# How do I map pixels to a coordinate system?

As often happens I'm not sure of the name of what I'm trying to do, so I'm having difficulty searching it. I know this is basic algebra, but my math is null so I'm struggling with it greatly.

I have a coordinate system that starts from 0,0 in the bottom left corner, and ends in 1,1 in the top right corner. I must "translate" from coordinates to pixels and viceversa. I'm including a diagram to clarify what I'm trying to do.

I'm trying to do this with Javascript, but I guess it's irrelevant. A formula is enough to get me started.

Thanks!

-
bottom left pixels should read "5, 195", sorry. – Duopixel Feb 16 '11 at 22:44
should it read 1,0 in the bottom right or top left? (instead of 0,1, which appears twice) – Henry Feb 16 '11 at 22:51
Ugh, true, uploaded fixed image. – Duopixel Feb 16 '11 at 22:55
An interesting related issue for you may what pixels correspond to the points on a particular straight line. One approach to this is known as Bresenham's Algorithm: en.wikipedia.org/wiki/Bresenham%27s_line_algorithm – Joseph Malkevitch Feb 16 '11 at 23:32

Your coordinates look odd, but going from co-ordinates to pixels, you probably want something like $$f(x,y) = (190y+5,195-190x)$$ and going from pixels to coordinates $$g(a,b) = \left(\frac{195-b}{190},\frac{a-5}{190},\right)$$ but you may need to adjust this slightly to deal with what happens on the edges