Matrix transformations for an image to be painted on a screen. Implemented on Octave.

output.txt

GNU Octave, version 3.8.0
Copyright (C) 2013 John W. Eaton and others.
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Continue?
ans = [](0x0)
Transformation 1
===========================

Pixel: 
 1
 1
Pixel falls in image point:
   2.1433
   1.7960
   1.0000
Drawn!
Interpolated Value: 
 2.0000
continue?
ans = [](0x0)
===========================

Pixel: 
 1
 2
Pixel falls in image point:
   2.3169
   3.7656
   1.0000
Drawn!
Interpolated Value: 
 15
continue?
ans = [](0x0)
===========================

Pixel: 
 1
 3
Pixel falls in image point:
   2.4906
   5.7352
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 1
 4
Pixel falls in image point:
   2.6642
   7.7048
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 2
 1
Pixel falls in image point:
   4.1129
   1.6223
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 2
 2
Pixel falls in image point:
   4.2865
   3.5919
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 2
 3
Pixel falls in image point:
   4.4602
   5.5616
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 2
 4
Pixel falls in image point:
   4.6338
   7.5312
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 3
 1
Pixel falls in image point:
   6.0825
   1.4487
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 3
 2
Pixel falls in image point:
   6.2561
   3.4183
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 3
 3
Pixel falls in image point:
   6.4298
   5.3879
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 3
 4
Pixel falls in image point:
   6.6034
   7.3575
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 4
 1
Pixel falls in image point:
   8.0521
   1.2750
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 4
 2
Pixel falls in image point:
   8.2258
   3.2446
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 4
 3
Pixel falls in image point:
   8.3994
   5.2143
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 4
 4
Pixel falls in image point:
   8.5731
   7.1839
   1.0000
Not Drawn
continue?
ans = [](0x0)
ans =

    2.00000    0.00000    0.00000    0.00000
   15.00000    0.00000    0.00000    0.00000
    0.00000    0.00000    0.00000    0.00000
    0.00000    0.00000    0.00000    0.00000

Continue with Transformation 2?
Transformation 2
===========================

Pixel: 
 1
 1
Pixel falls in image point:
  -0.066987
   0.933013
   1.000000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 1
 2
Pixel falls in image point:
  -0.56699
   1.36603
   1.00000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 1
 3
Pixel falls in image point:
  -1.0670
   1.7990
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 1
 4
Pixel falls in image point:
  -1.5670
   2.2321
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 2
 1
Pixel falls in image point:
   0.36603
   1.43301
   1.00000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 2
 2
Pixel falls in image point:
  -0.13397
   1.86603
   1.00000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 2
 3
Pixel falls in image point:
  -0.63397
   2.29904
   1.00000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 2
 4
Pixel falls in image point:
  -1.1340
   2.7321
   1.0000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 3
 1
Pixel falls in image point:
   0.79904
   1.93301
   1.00000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 3
 2
Pixel falls in image point:
   0.29904
   2.36603
   1.00000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 3
 3
Pixel falls in image point:
  -0.20096
   2.79904
   1.00000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 3
 4
Pixel falls in image point:
  -0.70096
   3.23205
   1.00000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 4
 1
Pixel falls in image point:
   1.2321
   2.4330
   1.0000
Drawn!
Interpolated Value: 
 4.0000
continue?
ans = [](0x0)
===========================

Pixel: 
 4
 2
Pixel falls in image point:
   0.73205
   2.86603
   1.00000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 4
 3
Pixel falls in image point:
   0.23205
   3.29904
   1.00000
Not Drawn
continue?
ans = [](0x0)
===========================

Pixel: 
 4
 4
Pixel falls in image point:
  -0.26795
   3.73205
   1.00000
Not Drawn
continue?
ans = [](0x0)
ans =

   0.00000   0.00000   0.00000   4.00000
   0.00000   0.00000   0.00000   0.00000
   0.00000   0.00000   0.00000   0.00000
   0.00000   0.00000   0.00000   0.00000

trans.m

Scene1 = [8,1,1,2;6,5,8,1;10,2,8,1;4,3,1,6];
imagesc(Scene1);
Screen = [];

input('Continue?')

t1 = [.5*cosd(10),-sind(10),0;sind(10),.5*cosd(10),0;0,0,1];
t1p = [2*cosd(10),sind(10),0;-sind(10),2*cosd(10),0;0,0,1];

t2 = [2*cosd(30),sind(30),0;-sind(30),2*cosd(30),0;0,0,1];
t2p = [.5*cosd(30),-sind(30),0;sind(30),.5*cosd(30),0;0,0,1];

disp('Transformation 1');
for i = 1:4
    for j = 1:4
        disp('===========================');
        disp('');
        disp('Pixel: '), disp(i), disp(j);
        pixel = [i;j;1];
        pixelAddress = t1p*pixel;
        disp('Pixel falls in image point:'), disp(pixelAddress);
        if (pixelAddress(1) >= 1) && (pixelAddress(1) <=4 && pixelAddress(2) >= 1) && (pixelAddress(2) <=4) 
            drawn = true;
            disp('Drawn!');
            if drawn
                % image address
                xLeft = floor(pixelAddress(1));
                xRight = ceil(pixelAddress(1));
                yUp = floor(pixelAddress(2));
                yDown = ceil(pixelAddress(2));
                % intensity
                i1 = Scene1(xLeft,yUp);
                i2 = Scene1(xRight,yUp);
                i3 = Scene1(xLeft,yDown);
                i4 = Scene1(xRight,yDown);
                % interpolation 1 x-x top

                    % Generate linear system
                    equations = [xLeft,1;xRight,1];
                    solutions = [i1;i2];
                    % Solve linear system
                    AB = equations\solutions;
                    % Replace A and B values in equations to get next intensity
                    ix1 = AB(1)*pixel(1) + AB(2);


                % interpolation 2 x-x bottom

                    % Generate linear system
                    equations = [xLeft,1;xRight,1];
                    solutions = [i3;i4];
                    % Solve linear system
                    AB = equations\solutions;
                    % Replace A and B values in equations to get next intensity
                    ix2 = AB(1)*pixel(1) + AB(2);

                % interpolation 3 y-y from previous interpolated points

                    % Generate linear system
                    equations = [yUp,1;yDown,1];
                    solutions = [ix1;ix2];
                    % Solve linear system
                    AB = equations\solutions;
                    % Replace A and B values in equations to get next intensity
                    InterpolatedValue = AB(1)*pixel(2) + AB(2);

                % Add value to Screen
                Screen(end+1) = InterpolatedValue;
                disp('Interpolated Value: '), disp(InterpolatedValue);
            end
        else
            Screen(end+1) = 0;
            disp('Not Drawn');

        end
        input('continue?')
    end
end
reshape(Screen,4,4)
imagesc(Screen);



input('Continue with Transformation 2?');


Screen = [];

disp('Transformation 2');
for i = 1:4
    for j = 1:4
        disp('===========================');
        disp('');
        disp('Pixel: '), disp(i), disp(j);
        % pixel address in homogenous form
        pixel = [i;j;1];
        % pixel adress within image
        pixelAddress = t2p*pixel;
        disp('Pixel falls in image point:'), disp(pixelAddress);
        % if the pixel is within the image, draw it
        if (pixelAddress(1) >= 1) && (pixelAddress(1) <=4 && pixelAddress(2) >= 1) && (pixelAddress(2) <=4) 
            drawn = true;
            disp('Drawn!');
            if drawn
                % image address
                xLeft = floor(pixelAddress(1));
                xRight = ceil(pixelAddress(1));
                yUp = floor(pixelAddress(2));
                yDown = ceil(pixelAddress(2));
                % intensity
                i1 = Scene1(xLeft,yUp);
                i2 = Scene1(xRight,yUp);
                i3 = Scene1(xLeft,yDown);
                i4 = Scene1(xRight,yDown);
                % interpolation 1 x-x top

                    % Generate linear system
                    equations = [xLeft,1;xRight,1];
                    solutions = [i1;i2];
                    % Solve linear system
                    AB = equations\solutions;
                    % Replace A and B values in equations to get next intensity
                    ix1 = AB(1)*pixel(1) + AB(2);


                % interpolation 2 x-x bottom

                    % Generate linear system
                    equations = [xLeft,1;xRight,1];
                    solutions = [i3;i4];
                    % Solve linear system
                    AB = equations\solutions;
                    % Replace A and B values in equations to get next intensity
                    ix2 = AB(1)*pixel(1) + AB(2);

                % interpolation 3 y-y from previous interpolated points

                    % Generate linear system
                    equations = [yUp,1;yDown,1];
                    solutions = [ix1;ix2];
                    % Solve linear system
                    AB = equations\solutions;
                    % Replace A and B values in equations to get next intensity
                    InterpolatedValue = AB(1)*pixel(2) + AB(2);

                % Add value to Screen
                Screen(end+1) = InterpolatedValue;
                disp('Interpolated Value: '), disp(InterpolatedValue);
            end
        else
            Screen(end+1) = 0;
            disp('Not Drawn');

        end
        input('continue?')
    end
end
reshape(Screen,4,4)
imagesc(Screen);