function bitmap_param(filename,nxx,pxx,nyy,pyy)%, knot_vectorx, knot_vectory)

%funkcja liczaca ilosc funkcji bazowych
compute_nr_basis_functions = @(knot_vector,p) size(knot_vector, 2) - p - 1;

knot_vectorx = simple_knot(nxx,pxx);
knot_vectory = simple_knot(nyy,pyy);

%filename = './2019-06-20 17.49.00.tif';
%to juz jest RGB
X = imread(filename);

R = X(:,:,1);
G = X(:,:,2);
B = X(:,:,3);

ix = size(X,1);
iy = size(X,2);

px = compute_p(knot_vectorx);
py = compute_p(knot_vectory);

elementsx = number_of_elements(knot_vectorx,px);
elementsy = number_of_elements(knot_vectory,py);

nx = number_of_dofs(knot_vectorx,px);
ny = number_of_dofs(knot_vectory,py);

A = sparse(nx*ny,nx*ny);
FR = zeros(nx*ny,1);
FG = zeros(nx*ny,1);
FB = zeros(nx*ny,1);

%calki z B^x_i(x) B^y_j(y) B^x_k(x) B^y_l(y)
%(i,k=1,...,Nx; j,l=1,...,Ny)
%petla po elementach w osi x
for ex = 1:elementsx;
  % zakres funkcji niezerowych nad elementem
  [xl,xh] = dofs_on_element(knot_vectorx,px,ex);
  % zakres elementu (lewy i prawy brzeg po x)
  [ex_bound_l,ex_bound_h] = element_boundary(knot_vectorx,px,ex);
  %petla po elementach w osi y
  for ey = 1:elementsy
    % zakres funkcji niezerowych nad elementem
    [yl,yh] = dofs_on_element(knot_vectory,py,ey);
    % zakres elementu (lewy i prawy brzeg po x)
    [ey_bound_l,ey_bound_h] = element_boundary(knot_vectory,py,ey);
    % jakobian - rozmiar elementu
    Jx = ex_bound_h - ex_bound_l;
    Jy = ey_bound_h - ey_bound_l;
    J = Jx*Jy;
    % petla po funkcjach niezerowych nad danym elementem
    for bi = xl:xh
      for bj = yl:yh
        for bk = xl:xh
          for bl = yl:yh
          
          % punkty kwadratury w osi x nad elementem
          qpx = quad_points(ex_bound_l,ex_bound_h,2*px+2*py+1);
          % punkty kwadratury w osi y nad elementem
          qpy = quad_points(ey_bound_l,ey_bound_h,2*px+2*py+1);
          % wagi kwadratury w osi x nad elementem
          qwx = quad_weights(ex_bound_l,ex_bound_h,2*px+2*py+1);
          % wagi kwadratury w osi y nad elementem
          qwy = quad_weights(ey_bound_l,ey_bound_h,2*px+2*py+1);
          % petla po punktach kwadratury
          for iqx = 1:size(qpx,2)
            for iqy = 1:size(qpy,2)
              % definicja funkcji ksztaltu
              % B^x_k(x)
              funk= compute_spline(knot_vectorx,px,bi,qpx(iqx));
              % B^y_l(y)
              funl= compute_spline(knot_vectory,py,bj,qpy(iqy));
              % B^x_i(x)
              funi= compute_spline(knot_vectorx,px,bk,qpx(iqx));
              % B^y_j(y)
              funj= compute_spline(knot_vectory,py,bl,qpy(iqy));
              % B^x_i(x) B^y_j(y) B^x_k(x) B^y_l(y)
              fun = funi*funj*funk*funl;
              
              % Calki z B^x_i(x) B^y_j(y) B^x_k(x) B^y_l(y)
              % (i,k=1,...,Nx; j,l=1,...,Ny)
              int = fun*qwx(iqx)*qwy(iqy)*J;
              if (int!=0)
                A((bj-1)*nx+bi,(bl-1)*nx+bk) = A((bj-1)*nx+bi,(bl-1)*nx+bk) + int;
              endif
              endfor
            endfor
          endfor
        endfor
      endfor
    endfor
  endfor
endfor
            
%Calki BITMAPA(x,y) B^x_k(x) B^y_l(y)
%petla po elementach w osi x
for ex = 1:elementsx;
  % zakres funkcji niezerowych nad elementem
  [xl,xh] = dofs_on_element(knot_vectorx,px,ex);
  % zakres elementu (lewy i prawy brzeg po x)
  [ex_bound_l,ex_bound_h] = element_boundary(knot_vectorx,px,ex);
  %petla po elementach w osi y
  for ey = 1:elementsy
    % zakres funkcji niezerowych nad elementem
    [yl,yh] = dofs_on_element(knot_vectory,py,ey);
    % zakres elementu (lewy i prawy brzeg po x)
    [ey_bound_l,ey_bound_h] = element_boundary(knot_vectory,py,ey);
    %jakobian - rozmiar elementu
    Jx = ex_bound_h - ex_bound_l;
    Jy = ey_bound_h - ey_bound_l;
    J = Jx * Jy;
    %petla po funkcjach niezerowych nad danym elementem
    for bi = xl:xh
      for bj = yl:yh
        %definicja funkcji ksztaltu
        
        % punkty kwadratury w osi x nad elementem
        qpx = quad_points(ex_bound_l,ex_bound_h,px*py+1);
        % punkty kwadratury w osi y nad elementem
        qpy = quad_points(ey_bound_l,ey_bound_h,px*py+1);
        % wagi kwadratury w osi x nad elementem
        qwx = quad_weights(ex_bound_l,ex_bound_h,px*py+1);
        % wagi kwadratury w osi y nad elementem
        qwy = quad_weights(ey_bound_l,ey_bound_h,px*py+1);
        %petla po punktach kwadratury
        for iqx = 1:size(qpx,2)
          for iqy = 1:size(qpy,2)
            % B^x_k(x)
            funk= compute_spline(knot_vectorx,px,bi,qpx(iqx));
            % B^y_l(y)
            funl = compute_spline(knot_vectory,py,bj,qpy(iqy));
            % Calki BITMAPA(x,y) B^x_k(x) B^y_l(y) po kolorach RGB
            intR = funk*funl*qwx(iqx)*qwy(iqy)*J*bitmp(R,qpx(iqx),qpy(iqy));
            intG = funk*funl*qwx(iqx)*qwy(iqy)*J*bitmp(G,qpx(iqx),qpy(iqy));
            intB = funk*funl*qwx(iqx)*qwy(iqy)*J*bitmp(B,qpx(iqx),qpy(iqy));
            FR((bj-1)*nx+bi) = FR((bj-1)*nx+bi) + intR;
            FG((bj-1)*nx+bi) = FG((bj-1)*nx+bi) + intG;
            FB((bj-1)*nx+bi) = FB((bj-1)*nx+bi) + intB;
          endfor
        endfor
      endfor
    endfor
  endfor
endfor

% rozwiazanie 3 ukladow rownan
RR=A\FR;
GG=A\FG;
BB=A\FB;

%odtworzenie wyniku

%wyzerowanie macierzy odtworzonego wyniku
R1 = zeros(ix,iy);
G1 = zeros(ix,iy);
B1 = zeros(ix,iy);

% petla po funkcjach
for bi = 1:nx
  for bj = 1:ny
% petla po pixelach obrazka %na których funkcje sa niezerowe
    for i=xx(knot_vectorx(bi)):xx(knot_vectorx(bi+px+1))
% przeliczenie wspolrzednych [1-szerokosc] -> [0-1]
      ii = (i-1)/(ix-1);
      % B^x_i(x)
      funi= compute_spline(knot_vectorx,px,bi,ii);
      for j=yy(knot_vectory(bj)):yy(knot_vectory(bj+py+1))  
% przeliczenie wspolrzednych [1-wysokosc] -> [0-1]
        jj = (j-1)/(iy-1);
        % B^y_j(y)
        funj= compute_spline(knot_vectory,py,bj,jj);
        ff = funi*funj;
        R1(i,j) = R1(i,j) + floor(ff*RR((bj-1)*nx+bi));
        G1(i,j) = G1(i,j) + floor(ff*GG((bj-1)*nx+bi));
        B1(i,j) = B1(i,j) + floor(ff*BB((bj-1)*nx+bi));
      endfor
    endfor
  endfor
endfor

RGB=X;
RGB(:,:,1) = R1;
RGB(:,:,2) = G1;
RGB(:,:,3) = B1;

imshow(RGB);





function resx=xx(x)
  resx = floor((ix-1)*x+1);
endfunction



function resy=yy(y)
  resy = floor((iy-1)*y+1);
endfunction


function val=bitmp(M,x,y)
  val = zeros(size(x));
  for i=1:size(x,1)
    for j=1:size(x,1)
      val(i,j)=M(xx(x(1,i)),yy(y(1,j)));
    endfor
  endfor
endfunction


%funkcja wyliczajaca stopien wielomianow
function p=compute_p(knot_vector)

%pierwszy wpis w knot_vector
  initial = knot_vector(1);
%dlugosc knot_vector
  kvsize = size(knot_vector,2);
  p = 0;

%sprawdzenie ilosci powtorzen pierwszego wpisu w knot_vector  
  while (p+2 <= kvsize) && (initial == knot_vector(p+2))
    p = p+1;
  endwhile
  
  return
endfunction
  
  
  
  
  
%funkcja sprawdzajaca poprawnosc knot_vector
function t=check_sanity(knot_vector,p)

  initial = knot_vector(1);
  kvsize = size(knot_vector,2);

  t = true;
  counter = 1;

%jesli ilosc powtorzen na poczatku nie jest zgodna ze stopniem wielomianow
  for i=1:p+1
    if (initial != knot_vector(i))
%zwroc falsz
      t = false;
      return
    endif
  endfor

%jesli w srodku knot_vector jest za duzo powtorzen
  for i=p+2:kvsize-p-1
    if (initial == knot_vector(i))
      counter = counter + 1;
      if (counter > p)
%zwroc falsz
        t = false;
        return
      endif
    else
      initial = knot_vector(i);
      counter = 1;
    endif
  endfor

  initial = knot_vector(kvsize);
  
%jesli ilosc powtorzen na poczatku nie jest zgodna ze stopniem wielomianow
  for i=kvsize-p:kvsize
    if (initial != knot_vector(i))
%zwroc falsz
      t = false;
      return
    endif
  endfor
  
%jesli kolejny element knot_vector jest mniejszy niz poprzedni
  for i=1:kvsize-1
    if (knot_vector(i)>knot_vector(i+1))
%zwroc falsz
      t = false;
      return
    endif
  endfor

  return

endfunction



%funkcja wyliczajaca rekurencyjnie funkcje bazowa zgodnie z wzorem Cox-de-Boor
function y=compute_spline(knot_vector,p,nr,x)
  
%funkcja (x-x_i)/(x_{i-p}-x_i)
  fC= @(x,a,b) (x-a)/(b-a);
%funkcja (x_{i+p+1}-x)/(x_{i+p+1}-x_{i+1})
  fD= @(x,c,d) (d-x)/(d-c);
  
%x_i  
  a = knot_vector(nr);
%x_{i-p} 
  b = knot_vector(nr+p);
%x_{i+1}
  c = knot_vector(nr+1);
%x_{i+p+1}
  d = knot_vector(nr+p+1);

%funkcja liniowa dla p=0
  if (p==0)
    y = 0 .* (x < a) + 1 .* (a <= x & x <= d) .+ 0 .* (x > d);
    return
  endif

%B_{i,p-1}  
  lp = compute_spline(knot_vector,p-1,nr,x);
%B_{i+1,p-1}
  rp = compute_spline(knot_vector,p-1,nr+1,x);
  
%(x-x_i)/(x_{i-p)-x_i)*B_{i,p-1}  
  if (a==b)
%jesli wezly w knot_vector sie powtarzaja trzeba to uwzglednic
    y1 = 0 .* (x < a) + 1 .* (a <= x & x <= b) + 0 .* (x > b);
  else
    y1 = 0 .* (x < a) + fC(x,a,b) .* (a <= x & x <= b) + 0 .* (x > b);
  endif
  
%(x_{i+p+1}-x)/(x_{i+p+1)-x_{i+1})*B_{i+1,p-1}
  if (c==d)
%jesli wezly w knot_vector sie powtarzaja trzeba to uwzglednic
    y2 = 0 .* (x < c) + 1 .* (c < x & x <= d) + 0 .* (d < x);
  else
    y2 = 0 .* (x < c) + fD(x,c,d) .* (c < x & x <= d) + 0 .* (d < x);
  endif
  
  y = lp .* y1 .+ rp .* y2;
  return
  
endfunction

  
  
% Ilosc elementow w knot vector
function n = number_of_elements(knot_vector,p)
  
  initial = knot_vector(1);
  kvsize = size(knot_vector,2);
  n = 0;
  
  for i=1:kvsize-1
    if (knot_vector(i) != initial)
      initial = knot_vector(i);
      n = n+1;
    endif
  endfor
  
endfunction
  
% Tworzy prosty knot vector bez powotrzen w srodku
function knot = simple_knot(elems, p)
  pad = ones(1, p);
  knot = [0 * pad, 0:elems, elems * pad];
  knot = knot/elems;
endfunction

% Ilosc funkcji bazowych w knot wektorze
function n = number_of_dofs(knot,p)
  n = length(knot) - p - 1;
endfunction


function first = first_dof_on_element(knot_vector,p,elem_number)
 [l,h] = element_boundary(knot_vector,p,elem_number);
 first = lookup(knot_vector, l) - p;
endfunction
  
function [low,high] = element_boundary(knot_vector,p,elem_number)
  initial = knot_vector(1);
  kvsize = size(knot_vector,2);
  k = 0;
  low=0;
  high=0;
  
  for i=1:kvsize
    if (knot_vector(i) != initial)
      initial = knot_vector(i);
      k = k+1;
    endif
    if (k == elem_number)
      low = knot_vector(i-1);
      high = knot_vector(i);
      return;
    endif
  endfor
endfunction

% Zwraca zakres (indeksy) funckji bedacych niezerowymi na zadanym wektorze wezlow
function [low,high] = dofs_on_element(knot_vector,p,elem_number)
  low = first_dof_on_element(knot_vector,p,elem_number);
  %poniewaz mamy dokladnie p+1 niezerowych funkcji nad elementem
  high = low + p;
endfunction

% Row vector of points of the k-point Gaussian quadrature on [a, b]
function xs = quad_points(a, b, k)
  % mapowanie punktow
  map = @(x) 0.5 * (a * (1 - x) + b * (x + 1));
  switch (k)
    case 1
      xs = [0];
    case 2
      xs = [-1/sqrt(3), ...
             1/sqrt(3)];
    case 3
      xs = [-sqrt(3/5), ...
             0,         ...
             sqrt(3/5)];
    case 4
      xs = [-sqrt((3+2*sqrt(6/5))/7), ...
             sqrt((3-2*sqrt(6/5))/7), ...
             sqrt((3-2*sqrt(6/5))/7), ...
             sqrt((3+2*sqrt(6/5))/7)];
    case 5
      xs = [-1/3*sqrt(5+2*sqrt(10/7)), ...
            -1/3*sqrt(5-2*sqrt(10/7)), ...
             0,                        ...
             1/3*sqrt(5-2*sqrt(10/7)), ...
             1/3*sqrt(5+2*sqrt(10/7))];
    otherwise
      xs = [-1/3*sqrt(5+2*sqrt(10/7)), ...
            -1/3*sqrt(5-2*sqrt(10/7)), ...
             0,                        ...
             1/3*sqrt(5-2*sqrt(10/7)), ...
             1/3*sqrt(5+2*sqrt(10/7))];
  endswitch
  xs = map(xs);
endfunction

% Row vector of weights of the k-point Gaussian quadrature on [a, b]
function ws = quad_weights(a, b, k)
  switch (k)
    case 1
      ws = [2];
    case 2
      ws = [1, 1];
    case 3
      ws = [5/9, ...
            8/9, ...
            5/9];
    case 4
      ws = [(18-sqrt(30))/36, ...
            (18+sqrt(30))/36, ...
            (18+sqrt(30))/36, ...
            (18-sqrt(30))/36];
    case 5
      ws = [(322-13.0*sqrt(70))/900, ...
            (322+13.0*sqrt(70))/900, ...
            128/225,                 ...
            (322+13.0*sqrt(70))/900, ...
            (322-13.0*sqrt(70))/900];
    otherwise
      ws = [(322-13.0*sqrt(70))/900, ...
            (322+13.0*sqrt(70))/900, ...
            128/225,                 ...
            (322+13.0*sqrt(70))/900, ...
            (322-13.0*sqrt(70))/900];
  endswitch
  % Gaussian quadrature is defined on [-1, 1], we use [a, b]
  %ws = ws * (b-a)/2;
endfunction



endfunction