[:,i]]
    Py = X[2,F[:,i]]
    Pz = X[3,F[:,i]]
    
    Points_x = lambd'*Px
    Points_y = lambd'*Py
    Points_z = lambd'*Pz

    scatter3D(Points_x,Points_y,Points_z,s=6,c=col,lw=0,alpha=1)
    ax[:view_init](80, -100)
    axis("off")
    ax[:dist]=6

end
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