When you have very small objects in an integer world then each pixel begins to matter for things like collision detection. For example if your object is a circle with a radius of, very roughly, 15 or more, you could choose not worry about how it is represented on screen and in your integer co-ordinate system.... but if you imagine of a circle with a radius of 2 then you'll see it's critical. In particular for circles and spheres the centres of them need to be considered. If yout think of every co-ordinate on your screen being represented by a pixel, then so must your circle centre -- which means all your circles must have a diameter that is an odd number of pixels. Or... if you decide that every co-ordinate on your screen is represented by the theoretical bottom left of pixels -- all your circle diameters must be even. The case of odd diameters is illustrated below.