Scaling
To scale a point relative to the origin, you want to multiply the x,y components by scaling factors sx and sy, respectively. In addition, you want no translation during the scaling operation. Here's the matrix you want:
sx 0 0
Ms =0 sy 0
0 0 1
Eg. p = [x y 1]
sx 0 0
p' = p*Ms = [x y 1] * 0 sy 0 = [(x*sx) (y*sy) 1]
0 0 1
Again, this is the desired result for scaling; that is
x' = sx*x
y' = sy*y
MATH
Note the 1 in the lowerright corner of the transformation matrix. Technically, it's not necessary because you're never going to use the result from the third column. Hence, you're wasting math cycles. The question is, can you remove the last column of all the transformation matrices and use a 3x2 instead? Let's see the rotation matrix before you answer that…
