I have a 1x3 matrix representing a point in space:
[x] [y] [1]
And a 3x3 matrix representing an affine 2d transformation matrix
[a][b][c] [d][e][f] [g][h][i]
How to I multiply the matrices so that I am given the matrix?
[newX] [newY] [w]
I have a 1x3 matrix representing a point in space:
[x] [y] [1]
And a 3x3 matrix representing an affine 2d transformation matrix
[a][b][c] [d][e][f] [g][h][i]
How to I multiply the matrices so that I am given the matrix?
[newX] [newY] [w]
Basic matrix multiplication works here.
$ \begin{bmatrix} c_x \\ c_y \\ c_w \end{bmatrix} = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} \begin{bmatrix} x \\ y \\ 1 \end{bmatrix} $
$ c_x = a\, x + b\, y + c $ $ c_y = d\, x + e\, y + f$ $ c_w = g\, x + h\, y + i$
with your new point at $(x,y) = (c_x/c_w, c_y/c_w)$
You will find examples here.