HW5

1) In order to draw the cube, I came up with a couple of helping functions.

Aside from those functions, the core of the program was fairly simple:

function newX = project(X,R,T,K)

%Project the image formation process

newX = ones(1,size(X,2));

newX = T*newX; %The translation

newX=newX+R*X; %The Rotation

newX = K* newX; %For K

newX(1,:) = newX(1,:) ./ newX(3,:);

newX(2,:) = newX(2,:) ./ newX(3,:);

newX(3,:) = newX(3,:) ./ newX(3,:);

end

And to call this function with the given parameters, one would use the following code:

X=zeros(3,8);

X(:,1) = [0 0 0]; X(:,2) = [0 0 1]; X(:,3) = [1 0 1];

X(:,4) = [1 0 0]; X(:,5) = [1 1 0]; X(:,6) = [0 1 0];

X(:,7) = [0 1 1]; X(:,8) = [1 1 1];

drawCube(X);

K = [800, 0, 250; 0, 800, 250; 0, 0, 1];

R = [ 1, 0, 0; 0, cosd(20), -sind(20); 0, sind(20), cosd(20)];

T = [0;0;100];

pam = project(X,R,T,K);

drawCube(pam);

As you can see below, this code would then give us the before and after transformation images of the cube. Since the camera is firmly placed on the Z axis however, the perspective is slightly obscure. For reassurance, I've rotated the before and after images aswell to show that they are in fact done correctly:

BEFORE:

Helping functions:

function cube = drawCube( v )

figure;

hold on;

title('cube');

xlabel('X','FontSize',18);

ylabel('Y','FontSize',18)

zlabel('Z','FontSize',18)

drawPoint(v(:,1) ,v(:,2) );

drawPoint(v(:,2) ,v(:,3) );

drawPoint(v(:,3) ,v(:,4) );

drawPoint(v(:,1) ,v(:,4) );

drawPoint(v(:,4) ,v(:,5) );

drawPoint(v(:,5) ,v(:,6) );

drawPoint(v(:,7) ,v(:,6) );

drawPoint(v(:,7) ,v(:,8) );

drawPoint(v(:,3) ,v(:,8) );

drawPoint(v(:,7) ,v(:,2) );

drawPoint(v(:,1) ,v(:,6) );

drawPoint(v(:,5) ,v(:,8) )

hold off;

cube = true;

end

__________________________________________________________________________

function g= drawPoint( p1,p2 )

plot3([p1(1),p2(1)],[p1(2),p2(2)],[p1(3),p2(3)]);

g = true;

end

AFTER:

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