如何在矩形坐标上应用变换

Question

I am detecting an object in my code and drawing a rectangle around it. I have four variables to draw rectangle: X, Y, Width, and Height. I have found a transformation matrix that needs to be applied on the rectangle. The transformation matrix returned is a 3*3 matrix like this:

Tinv =

    1.0022    0.0018        0

   -0.0018    1.0022         0

   -0.4353   -0.9079    1.0000

How to apply the transformation on the rectangle using this matrix?

Answer 1

What you should do is calculate all four vertices of the rectangle and then apply the transformation on each individual vertex. This should be easy enough; if I get what you're trying to do, then you could use something like the following for say:

X = 1;
Y = 2.34;
W = 3.21;
H = 2;

The vertices could now be (assuming that (X,Y) denotes the top left vertex of your rectangle with its base at 0 radian:

(x1,y1) = (1,2.34)
(x2,y2) = (4.21,2.34)
(x3,y3) = (4.21,0.34)
(x4,y4) = (1,0.34)

This could now be represented as:

[
1.00    2.34    0.00
4.21    2.34    0.00
4.21    0.34    0.00
1.00    0.34    1.00
]

This could now be transformed as required by simple matrix multiplication.