function classifyShapes = ClassifyShapes (thisImage)

% read the file in
RGB = imread(thisImage);

% convert to gray scale
GRAY = rgb2gray(RGB);

% turn the image into a binary image and invert the color scheme
threshold = graythresh(GRAY);
BW = im2bw(GRAY, threshold);
BW = ~ BW;
L = bwlabel(BW);

% Trace the region boundaries in the binary image 
% Using noholes option for performance
[boundaries,labelMatrix] = bwboundaries(BW, 'noholes');

% Find the bounding box of the object
STATS = regionprops(labelMatrix, 'all'); 

Centroid  = regionprops(L, 'centroid');
Area  = regionprops(L, 'area');
centroidSize = size(Centroid);

figure, imshow(RGB), title('Results');
hold on

for x=1:centroidSize(1)
    b= boundaries{x};
    centroidSize = size(b);
    for i=1:centroidSize(1);
        distance{x}(1,i) = sqrt ( ( b(i,2) - Centroid(x).Centroid(1) )^2 + ( b(i,1) - Centroid(x).Centroid(2) )^2 );
    end 

    a=max(distance{x});
    b=min(distance{x});
    c=Area(x).Area;

    distDiff=a-b;
    square= c/(4*b^2);
    triangle=(c*3^0.5)/((a+b)^2);

    if distDiff < 10
            findSphere(STATS);
    elseif (square < 1.05 ) && (square > 0.95 )
            findCube(STATS);
    elseif  (triangle < 1.05 ) && (triangle > 0.95 )
            findTriangle(STATS);
    end
end


end



function findCube = FindCube(STATS);


stats = STATS;

%rect = [left, bottom, width, height]
area = stats.Area;
%since this is a cube, we only need one side
side = sqrt(area);

format compact 
set(gcf,'Menubar','none','Name','Cube', ... 
    'NumberTitle','off','Position',[500,300,side*2.5,side*2.5], ... 
    'Color',[0.1 0.3 0.2]); 


% set up the cube axes 
h1 = axes('Position',[.2 .2 .9 .9]); 

vert = [1 1 1;
    1 side 1;
    side side 1;
    side 1 1 ;
    ... 
        1 1 side;
        1 side side;
        side side side;
        side 1 side];
    
fac = [1 2 3 4; ... 
    2 6 7 3; ... 
    4 3 7 8; ... 
    1 5 8 4; ... 
    1 2 6 5; ... 
    5 6 7 8]; 

tempFac = [1 2 3; 
1 3 4;  
2 3 7;  
2 7 6;  
5 6 7;  
5 7 8;  
7 8 4;  
4 3 7;  
5 4 8;  
5 1 4;  
6 5 1;  
2 6 1]; 

patch('Faces',fac,'Vertices',vert,'FaceColor','r');  % patch function 

saveobjmesh('cube.obj',vert, tempFac, 'cube');


% color and lighting stuff
light('Position',[1 3 2]); 
light('Position',[-3 -1 3]); 
material shiny; 
alpha('color'); 
alphamap('rampdown'); 
camlight(45,45); 
lighting phong 
view(30,30); 




end



function findSphere = FindSphere(STATS);

stats = STATS;
% area = pi * r^2 so sqrt{ area / pi } = R 
radius = sqrt (stats.Area/pi);
diameter = radius *2;

format compact 
set(gcf,'Menubar','none','Name','Sphere', ... 
    'NumberTitle','off','Position',[500,300,diameter * 5,diameter*5], ... 
    'Color',[0.2 0.3 0.4]); 
 
h(1) = axes('Position',[0 0 1 1]); 



vertices = [1 diameter 1;
            1 -diameter 1;
            diameter -radius 1;
            1 -radius diameter;
            ...
            -diameter -radius 1;
            1 -radius -diameter;
            diameter radius 1;
            1 radius diameter;
            ...
            -diameter radius 1;
            1 radius -diameter
         ];
     
faces = [ 2 3 4;
         1 8 7;
         2 4 5;
         1 9 8;
         ...
         2 5 6;
         1 10 9;
         2 6 3;
         1 7 10;
         3 7 8;
         ...
         3 8 4;
         4 8 5;
         8 9 5;
         5 9 10;
         ...
         5 10 6;
         6 10 3;
];

patch('Faces',faces,'Vertices',vertices,'FaceColor','r');  % patch function 
saveobjmesh('sphere.obj',vertices, faces, 'sphere');

set(hs1,'EdgeColor','none', ... 
    'FaceColor','red', ... 
    'FaceAlpha','interp'); 
alpha('color'); 
alphamap('rampdown'); 
camlight(45,45); 
lighting phong 
hidden off 
axis square 

end

function findTriangle = FindTriangle(STATS);

stats = STATS;
base = stats.MajorAxisLength;
%rect = [left, bottom, width, height]
area = stats.Area;
%since this is a triangle, we need to solve
height = (2*area)/base;

format compact 
set(gcf,'Menubar','none','Name','Triangle', ... 
    'NumberTitle','off','Position',[500,300,base*2,base*2], ... 
    'Color',[0.1 0.3 0.2]); 


% set up the cube axes 
h1 = axes('Position',[.2 .2 .9 .9]); 

center = stats.Centroid(1);
triVert = [center height center;
    1 1 1;
    1 1 height;
    height 1 height ;
    height 1 1;
    center 1 center;
        ];
    
triFac = [ 3 1 2;
         2 5 1;
         4 5 1;
         4 3 1;
         6 6 2;
         5 6 6;
         2 5 6;
         6 3 2;
         6 4 3;
         6 5 4
        ]; 



patch('Faces',triFac,'Vertices',triVert,'FaceColor','r');  % patch function 

saveobjmesh('fred.obj',triVert, triFac, 'Triangle');


% color and lighting stuff
light('Position',[1 3 2]); 
light('Position',[-3 -1 3]); 
material shiny; 
alpha('color'); 
alphamap('rampdown'); 
camlight(45,45); 
lighting phong 
view(30,30); 




end

function saveobjmesh(name,vert,fac, objName)
 
  fid=fopen(name,'w');

[vrow, vcol] = size(vert);
% for each row print v
  for row = 1: vrow;
      fprintf(fid, 'v ');
        for col = 1: vcol; 
            %then print out each column on the same line
          fprintf(fid, '%g %g %g', vert(row,col));
        end
      fprintf(fid, '\r\n');
  end
  
  [frow, fcol] = size(fac);
    for row = 1: frow;
      fprintf(fid, 'f ');
        for col = 1: fcol; 
            %then print out each column on the same line
          fprintf(fid, '%g %g %g', fac(int8(row),int8(col)));
        end
      fprintf(fid, '\r\n');
  end
  
  fprintf(fid,'g ' );

  fprintf(fid,'g\n\n');
  fclose(fid);