[HN Gopher] Triangle Grids
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       Triangle Grids
        
       Author : jsnell
       Score  : 156 points
       Date   : 2022-07-10 15:48 UTC (7 hours ago)
        
 (HTM) web link (kvachev.com)
 (TXT) w3m dump (kvachev.com)
        
       | lbotos wrote:
       | Anyone know the game on the square grid example here:
       | https://kvachev.com/blog/posts/images/triangle-1.jpg
       | 
       | I thought it was advanced wars but I don't remember walker mech
       | units?
        
         | theandrew168 wrote:
         | Appears to be Into the Breach [1].
         | 
         | [1] https://subsetgames.com/itb.html
        
         | the_af wrote:
         | It looks like Into the Breach: https://subsetgames.com/itb.html
        
         | janderson3 wrote:
         | Into the Breach. It's an excellent tactics game where each
         | mission only has about five turns, and every move matters.
        
       | [deleted]
        
       | yellowapple wrote:
       | Another advantage of triangle grids: they work great for
       | spherical maps, whether that sphere's mesh derives from a
       | tetrahedron or octahedron or icosahedron. You'd need some fancier
       | logic for movements around the edges of the "sphere's" base mesh,
       | but once that's solved you're golden.
        
       | jiaaro wrote:
       | I'm working on a triangle-grid board game, probably for playdate
       | (wip builds: https://jiaaro.itch.io/3nclosure)
       | 
       | I was surprised to find play testers had a hard time
       | internalizing the grid - e.g. making mistakes that result in
       | losing the game in the opponents next turn.
       | 
       | Also, I used simple x, y coordinates for each cell with even-
       | numbered indexes being the upward-pointing triangles and odds
       | being the downward-pointing ones. Similarly odd-indexed rows were
       | offset right by half a triangle to make them align properly
       | 
       | [edits]: added details
        
       | cragwind wrote:
       | I quite like triangle grids, but they definitely have more
       | complications than squares or hexagons.
       | 
       | For a few years I've been working on a tri-grid RTS with
       | buildable units: https://cragwind.com/blog/posts/triangle-text-
       | grids/
       | 
       | I originally tried hexagons, but I ultimately chose triangles
       | because they can compose into hexes and there were already so
       | many hex-based games. First I tried a design using separate grids
       | floating in continuous space but later switched to a complete
       | grid-based world as it could make for a novel turn-based classic
       | roguelike or strategy game. It's more limited than continuous
       | space, although with tri- or hex-grids you get six rotations
       | versus four with squares.
       | 
       | One difficulty with tri-grids is the poor spatial locality of
       | triangles versus squares or hexes. For example, when calculating
       | influence maps for AI on a triangle grid, each cell score is
       | effectively stretched to the triangle vertices rather than
       | representing a more consolidated or circular region (so for this
       | purpose hexes would be ideal).
       | 
       | Like other grids, transforms (translation/rotation) on a tri-grid
       | can be done with all integer math (and generally, if the game
       | world is grid-based, everything but graphics/animations can be
       | integer math). Rotations about a cell center are trickier (and
       | are limited to three distinct rotations) but can be done by
       | scaling up coordinates and then back down. I'll write up more
       | details if anyone is interested.
        
         | 0xMatt wrote:
        
       | Karellen wrote:
       | In the section "Directions and Adjacent Tiles", _before_ it
       | starts to consider diagonals, it says that triangle grids have 3
       | adjacent tiles and 6 directions of movement.
       | 
       | I don't follow this. Aren't 3 of the 6 directions it's
       | considering going through the corners of the origin triangle? If
       | so, how do those not count as diagonals? What is the definition
       | of "diagonal" being used?
        
         | the_af wrote:
         | I'm likewise unconvinced by that section of the article (which
         | is interesting to read nonetheless!).
         | 
         | The benefit of hexes is that every neighbor is the same. There
         | are no "special" kind of adjacencies, like with squares or
         | triangles, where you must decide how to consider corners,
         | whether to allow diagonals, etc. So hexes are the only ones
         | that don't mess up distances nor require separate kinds of
         | adjacencies.
         | 
         | Also: if tracing a line from the center point of the origin
         | triangle, some of those paths require crossing another adjacent
         | triangle (different from the "direction" triangle). This to me
         | signals this triangular grid is wonky for wargames/games.
        
         | jameshart wrote:
         | From an individual cell, there are three movements available.
         | But there are two kinds of cell - north pointing and south
         | pointing - and the set of three directions you can move in from
         | each is different.
         | 
         | From a north-pointing triangle, you can move south, northwest
         | or northeast. From a south-pointing triangle, you can move
         | north, southwest or southeast.
         | 
         | So across the grid as a whole, six movement directions exist.
        
       | citelao wrote:
       | I thought the video was pretty, but it took me a while to find
       | out what game it was from: Colossal Citadels. I think the blog
       | poster works on it?
       | 
       | https://store.steampowered.com/app/1854570/Colossal_Citadels...
       | 
       | I wish the blog post just had a link to it :(
        
         | the_af wrote:
         | He probably does, since he wrote:
         | 
         | > _In Colossal Citadels I made walls and houses follow the
         | triangular grid and I love how these procedurally-generated
         | castles turned out [...]_
         | 
         | Note in the sentence I quoted, "Colossal Citadels" is a link to
         | http://colossalcitadels.com/ :)
        
       | wodenokoto wrote:
       | I like how units in the screenshots have different grid sizes.
       | One was a square another a hexagon. The way the mountains can
       | form differently shaped peaks also looks great
        
       | philipov wrote:
       | My favorite recent game with a triangle grid is Vagrus, a dark
       | fantasy caravan management RPG. The number next to each line
       | shows how many movement points it costs to travel that path. It
       | makes it a little hard to see the visual style of the terrain
       | underneath, but it functions well.
       | 
       | https://store.steampowered.com/app/909660/Vagrus__The_Riven_...
        
         | the_af wrote:
         | Thanks for pointing this game out: seems interesting, cool
         | artwork, Dark Sun vibes, works on Linux --> autobuy.
         | 
         | That said, most reviews mention it's punishingly, almost
         | unfairly difficult. I took the plunge anyway, sending my money
         | to indie devs that want to try something new, but if I find it
         | too difficult I'll probably end up giving up in frustration.
         | 
         | What was your experience with this game?
        
           | philipov wrote:
           | It's not an easy game, but less punishing than a game like
           | Darkest Dungeon, because it doesn't force you to play on
           | Ironman. You can save and reload if you need to.
        
             | the_af wrote:
             | Save and reload like in XCOM? I can live with that.
             | 
             | Started playing this, going through the tutorial scenario.
             | The world building indeed has strong vibes of Dark Sun and
             | the Dying Earth genre.
             | 
             | Again, thanks for the recommendation!
        
       | klyrs wrote:
       | I love hyperrogue, if more in concept than practice -- why settle
       | for triangle grids when you can make a septagon grid! It's fun to
       | get lost on a hyperbolic plane, though the gameplay itself is a
       | little lacking. I'm hoping that somebody else will pick up the
       | concept and do something even cooler.
        
       | axelerator wrote:
       | Very inspiring! I just started out to play around with the wave
       | function collapse algorithm [1]. I'm in the middle of porting it
       | to a cube based 3d grid. And now I'm wondering what a triangle
       | based volume presentation would look like
       | 
       | [1] https://github.com/axelerator/wave-function-collapse-2d
        
         | Someone wrote:
         | How do you plan to fill 3D space with 'triangles'?
         | 
         | You can't do that with tetrahedrons. You can use triangular
         | prisms, but IMO, that's cheating. You can also split a cube
         | into six pyramids with a square base and height 1/2, but I
         | don't think that's a natural way to fill space.
         | 
         | Looking at https://mathworld.wolfram.com/Space-
         | FillingPolyhedron.html, the Truncated Octahedron probably is
         | the nicest alternative to the cube.
        
           | kragen wrote:
           | I think this question is sort of another way to phrase, "What
           | are the crystal systems [or possibly lattice systems] other
           | than primitive cubic?" And the answer is in
           | https://en.wikipedia.org/wiki/Crystal_system; there are 6 or
           | 31 answers depending on how you look at it. Or maybe the
           | question is "What are the 3-honeycombs other than the cubic
           | honeycomb?" which is discussed in
           | https://en.wikipedia.org/wiki/Honeycomb_%28geometry%29 and to
           | which there are an infinite number of answers.
           | 
           | Crystal systems are usually described in terms of point
           | lattices, while you're talking about polyhedra, but the
           | Voronoi polyhedra of the points in the lattice are the
           | polyhedra you're looking for. (This is mentioned at the end
           | of the Wolfram(tm)r MathWorld(tm)r article you linked.) One
           | of my favorites is the cuboctahedral honeycomb corresponding
           | to hexagonal close-packed crystals.
           | 
           | Even within cubic crystals, you could reasonably argue that
           | face-centered cubic crystals "fill[] 3-D space with
           | 'triangles'".
           | 
           | Honeycombs do not, as I understand it, have to be periodic.
           | In particular, any 3-D rep-tile can be used to tile space in
           | a manner similar to the Penrose tiling, and usually the
           | result is aperiodic. I wrote a 2-D demonstration of this
           | process is at http://canonical.org/~kragen/sw/dev3/skitch#!ff
           | ffrrrfffffrrr...].
        
           | scotty79 wrote:
           | https://mathworld.wolfram.com/RhombicDodecahedron.html
           | 
           | Rhombic dodecahedron looks quite nice.
           | 
           | And you could mix it with cube grid for artificial structures
           | in your world.
        
           | jedharris wrote:
           | From Wikipedia: The tetragonal disphenoid tetrahedral
           | honeycomb is a space-filling tessellation (or honeycomb) in
           | Euclidean 3-space made up of identical tetragonal
           | disphenoidal cells.
           | 
           | https://en.wikipedia.org/wiki/Tetragonal_disphenoid_honeycom.
           | ..
        
           | smegsicle wrote:
           | > Truncated Octahedron
           | 
           | looks to me like they fill space pretty nicely as an offset
           | of cubes, in the same way as hexgrid is sort of an offset of
           | squares
           | 
           | https://en.wikipedia.org/wiki/Bitruncated_cubic_honeycomb
        
       | alehlopeh wrote:
       | Chinese checkers is an existing game that uses a triangle grid.
       | Surprised the article didn't mention that.
        
         | kragen wrote:
         | In the terms of the article, it uses a hex grid.
        
       | zelphirkalt wrote:
       | A fact that I learned from some old DOS game many years ago, of
       | which I do not remember the name: You can play "6 in a line wins"
       | on a grid of triangles.
        
       | swayvil wrote:
       | Kisrhombille grid. It's worth a look. It's free scaling, like
       | triangles and squares. Has 6 axii. Nice.
       | 
       | https://en.m.wikipedia.org/wiki/Kisrhombille
       | 
       | https://github.com/johnalexandergreene/Geom_Kisrhombille#rea...
       | 
       | http://www.fleen.org/generative-art/i0.png
        
       | loupol wrote:
       | Cool article. An excellent resource for grids of all kinds is Red
       | Blob Games' site. It's mentioned in the article, but only with a
       | link leading to a somewhat empty page and not this very useful
       | one : https://www.redblobgames.com/grids/parts/
        
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       (page generated 2022-07-10 23:00 UTC)