I am filling a square tile of width wTile with equal hexagons stacked flat side on top of each other at an angle I call colourAngle as shown in the diagram. I call the rows of hexagons "Perp Line" which go from 0 to n. For clarity, I have not filled in all the hexagons in the diagram.
If I want to completely fill the square tile with hexagons and I am given a required colourAngle A and a hexagon density d, then
- How many Perp Lines do I need and
- How many hexagons are needed
- What is the radius of the hexagons, rHex.
In the example shown there are 18 Perp Lines (including 0)
I have been having much more trouble than I expected trying to work this out.
Thoughts so far: The hexagon density (see diagram for equation) is dependent on the size of the hexagons, i.e. rHex.
The number of perp lines is also dependent on the density.
The density is the area of the square tile divided by the area of a single hexagon.
Perhaps the problem would be easier if the hexagons were decomposed into 6 equilateral triangles.
