How to preform simple Matrix Transmormations

I can't figure out how to do translations, rotations and scaling by using matrices. Here is the code. We were told only to use matrices to achieve the effect.

Thanks in advance!

    %%Initialize

    clc
    clear all
    close all

    %%Part a

    shape=[0 1 0; 0 0 1];
    Mshape=[0 1 0; 0 0 1;1 1 1];
    DX =-3;
    DY= 4;

    dx =DX/100;
    dy = DY/100;

    steps = 100

    Trans = [1 0 dx ; 0 1 dy; 0 0 1]

    for n=1:steps

        Mshape =Trans*Mshape 

        fill(Mshape(1,:),Mshape(2,:),'g')
        axis([-8 8 -8 8])

        drawnow
    end
    rev=720;
    theta = 1;

    Transto0 = [1 0 -DX ; 0 1 -DY; 0 0 1]
    TransT = [1 0 DX ; 0 1 DY; 0 0 1]

    for n=1:rev

        thetaT = n*theta

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

        Mshape = Trans*R*Transto0*Mshape

        fill(Mshape(1,:),Mshape(2,:),'g')
        axis([-8 8 -8 8])
        Mshape

        drawnow
    end
    S = 2

    s =S/100;

    steps = 100

    Scale = [S 0 0 ; 0 S 0; 0 0 1]

    for n=1:steps

        Mshape =Scale*Mshape 

        fill(Mshape(1,:),Mshape(2,:),'g')
        axis([-8 8 -8 8])

        drawnow
    end

Answer 1

[Madhav Rajan]

I understand that you want to perform Matrix transformations such as rotation and scaling. Assuming that you want to scale or rotate a matrix M, you would have to first translate your matrix to the origin then perform the rotation or the scaling and then translate your matrix back to its original position. This is because scaling and rotation always happen with respect to the origin.

In the script attached, you can see the effect of applying scaling and rotation on a triangle which has not been translated to its origin and also the effect of first translating the object to the origin and then applying the transformations.

You can refer the following links for more information about scaling and rotations about the origin: http://www.willamette.edu/~gorr/classes/GeneralGraphics/Transforms/transforms2d.htm#Combining

You can also also refer the following documentation for 2d affine transformations in MATLAB: http://www.mathworks.com/help/images/performing-general-2-d-spatial-transformations.html