Calculation of Hexagon Coordinates given row and column?

I have the following example image of my hexagon "grid": Each Hexagon has a column and row. The coordinate system I am choosing for my hex layout is an X,Y coordinate system, with the X coordinates landing across the red lines and the Y coordinates simply equal to the row. In my image I have the X,Y coordinate for each hex displayed in the middle in the middle of the hex.

My Question: Given the row and column of a hex, how do you calculate the X,Y coordinate of the hex (or more simply, how do you calculate the X coordinate, since the Y coord = row number)?

I have tried to come up with various equations that work for each hex but no luck yet. An equation that comes close is:

x = Math.floor(column/2) + (row%2)


But that doesn't satisfy all the hex's. I think I am on the right track.

Also, please assume that the hex grid continues infinitely down and to the right.

Observe that if the sum of the row and column (i'm using matrix (row, column) = $(r,c)$ notation) is even, there is a hexagon but if it is odd, there is a common side of two adjacent hexagon.
The new coordinates of the hexagon at $(r,c)$ is $$(x,y)=\left(\cfrac {r+c}{2}\ ,\ r\right) \ \ \ if \ \ \ \ \ r+c \ \ \ \text{ is even }$$
• @Jakobud $(r,c)$ is (row, column) and $x=\cfrac{r+c}{2}$. – user31280 Nov 29 '12 at 21:58
• (r+c)/2... geez how did I not see that? Thank you very much! – Jake Wilson Nov 29 '12 at 22:06