optimized grid for rectangular items
Note: I couldn't quite understand Frédéric's answer, so I worked the problem out myself and came up with what appears to be the same solution. I figured I might as well explain what I did in case it is helpful.
First I normalized the aspect ratio of the view to that of the items. (I'm assuming you don't want to rotate the items.)
a = (view_width/view_height) / (item_width/item_height)
Now packing a rectangle of width/height ratio a
with squares is equivalent to packing the view with items. The ideal case would be for our grid (of squares now) to fill the rectangle completely, which would give us
a = c/r
where r
and c
are the numbers of rows and columns:
N = r*c
Multiplying/dividing these two equations gives us
N*a = c^2 N/a = r^2
c = sqrt(N*a) r = sqrt(N/a)
If the grid is perfect, r
and c
will be integers, but if not, you have to try the three options Frédéric mentioned and keep the one where r*c
is smallest but still more than N
:
floor(r), ceil(c)
ceil(r), floor(c)
ceil(r), ceil(c)