How do I do what is in the picture?
I took the point * change of coordinate matrix * scale matrix but it didn't work.
[1,1,0,1] * [1 0 0 0, 0 1 0 0, 0 0 1 0, 2 2 0 1] * [2 0 0 0, 0 1 0 0, 0 0 1 0, 0 0 0 1]
this didn't work.
Change of coordinate matrix
You need to apply a translation to move the point (2,2) to the origin, then do the scaling, then undo the translation.
http://www.wolframalpha.com/input/?i={{1%2C0%2C2}%2C{0%2C1%2C2}%2C{0%2C0%2C1}}.{{2%2C0%2C0}%2C{0%2C1%2C0}%2C{0%2C0%2C1}}.{{1%2C0%2C-2}%2C{0%2C1%2C-2}%2C{0%2C0%2C1}}
EDIT: Sorry, I follow the convention that points and vectors are columns, not rows. Transpose everything if you wish.
http://www.wolframalpha.com/input/?i={{1%2C0%2C2}%2C{0%2C1%2C2}%2C{0%2C0%2C1}}.{{2%2C0%2C0}%2C{0%2C1%2C0}%2C{0%2C0%2C1}}.{{1%2C0%2C-2}%2C{0%2C1%2C-2}%2C{0%2C0%2C1}}
EDIT: Sorry, I follow the convention that points and vectors are columns, not rows. Transpose everything if you wish.
Author
Ok. after I multiply all these matrix with the point, will one matrix do it all for all four points of the box. or do I have to change the coordinate of the points .that is one negative x value and the other positive .
like in order to make [1,1,0] to [4,1,0]......I use point [1,1,0]
to make [1,1,0] to [0,1,0]..I use point [-1,1,0]
Yes, one matrix is used to transform all the points.
The matrix I provided is used in the following way: If you multiply it by the column (1,1,1) on the right, you'll get the column (0,1,1) back. Similarly, if you multiply it by the column (3,3,1), you'll get (4,3,1) back.
The matrix I provided is used in the following way: If you multiply it by the column (1,1,1) on the right, you'll get the column (0,1,1) back. Similarly, if you multiply it by the column (3,3,1), you'll get (4,3,1) back.
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