How many squared Columns can be arranged on a squared Parking Level using the "Array Modifier" without any Intersections?
Not an easy answer for me but maybe for an excellent mathematician like spikeyxxx. For the sake of simplicity, we assume that the distance between one column and the next one is a whole number multiple of the column's "Bounding Box" dimension in the direction of duplication.
So here're my reflections:
We use the "Array Modifier" with its default settings "Fixed Count" and "Relative Offset" (X=1, Y=0, Z=0) so that we get a whole number of duplicates tightly packed along their aligned "Local X Axes" where each duplicate's "Bounding Box" touches the "Bounding Box" of its direct neighbour. With our 72 times 72 meters parking level and 2 times 2 meters columns, 36 columns would fit into the garage with the "Array Modifier's" default settings. But this construction wouldn't be useful 😉😁!
We could set the "Relative Offset" to a higher value so that we get a whole number multiple of our object's "Bounding Box" extension in "Local X". This offset can be a "Decimal Fraction" but for the sake of simplicity mentioned at the beginning, we limit ourselves in the following to whole numbers.
What combinations are possible in general?
Two criterias must be fulfilled after subtracting one time the duplicated object's "Bounding Box" extension in the direction of duplication (default: "Local X"):
1) The result of this first subtraction must be divisible by a whole number so that you get again a whole number.
2) This division result must be a whole number which is at the same time a whole number multiple the duplicated object's "Bounding Box" extension in the direction of duplication (still "Local X" in our example 😉)
Unless you're good in mental math and have a lot of time (depending on the specific dimensions of your scene 😉), you would need a programm for automated calculations, maybe one you've developed yourself 😉. So, Kent theluthier, don't worry, you're not alone with your headache when figuring out settings for the "Array Modifier" that make the columns fit the dimensions of the parking level😉!
Finally, this is the specific parking level at the end of this lesson: