from __future__ import division
import nt_toolbox as nt
from nt_solutions import meshdeform_1_parameterization as solutions
%matplotlib inline
%load_ext autoreload
%autoreload 2

name = 'nefertiti'
[X, F] = read_mesh(name)
n = size(X, 2)
clear options; options.name = name

options.verb = 0
B = compute_boundary(F, options)

p = length(B)

clf; hold on
plot_mesh(X, F, options)
shading('faceted')
hh = plot3(X(1, B), X(2, B), X(3, B), 'r')
set_linewidth(hh, 4)

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

d = full(sum(W, 1))
D = spdiags(d(: ), 0, n, n)
L = D - W

p = length(B)
t = linspace(0, 2*pi(), p + 1); t(p + 1) = []
Z = [cos(t); sin(t)]

L1 = L
L1(B, : ) = 0
for i in 1: length(B):
    L1(B(i), B(i)) = 1

R = zeros(2, n)
R(: , B) = Z

if using_matlab()
    Y = (L1 \ R')'
else
    options.maxit = 300
    Y(1, : ) = perform_cg(L1, R(1, : )', options)'
    Y(2, : ) = perform_cg(L1, R(2, : )', options)'

options.lighting = 0
plot_mesh([Y; zeros(1, n)], F)
shading('faceted')

solutions.exo1()

## Insert your code here.

solutions.exo2()

## Insert your code here.

solutions.exo3()

## Insert your code here.

n1 = 256
T = load_image('lena', n1)
T = T(n1: -1: 1, : )

options.texture = T
options.texture_coords = Y

plot_mesh(X, F, options)
zoom(1.5)

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

clf; hold('on')
if using_matlab()
    imageplot(T)
else
    imageplot(T(n1: -1: 1, : ))

h = plot([u1(2) u2(2) u3(2) u1(2)], [u1(1) u2(1) u3(1) u1(1)], '.-b')
if using_matlab()
    set(h, 'LineWidth', 2)
    set(h, 'MarkerSize', 20)

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

clf; hold('on')
plot_graph(W, Y'*(n1-1) + 1, 'b')
h = plot([v1(2) v2(2) v3(2) v1(2)], [v1(1) v2(1) v3(1) v1(1)], '.-r')
axis('off'); axis('equal')
if using_matlab()
    set(h, 'LineWidth', 2)
    set(h, 'MarkerSize', 20)

T1 = perform_image_similitude(T', 'affine', (u1-1)/ n1, (v1-1)/ n1, (u2-1)/ n1, (v2-1)/ n1, (u3-1)/ n1, (v3-1)/ n1)'

clf; hold on
if using_matlab()
    imageplot(T1)
else
    imageplot(T1(n1: -1: 1, : ))

plot_graph(W, Y'*(n1-1) + 1, 'b')
h = plot([v1(2) v2(2) v3(2) v1(2)], [v1(1) v2(1) v3(1) v1(1)], '.-r')
axis('off'); axis('equal')
if using_matlab()
    set(h, 'LineWidth', 2)
    set(h, 'MarkerSize', 20)

options.texture = T1

plot_mesh(X, F, options)
zoom(1.5)

q = 64
M = zeros(q, q, 3)
for i in 1: 3:
    M(: , : , i) = compute_triang_interp(F, Y, X(i, : ), q)

imageplot(M)

C = ones(q, q)*0.8; % color

colormap(gray(256))
surf(M(: , : , 1), M(: , : , 2), M(: , : , 3), C)
view(-40, 70)
zoom(1.5)
axis tight; axis square; axis off
camlight local;  shading faceted

[V, U] = meshgrid(1: 32, 1: 32)
T = mod(V + U, 2)

colormap(gray(256))
plot_surf_texture(M, T)
view(-40, 70); zoom(1.5)
axis tight; axis square; axis off
camlight

A = make_sparse(2*n, 2*n)
A(1: n, 1: n) = L
A(n + 1: 2*n, n + 1: 2*n) = L

for s  in  1: p:
    s1 = mod(s-2, p) + 1
    s2 = mod(s, p) + 1
    i = B(s)
    i1 = B(s1)
    i2 = B(s2)
    A(i, [i1 i2] + n) = [1, -1]
    A(i + n, [i1 i2]) = [-1, + 1]

i1 = B(1)
i2 = B(round(p/ 2))

A(i1, : ) = 0;  A(i1 + n, : ) = 0
A(i1, i1) = 1; A(i1 + n, i1 + n) = 1
A(i2, : ) = 0;  A(i2 + n, : ) = 0
A(i2, i2) = 1; A(i2 + n, i2 + n) = 1

y = zeros(2*n, 1)
y([i1 i2]) = [0 1]
y([i1 i2] + n) = [0 0]

if using_matlab()
    Y = reshape(A\y, [n 2])'
else
    options.maxit = 300
    Y = reshape(perform_cg(A, y, options), [n 2])'

Y = Y - repmat(min(Y, [], 2), [1 n])
Y = Y/ max(Y(: ))

plot_mesh([Y; zeros(1, n)], F)
shading faceted; axis tight

solutions.exo4()

## Insert your code here.

name = 'david-head'
[X, F] = read_mesh(name)
n = size(X, 2)
clear options; options.name = name

options.lighting = 1
plot_mesh(X, F, options)
shading faceted

solutions.exo5()

## Insert your code here.

hold on
plot_mesh(X, F, options)
hh = plot3(X(1, B), X(2, B), X(3, B), 'r')
set_linewidth(hh, 3)
view(-150, -30)

solutions.exo6()

## Insert your code here.

solutions.exo7()

## Insert your code here.