Amit's Site - Latest Comments in Amit’s Thoughts on Grids

Re: Amit’s Thoughts on Grids

haleyysz — Mon, 18 Feb 2019 20:54:07 -0000

You are a god among men. Thanks

Re: Amit’s Thoughts on Grids

amitp — Fri, 04 Jan 2019 18:42:58 -0000

This is a cool layout!

Re: Amit’s Thoughts on Grids

Zeno Rogue — Fri, 04 Jan 2019 13:25:33 -0000

I have already posted about this in the hex tutorial, but this is a more relevant place. With a picture now, too!

http://roguetemple.com/z/gi...

A cool way to implement a triangular map in a game, . Fits in a 2D array
with no wasted space! The cells adjacent to (x,y) are always (y,x),
(y,x-1), (y+1,x). Reflect ∇s in the blue edge to see how it works. Found
it several years ago, but it does not seem to be known.

Re: Amit’s Thoughts on Grids

amitp — Tue, 24 Jul 2018 13:03:43 -0000

See the "Square to Hexagon" section of the page. A hexagonal grid slides the squares over. You can think of this as a change in basis vectors x=(1,0) y=(0,1) to x=(1,0) y=(1,1/2) or x=(1,1/2) y=(1,0). You can slide them back by setting y += x/2 or x += y/2 (or -= depending on how your grid is set up)

Re: Amit’s Thoughts on Grids

MrJox — Tue, 24 Jul 2018 07:22:20 -0000

Is there a way to convert a hex grid to square grid? any particular algorithm?

Re: Amit’s Thoughts on Grids

amitp — Fri, 24 Nov 2017 12:11:59 -0000

Thank you!

Re: Amit’s Thoughts on Grids

amitp — Fri, 24 Nov 2017 12:11:50 -0000

Glad it helped! Although you can do something with weirdly shaped pentagons, I don't see games using them. There are only three shapes for "regular" tilings: https://en.wikipedia.org/wi... and all the other shapes have to be tiled irregularly. I think once you get to that point it might be easier to think of it as a graph (see the "voronoi" section on this page) instead of a grid.

Re: Amit’s Thoughts on Grids

m sorin — Fri, 24 Nov 2017 10:14:14 -0000

Hello Mr Amit, thank you so much for your great references. I want to pull together once and for all a decent map generator for all of my future games array starting with my_game[0] ... :)
Have tryed having pentagon shaped grid cells ? any comparison with hex?

Re: Amit’s Thoughts on Grids

Lazar Ljubenovic — Sun, 28 May 2017 12:09:25 -0000

I keep coming back to this blog month after month and I'm amazed each time by the detailed explanation. Can't believe this is over 10 years old!

Re: Amit’s Thoughts on Grids

Phil — Thu, 04 May 2017 16:32:00 -0000

Modern Chess is indeed "Western", having been transformed from shatranj in southern Europe.

More detail here: https://en.wikipedia.org/wi...

It was not until 1960s that modern chess became popular in India https://en.wikipedia.org/wi...

That said, the "Eastern" shatranj indeed favors faces

Re: Amit’s Thoughts on Grids

amitp — Mon, 18 Jul 2016 15:15:14 -0000

Thanks! I wrote it over ten years ago so I'm trying to figure out what I did wrong here.

1. This does seem wrong. It doesn't even make sense, as i,j are vectors. I think it will end up being (0.5*ix, 0.33*jy) and (1.0*ix, 0.66*jy). However, I should work this out on paper to make sure.

2. The notation I used was terrible, and when I rewrite this page I'll do a better job. It's the x,y components of the i,j vectors. It would've been clearer if I wrote i.x, i.y, j.x, j.y.

3. I've since learned that I should never ever write that something is “easy”, because whatever was easy to me back when I was writing it is not easy for me now, nor necessarily easy for the reader. I believe what you have to do is look at the equation that computes world coordinate x,y from the matrix ix,iy,jx,jy and the grid coordinate u,v. You can solve for u,v by inverting the matrix. I never did work out the details on this page :(

4. I think you're right! I will correct the text.

Part of the problem is that I never did end up using triangle grids for a real project, so I never worked out the bugs :( I've updated the page.

Re: Amit’s Thoughts on Grids

Alivender — Thu, 14 Jul 2016 17:45:07 -0000

Hey. Fantastic guide, just what I was looking. I have a few questions though.

1. "The L triangle face center is (0.25*i, 0.25*j) from the lower left vertex. The R triangle face center is (0.75*i, 0.75*j) from the lower left vertex."

I think those values should be 0.33 and 0.66, not 0.25 and 0.75 respectively. That is, if the triangles are equilateral, of course.

2. I am very confused about the values you wrote as ix, iy, jx, and jx. What are they exactly? Do you mean those vectors (i and j) multiplied by world coordinates (x,y)? But that's the formula to calculate world coordinates, so i can't use them to calculate them. I think I am misunderstanding this terribly.

3. "To convert from world coordinates to triangle vertices is easy. Solve for (u, v) using algebra." I don't know what I am supposed to solve for (u,v).

4. "I believe it’s R when frac(u) + frac(v) >= 0.5."

Since the Left-Right edge runs between (0,1) and (1,0) vertices, right through (0.5,0.5) centre of the sheered square, I believe it's frac(u) + frac(v) >= 1, that's correct.

Re: Amit’s Thoughts on Grids

DÁvidám Horváth — Sat, 14 Nov 2015 19:10:47 -0000

Broken again. I have found it on the internet, just an FYI.
Thx for the great stuff!

Re: Amit’s Thoughts on Grids

Jafeth Díaz Castañeda — Fri, 16 Oct 2015 19:00:32 -0000

The counting parts section isn't very clear for me...Where could I find a more detailed explanation?

Re: Amit’s Thoughts on Grids

amitp — Fri, 03 Jul 2015 13:13:18 -0000

Interesting — thanks. I put that link in the More section because I haven't studied it yet. I'm guessing there are additional properties that make rectangles different from parallelograms in that context, but I don't really know.

Re: Amit’s Thoughts on Grids

Daniel Kelly — Thu, 02 Jul 2015 22:11:41 -0000

Great read, thanks. One observation; in the last paragraph you state 'Mathematicians have found five types of grids in 2D space: squares, triangles, hexagons, rectangles, and parallelograms.' Actually, a rectangle is technically a parallelogram (as is a square). I believe the 5th shape, discounting the rectangle, that could be made into a grid is an isosceles trapezoid.

Re: Amit’s Thoughts on Grids

skaps — Mon, 15 Jun 2015 12:56:03 -0000

Is it okay if we discuss there?

Re: Amit’s Thoughts on Grids

skaps — Mon, 15 Jun 2015 12:55:42 -0000

I sent you an email regarding the same.

Re: Amit’s Thoughts on Grids

amitp — Mon, 15 Jun 2015 10:18:27 -0000

What trouble are you having? These algorithms should work the same in most any language.

Re: Amit’s Thoughts on Grids

skaps — Mon, 15 Jun 2015 02:37:12 -0000

Hey, great work with the detailed explanations. I wanted to implement a similar algorithm in java but am having trouble with it. Was wondering whether anyone has tried that? Or if you've tried it, Amit?

Thanks

Re: Amit’s Thoughts on Grids

amitp — Fri, 23 Jan 2015 14:21:09 -0000

Hi Mark, sorry, I don't have any pointers for more advanced uses of grids. I've collected just enough for the way I use grids in games, and haven't looked at more.

Re: Amit’s Thoughts on Grids

Mark Szl — Wed, 21 Jan 2015 09:14:36 -0000

Thank you for all the work about grids. Do you have anything on floating point coordinates and mapping them to grids? I know this can become complicated if the point coordinates are ends of segments that make up structures. Snap rounding nerds to be then used on the vertices of these structures (i.e. "Stable Snap Rounding" by John Hershberger).

Another issue is pairing functions like Szudzik's for grids. With the single integer from the pairing one then could construct a hash table for the points on the grid.

Do you have any pages or pointers to good and easy to understand articles on these topics?

Thanks again.

Re: Amit’s Thoughts on Grids

BenH — Mon, 17 Nov 2014 23:01:21 -0000

You are a god among men. Thanks.

Re: Amit’s Thoughts on Grids

amitp — Wed, 27 Aug 2014 11:16:34 -0000

Hi mkv25.net games, take a look here: http://www.redblobgames.com... ; you can see that a rectangle map in axial hex coordinates is a "parallelogram" in q, r coordinates, where 0 ≤ q + r/2 < N

Re: Amit’s Thoughts on Grids

mkv25.net games — Sun, 24 Aug 2014 18:26:32 -0000

Question: what's the best way to cover a rectangle with hexagons? Assuming I'm storing hexagons in axial q, r coordinates...