Let’s start with the basics. What is a hex grid system?
Simply put, it’s a grid that uses hexagons instead of squares.

On the surface, this seems pretty arbitrary, but hex grids
have some advantages over traditional square grids.

For instance, in a square grid system there’s some ambiguity
when it comes to defining “adjacent” spaces. Do you include diagonal spaces, or
just those who share a side with the current square? For the purpose of this blog,
I will be defining adjacent spaces as any spaces that “touch” the current
space. So, in a square grid, that’s eight adjacent squares for any square
that’s not an “edge” or “corner” square. With a hex grid, there’s no ambiguity.
Every adjacent hex shares a side with the current hex, and thus there are
always 6 adjacent hexes for any hex that’s not an “edge” hex.

Similarly, there’s ambiguity when discussing distance in a
square grid system. Any adjacent square that shares a side with the current
square is a distance of one square away. Logically, you could say the same for
diagonally adjacent squares in the sense that a chess piece such as the king,
which can move one space in any direction, can move to diagonal squares and it
“counts” as having moved a single space. In reality however, the distance from
a square to a diagonally adjacent square is the square root of two. So
accurately calculating distance from one square on a grid to another could
potentially be quite difficult to do. By contrast, distance from a hex to an
adjacent hex is always one, which can make calculating distance in some cases much
easier. It also makes it easier to define distance-related rules such as “game
piece X may move Y number of spaces.” While this seems like a simple rule to
us, it’s because we can view grids in a more abstract way. If you try to write
this as an algorithm, it becomes much more complex when you have to factor in
diagonals as well as horizontal or vertical adjacent spaces.

You may be asking at this point, if there are so many
advantages to using a hex grid system, why is the square system more common?
For one, a square system is more intuitive to navigate. In a square grid, the
two axes (commonly referred to as X and Y) are perpendicular, so one of them
runs vertically and the other runs horizontally. This makes it very easy for us
to see that the distance between two spaces is X spaces horizontally and Y
spaces vertically. In a hex grid system, the axes are generally not
perpendicular, but rather at an angle to one another, which is more challenging
for us to visually navigate. Some calculations may be simpler with a hex
system, but a square system is easier for us as humans to understand.

(Please note that the third axis for the grid system is unnecessary. I’ll be going more in depth into the differences between a hex grid coordinate system and a square grid coordinate system in the next post.) |

Both systems have their advantages and disadvantages.
Ideally, we would like to be able to convert data from one system to another,
but this has many challenges, and it is the goal of this blog to explore some
of those challenges.

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