# Thread: Give a product of matrices that maps the rectangle[...]using homogeneous coordinates.

1. ## Give a product of matrices that maps the rectangle[...]using homogeneous coordinates.

For the "fourth solution" part of the solution for question #2 of this document ( https://www.docdroid.net/fw8ZORs/midterm.pdf#page=3 ), could someone please elaborate on the solution’s explanation for how the numbers –0.5 and 3 were obtained?

Any input would be GREATLY appreciated!

2. ## Re: Give a product of matrices that maps the rectangle[...]using homogeneous coordina

Apparently, I'm supposed to translate (1,-3) to (0.5,0), which means I'd have to go backwards 0.5 and forwards 3 (hence the -0.5 and 3) and move (3,3) by the same amount, but how do I get (0.5,0) in the first place?

3. ## Re: Give a product of matrices that maps the rectangle[...]using homogeneous coordina

Here's an algebraic way to look at it. This is almost like the affine transformation SX + T, where S is a scaling and T is a translation. I assume you've seen the latter, say in conjunction with a window to viewport map.