options(repr.plot.width=3.5, repr.plot.height=3.5)
options(warn=-1) # turns off warnings, to turn on: "options(warn=0)"

library(Matrix)
library(rgl)
library(geometry)
library(plotly)
library(akima)
library(plot3D)
library(network)

# Importing the libraries
for (f in list.files(path="nt_toolbox/toolbox_general/", pattern="*.R")) {
    source(paste("nt_toolbox/toolbox_general/", f, sep=""))
}
for (f in list.files(path="nt_toolbox/toolbox_signal/", pattern="*.R")) {
    source(paste("nt_toolbox/toolbox_signal/", f, sep=""))
}

X = read_mesh("nt_toolbox/data/nefertiti.off")$X0
F = read_mesh("nt_toolbox/data/nefertiti.off")$F0
n = dim(X)[2]

B = compute_boundary(F)

p = length(B)

options(repr.plot.width=3.5, repr.plot.height=5)
# plot mesh
plot_mesh(X,F)

#plot boundary
lines(X[1,B+1], X[2,B+1], col="red", lwd=3)

W = Matrix(0, nrow=n, ncol=n, sparse=TRUE)

for (i in (0:2))
{
  i2 = (i+1)%%3
  i3 = (i+2)%%3
  u = X[,(F+1)[i2+1,]] - X[,(F+1)[i+1,]]
  v = X[,(F+1)[i3+1,]] - X[,(F+1)[i+1,]]
  u = u/rbind(sqrt(colSums(u**2)), sqrt(colSums(u**2)),sqrt(colSums(u**2)));
  v = v/rbind(sqrt(colSums(v**2)), sqrt(colSums(v**2)),sqrt(colSums(v**2)));
  alpha = 1/(tan(acos(colSums(u*v))))
  alpha = pmax(alpha, 10^(-2)*matrix(1,nrow=1, ncol=length(alpha)))
  W = W+sparseMatrix(x=alpha, i=(F+1)[i2+1,], j=(F+1)[i3+1,], dims=c(n,n))
  W = W+sparseMatrix(x=alpha, i=(F+1)[i3+1,], j=(F+1)[i2+1,], dims=c(n,n))
}

d = as.vector(colSums(W))
D = Diagonal(length(d),d)
L = D - W 

p = length(B)
t = seq(from=0,to=2*pi,by=(2*pi/p))
t = t[-(p+1)]
Z = rbind(cos(t),sin(t))

L1 = Matrix(L, sparse=TRUE)

L1[B+1,] = 0

for (i in (1:length(B)))
{
   L1[(B + 1)[i], (B + 1)[i]] = 1
}

R = Matrix(0, nrow=2, ncol=n)
R[,B+1] = Z

Y = Matrix(0, nrow=2, ncol=n)

Y[1,] = solve(L1,R[1,])
Y[2,] = solve(L1,R[2,])

options(repr.plot.width=4, repr.plot.height=5, colorscale=gray)

plot_mesh(as.matrix(rbind(Y,matrix(0,nrow=1,ncol=n))),F)


source("nt_solutions/meshdeform_1_parameterization/exo1.R")

## Insert your code here.

source("nt_solutions/meshdeform_1_parameterization/exo2.R")

## Insert your code here.

source("nt_solutions/meshdeform_1_parameterization/exo3.R")

## Insert your code here.

library(Matrix)
C  =  replicate(3, runif(1000, 0, 1)) 
C  =  C/cbind(Matrix(rowSums(C)),Matrix(rowSums(C)),Matrix(rowSums(C))) 
C  =  C[order(C[,1], C[,2], C[,3]),]
lambd = t(C)

library(imager)
library(magick)

n1  =  256
T  =  load_image("nt_toolbox/data/lena.png", n1)

options(repr.plot.width=6, repr.plot.height=5)

x  =  seq(from = 0, to = 1, by = 1/(dim(T)[1]-1))

for (i in (1:100)){
    
    px  =  Y[1,(F+1)[,i]]
    py  =  Y[2, (F+1)[,i]]
        
    points_x  =  t(lambd) %*% px
    points_y  =  t(lambd) %*% py
    points  =  cbind(points_x,points_y)
    
    col  =  rescale(bicubic(x, x, T, points_x, points_y )$z)
    col1  =  cbind(col, col, col)
                   
    Px = X[1,(F+1)[,i]]
    Py = X[2,(F+1)[,i]]
    Pz = X[3,(F+1)[,i]]
    
    Points_x  =  t(lambd) %*% Px
    Points_y  =  t(lambd) %*% Py
    Points_z  =  t(lambd) %*% Pz
    
    points3D(matrix(Points_x), matrix(Points_y), matrix(Points_z), col=as.color(col), pch=20, box=FALSE,colkey=FALSE,cex=0.05, theta=10)
    par(new=TRUE)
}


u1  =  c(267,266)*n1/512
u2  =  c(267,328)*n1/512
u3  =  c(355,301)*n1/512

imageplot(T)
lines(c(u1[2],u2[2],u3[2], u1[2]),c(u1[1],u2[1],u3[1],u1[1]), col="blue")

v1  =  c(310,125)*n1/512.
v2  =  c(315,350)*n1/512.
v3  =  c(105,232)*n1/512.

options(repr.plot.width=5, repr.plot.height=5)

Y_big  =  Y*(n1-1) + 1
beg  =  sort(W@i)
end  =  W@i

plot (NA, xlim=c(0,250), ylim=c(0,250), box=FALSE, clab="", ylab="", axes=FALSE)
for (i in (1:length(beg))){
    lines(c(Y_big[1, (beg+1)[i]],Y_big[1,(end+1)[i]]), c(Y_big[2,(beg+1)[i]], Y_big[2,(end+1)[i]]), col="Blue", xlab="", ylab="", axes=FALSE)
}

lines (c(v1[2],v2[2],v3[2], v1[2]),c(v1[1],v2[1],v3[1],v1[1]), col="red")

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

imageplot(T1)
for (i in (1:length(beg))){
    lines(c(Y_big[1, (beg+1)[i]],Y_big[1,(end+1)[i]]), c(Y_big[2,(beg+1)[i]], Y_big[2,(end+1)[i]]), col="Blue", xlab="", ylab="", axes=FALSE)
}

lines (c(v1[2],v2[2],v3[2], v1[2]),c(v1[1],v2[1],v3[1],v1[1]), col="red")

options(repr.plot.width=6, repr.plot.height=5)

x  =  seq(from = 0, to = 1, by = 1/(dim(T)[1]-1))

for (i in (1:100)){
    
    px  =  Y[1,(F+1)[,i]]
    py  =  Y[2, (F+1)[,i]]
        
    points_x  =  t(lambd) %*% px
    points_y  =  t(lambd) %*% py
    points  =  cbind(points_x,points_y)
    
    col  =  rescale(bicubic(x, x, T1, points_x, points_y )$z)
    col1  =  cbind(col, col, col)
                   
    Px = X[1,(F+1)[,i]]
    Py = X[2,(F+1)[,i]]
    Pz = X[3,(F+1)[,i]]
    
    Points_x  =  t(lambd) %*% Px
    Points_y  =  t(lambd) %*% Py
    Points_z  =  t(lambd) %*% Pz
    
    points3D(matrix(Points_x), matrix(Points_y), matrix(Points_z), col=as.color(col), pch=20, box=FALSE,colkey=FALSE,cex=0.05, theta=10)
    par(new=TRUE)
}