Amit’s Thoughts on Grids

Is it it just me, or is the font, clarity of writing, color combination and diagram presentation extraordinarily clean on that site. There is a small bug with word wrapping beside some diagrams on my iPad, but everything else pulled me into about 25 minutes of awesome reading on grids.

I don't like the way he does coordinates for triangles and hexagons, having hexes with the same y-coordinate slope up to the right. I prefer having hexes with the same y-coordinate stay as close to horizontal as possible, meaning that even hexes will be shifted up or down by half a hex compared to odd hexes.

I found that keeping the hex coordinates as close as possible to the square coordinates that your GUI library uses makes things easier.

I'm not exactly sure what's new on this page, but his articles about game design and path finding were huge help to me when I was starting out in game development.

Regarding implementation, he says "All the algorithms are straightforward. How might you implement them? You’ll first want to choose data structures for each of the three coordinate systems. I recommend keeping it very simple and transparent. All the coordinate systems I listed have an integer u and an integer v, and some of them have an annotation like L or W ; in Java use a class with public fields; The next step is to implement the algorithms you need. The simplest thing to do is to write functions (or methods) that take A and return a list of B. "

Atleast in Java ( and therefore in Scala, Clojure etc), the data-structure of choice is a general path, and all of those algorithms have built-in implementations, mostly on Path2D or other concretes. Also, instead of dealing with squares, hexagons & triangles separately... a square is just 2 isosceles triangles, and a hex is 6 equilateral triangles. So if you have a Triangle2D class extending Path2D, you get all of the algorithms and the you can handle all 3 face types. The transformation between cooordinate systems is handled by affine transforms

Path2D: http://docs.oracle.com/javase/6/docs/api/java/awt/geom/Path2...

AffineTransform: http://docs.oracle.com/javase/6/docs/api/java/awt/geom/Affin...

Love it, I have had to design 2d and 3d grids before now and the information you gave on faces for polygonal grids has been really helpful and will help me to break the square mold, so to speak.

For some background, Amit Patel is likely best known for an old BBS game called Solar Realms Elite.

That's a very nice talk especially if you are interested in 3D mobile games development (like I was once in the past). I wish I'd knew all these before. Thanks for the post.