%% title = "tairu - an interactive exploration of 2D autotiling techniques" scripts = [ "components/literate-programming.js", "vendor/codejar.js", ] styles = ["page/tairu.css"] % id = "01HPD4XQPWM8ECT2QM6AT9YRWB" - I remember since my early days doing programming, I've been interested in how games like Terraria handle automatically tiling their terrain. % id = "01HPD4XQPWPDBH6QQAZER7A05G" - in Terraria, you can fully modify the terrain however you want, and the tiles will connect to each other seamlessly. % id = "01HPD4XQPW8HE7681P7H686X4N" - TODO: short videos demoing this here % id = "01HPD4XQPWJBTJ4DWAQE3J87C9" - once upon a time I stumbled upon a technique called… % id = "01HQ162WWA1KXZPBDWJXSCQA1D" - ### bitwise autotiling % id = "01HPD4XQPW6VK3FDW5QRCE6HSS" + I learned about it way back when I was just a kid building 2D Minecraft clones using [Construct 2](https://www.construct.net/en/construct-2/manuals/construct-2), and I wanted my terrain to look nice as it does in Terraria % id = "01HPD4XQPWJ1CE9ZVRW98X7HE6" - Construct 2 was one of my first programming experiences and the first game engine I truly actually liked :smile: % id = "01HQ162WWAMCPC5M88QAXHX4BT" - so to help us learn, I made a little tile editor so that we can experiment with rendering tiles! have a look: ```javascript tairu import { Tilemap } from "tairu/tilemap.js"; import { TileEditor } from "tairu/editor.js"; export const tilemapSquare = Tilemap.parse(" x", [ " ", " xxx ", " xxx ", " xxx ", " ", ]); new TileEditor({ tilemap: tilemapSquare, tileSize: 40, }); ``` ```output tairu 01HQ47ZX7520PJNPJ75M793R5G ``` % id = "01HQ162WWAC3FN565QE3JAB87D" - `Tilemap` is a class wrapping a flat [`Uint8Array`] with a `width` and a `height`, so that we can index it using (x, y) coordinates. ```javascript tairu console.log(tilemapSquare.at(0, 0)); console.log(tilemapSquare.at(3, 1)); ``` ```output tairu 0 1 ``` [`Uint8Array`]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Uint8Array % id = "01HQ162WWA090YW5BR1XW68XJN" - `at` has a `setAt` counterpart which sets tiles instead of getting them. % id = "01HQ162WWAMD68SY56P7TVT2DJ" - `TileEditor` provides a graphical editor for a `Tilemap` based on a ``. % id = "01HQ162WWABTFQ0J83C4VZYZB5" - this editor is _Certified Battery Efficient™_, so it won't redraw unless it needs to!\ we'll need to keep this in mind for later when we try to draw images, which may not be loaded during the initial draw. % id = "01HQ162WWA8Y1AD22MSN71V2E4" - to kick this off, let's set off a goal. I would like the tiles in our little renderer to connect together, like this: ![red rectangle with a black outline, made out of 3x3 tiles][pic:01HPYW5SNTY0Z0ENDE5K3XWMTH] % id = "01HQ162WWAZV559ABQD1NVXPMA" - let's break this down into smaller steps. drawing a border around the rectangle will involve: % id = "01HQ162WWATV30HXGBQVWERP2M" - determining *on which tiles* to draw it, % id = "01HQ162WWAA0V0SS0D1Y38BDS1" - determining *where in these tiles* to draw it, % id = "01HQ162WWAGBCBDYF4VH26MX1B" - and actually drawing it! % id = "01HQ162WWA2PNGVV075HR3WMER" - so let's zoom in a bit and look at the tiles one by one. in particular, let's focus on *these* two tiles: ![the same red rectangle, now with a focus on the northern tile at its center][pic:01HPYWPJB1P0GK53BSJFJFRAGR] % id = "01HQ162WWAYDS6CSD3T102NA9X" - notice how the two highlighted tiles are *different.* therefore, we can infer we should probably connect together any tiles that are *the same*. % id = "01HQ162WWATDD86D4GY7RMT0BZ" - knowing that, we can extract the logic to a function: ```javascript tairu export function shouldConnect(a, b) { return a == b; } ``` % id = "01HQ162WWA9M6801Q0RNRSF09H" + now, also note that the border around this particular tile is only drawn on its *northern* edge - therefore we can infer that borders should only be drawn on edges for whom `shouldConnect(thisTile, adjacentTile)` is **`false`** (not `true`!). a tile generally has four edges - east, south, west, north - so we need to perform this check for all of them, and draw our border accordingly. % id = "01HQ162WWAM5YYQCEXH791T0E9" - you might be wondering why I'm using this particular order for cardinal directions - why not [north, south, east, west]? or [north, east, south, west]? % id = "01HQ162WWABJ696HCJ09WDC0NX" - the reason comes from math - `[cos(0) sin(0)]` is a vector pointing rightwards, not upwards! and I chose clockwise order, because that's how the vector rotates as we increase the angle, in a coordinate space where +Y points downward - such as the `` coordinate space. % id = "01HQ162WWABNXV4N2AHZBQC5B7" - this choice yields some nice orderliness in the code that handles fetching tiles for connections - first you check `+X`, then `+Y`, then `-X`, and then `-Y` - which my pedantic mind really appreciates :ahyes:\ as `X` is first alphabetically, so checking `Y` first would feel wrong. % id = "01HQ162WWA5W8NXSXVZY3BBQ0H" - to do that, I'm gonna override the tile editor's `drawTilemap` function - as this is where the actual tilemap rendering happens! ```javascript tairu import { TileEditor } from "tairu/editor.js"; export class TileEditorWithBorders extends TileEditor { constructor({ borderWidth, ...options }) { super(options); this.borderWidth = borderWidth; this.colorScheme.borderColor = "#000000"; } drawTilemap() { // Let the base class render out the infill, we'll just handle the borders. super.drawTilemap(); this.ctx.fillStyle = this.colorScheme.borderColor; for (let y = 0; y < this.tilemap.height; ++y) { for (let x = 0; x < this.tilemap.width; ++x) { let tile = this.tilemap.at(x, y); // We only want to draw non-empty tiles, so skip tile 0. if (tile == 0) { continue; } // Check which of this tile's neighbors should *not* connect to it. let disjointWithEast = !shouldConnect(tile, this.tilemap.at(x + 1, y)); let disjointWithSouth = !shouldConnect(tile, this.tilemap.at(x, y + 1)); let disjointWithWest = !shouldConnect(tile, this.tilemap.at(x - 1, y)); let disjointWithNorth = !shouldConnect(tile, this.tilemap.at(x, y - 1)); let { borderWidth, tileSize } = this; let tx = x * tileSize; let ty = y * tileSize; // For each disjoint neighbor, we want to draw a border between us and them. if (disjointWithEast) { this.ctx.fillRect(tx + tileSize - borderWidth, ty, borderWidth, tileSize); } if (disjointWithSouth) { this.ctx.fillRect(tx, ty + tileSize - borderWidth, tileSize, borderWidth); } if (disjointWithWest) { this.ctx.fillRect(tx, ty, borderWidth, tileSize); } if (disjointWithNorth) { this.ctx.fillRect(tx, ty, tileSize, borderWidth); } } } } } ``` and here's the result: ```javascript tairu new TileEditorWithBorders({ tilemap: tilemapSquare, tileSize: 40, borderWidth: 4, }); ``` ```output tairu 01HQ49TJZFMK719KSE16SG3F7B ``` % id = "01HQ162WWAAEKW1ECV5G3ZEY47" - this looks pretty perfect - maybe sans corners, which I'll conveniently skip for now, because most games don't actually render graphics in a vectorial way like this! instead, the more common way is to use a tileset - a big texture with a bunch of sprites to use for rendering each tile. % id = "01HQ162WWACD5CD7GCZE53ZPD7" - not only does this have the advantage of allowing for richer graphics, but it is also a lot easier to modify by artists, because you no longer need knowledge of graphics APIs to draw tiles. % template = true classes.branch = "tileset-cardinal-directions-demo" id = "01HQ162WWAADKPDQE69W3QZG0M" - for example, here's a tileset I drew for the 3rd iteration of my game [Planet Overgamma] - though tweaked a bit because I had never used it before writing this post :hueh: ![heavy metal sheet tileset from Planet Overgamma, made out of 16 tiles. it looks like heavy embossed sheets of metal, resembling steel in its heavyness][pic:01HPHVDRV0F0251MD0A2EG66C4] [Planet Overgamma]: https://github.com/liquidev/planet-overgamma % classes.branch = "tileset-cardinal-directions-demo" id = "01HQ162WWAS502000K8QZWVBDW" - we can split this tileset up into 16 individual tiles, each one 8 × 8 pixels; people choose various resolutions, I chose a fairly low one to hide my lack of artistic skill.
% classes.branch = "tileset-cardinal-directions-demo" id = "01HQ162WWANBTYH1JJWCTZYYVN" - the keen eyed among you have probably noticed that this is very similar to the case we had before with drawing procedural borders - except that instead of determining which borders to draw based on a tile's neighbors, this time we'll determine which *whole tile* to draw based on its neighbors!
ES ESW SW S ESN ESWN SWN SN EN EWN WN N E EW W
% id = "01HQ162WWA4Z6KKWFV59BR4WD3" - previously we represented which single border to draw with a single boolean. now we will represent which single tile to draw with *four* booleans, because each tile can connect to four different directions. % id = "01HQ162WWAQ9GZ6JD8KESW4N53" - four booleans like this can easily be packed into a single integer using some bitwise operations, hence we get ***bitwise autotiling*** - autotiling using bitwise operations! % id = "01HQ162WWAMBM8RXKQTN3D0XR2" - now the clever part of bitwise autotiling is that we can use this packed integer *as an array index* - therefore selecting which tile to draw can be determined using just a single lookup table! neat, huh? % id = "01HQ162WWA0ZGZ97JZZBFS41TF" - but because I'm lazy, and CPU time is valuable, instead of using an array I'll just rearrange the tileset texture a bit to be able to slice it in place using this index. % id = "01HQ162WWAQQ99TRBDY5DCSW3Z" - say we arrange our bits like this: ```javascript tairu export const E = 0b0001; export const S = 0b0010; export const W = 0b0100; export const N = 0b1000; ``` % classes.branch = "tileset-cardinal-directions-demo" id = "01HQ162WWABANND0WGT933TBMV" - that means we'll need to arrange our tiles like so, where the leftmost tile is at index 0 (`0b0000`) and the rightmost tile is at index 15 (`0b1111`):
E S ES W EW SW ESW N EN SN ESN WN EWN SWN ESWN
% id = "01HQ162WWAJPW00XA25N0K6KS7" - packing that into a single tileset, or rather this time, a *tile strip*, we get this image: ![horizontal tile strip of 16 8x8 pixel metal tiles][pic:01HPMMR6DGKYTPZ9CK0WQWKNX5] % id = "01HQ162WWAT2ZC7T2P9ATD6WG2" - now it's time to actually implement it as code! I'll start by defining a *tile index* function as a general way of looking up tiles in a tileset. % id = "01HQ162WWA0NRHBB6HP2RERNBK" - I want to make the tile renderer a bit more general, so being able to attach a different tile lookup function to each tileset sounds like a great feature. % id = "01HQ162WWA9PGSHH5E97RVE1PB" - just imagine some game where glass connects to metal, but metal doesn't connect to glass - I bet that would look pretty great! % id = "01HQ162WWAYJ4JCG3Z24SJR8S9" - …but anyways, here's the basic bitwise magic function: ```javascript tairu export function tileIndexInBitwiseTileset(tilemap, x, y) { let tile = tilemap.at(x, y); let tileIndex = 0; tileIndex |= shouldConnect(tile, tilemap.at(x + 1, y)) ? E : 0; tileIndex |= shouldConnect(tile, tilemap.at(x, y + 1)) ? S : 0; tileIndex |= shouldConnect(tile, tilemap.at(x - 1, y)) ? W : 0; tileIndex |= shouldConnect(tile, tilemap.at(x, y - 1)) ? N : 0; return tileIndex; } ``` % template = true id = "01HQ162WWAS813ANMBG1PWDZHC" - we'll define our tilesets by their texture, tile size, and a tile indexing function. so let's create an object that will hold our tileset data: ```javascript tairu // You'll probably want to host the assets on your own website rather than // hotlinking to others. It helps longevity! let tilesetImage = new Image(); tilesetImage.src = "{% pic 01HPMMR6DGKYTPZ9CK0WQWKNX5 %}"; export const heavyMetalTileset = { image: tilesetImage, tileSize: 8, tileIndex: tileIndexInBitwiseTileset, }; ``` % id = "01HQ162WWA0SC2GA7Y3KJE0W5F" - with all that, we should now be able to write a tile renderer which can handle textures! so let's try it: ```javascript tairu import { TileEditor } from "tairu/editor.js"; export class TilesetTileEditor extends TileEditor { constructor({ tilesets, ...options }) { super(options); this.tilesets = tilesets; // The image may not be loaded once the editor is first drawn, so we need to request a // redraw for each image that gets loaded in. for (let tileset of this.tilesets) { tileset.image.addEventListener("load", () => this.draw()); } } drawTilemap() { // We're dealing with pixel tiles so we want our images to be pixelated, // not interpolated. this.ctx.imageSmoothingEnabled = false; for (let y = 0; y < this.tilemap.height; ++y) { for (let x = 0; x < this.tilemap.width; ++x) { let tile = this.tilemap.at(x, y); if (tile == 0) { continue; } // Subtract one from the tile because tile 0 is always empty. // Having to specify a null entry at array index 0 would be pretty annoying. let tileset = this.tilesets[tile - 1]; if (tileset != null) { let { tileSize } = this; let tileIndex = tileset.tileIndex(this.tilemap, x, y); this.ctx.drawImage( tileset.image, tileIndex * tileset.tileSize, 0, tileset.tileSize, tileset.tileSize, x * tileSize, y * tileSize, tileSize, tileSize, ); } } } } } ``` % id = "01HQ162WWAS2HYF41MZNJ18BXC" - drum roll please… ```javascript tairu new TilesetTileEditor({ tilemap: tilemapSquare, tileSize: 40, tilesets: [heavyMetalTileset], }); ``` ```output tairu 01HQ49X8Z57FNMN3E79FYF8CMG ``` % id = "01HQ162WWA03JAGJYCT0DRZP24" - it works! buuuut if you play around with it you'll quickly start noticing some problems: ```javascript tairu import { Tilemap } from "tairu/tilemap.js"; export const tilemapEdgeCase = Tilemap.parse(" x", [ " ", " xxx ", " x x ", " xxx ", " ", ]); new TilesetTileEditor({ tilemap: tilemapEdgeCase, tileSize: 40, tilesets: [heavyMetalTileset], }); ``` ```output tairu 01HQ49YDPQXYSAT5N6P241DG3C ``` % id = "01HQ162WWAB0AYSPGB4AEVT03Z" - where did our nice seamless connections go!? % id = "01HQ162WWA3Q095ZGXDFZ1V2Q1" - ### thing is, it was never good in the first place % id = "01HQ162WWARSVDRNHZE13ZF6W6" - I'll be blunt: we don't have enough tiles to represent *corners*! like in this case: ```javacript tairu import { Tilemap } from "tairu/tilemap.js"; new TilesetTileEditor({ tilemap: Tilemap.parse(" x", [ " ", " xx ", " x ", " ", ]), tileSize: 40, tilesets: [heavyMetalTileset], }); ``` ```output tairu 01HQ49Z8JWR75D85DGHCB34K8E ``` % id = "01HQ1K39AS4VDW7DVTAGQ03WFM" - have a closer look at the top-left tile: ![the above example, showing an L shape rotated 180°, with the top left corner highlighted][pic:01HQ167GJEPTKHAKAVNW3WN1SZ] % id = "01HQ1K39AS6Y9XMJTMMQYTWRMC" - it should kind of _"bend"_ to fit in with the tiles to the north and the south, but it doesn't :kamien: % id = "01HQ1K39ASQQNF7B881SYJWRC7" - so what if we made the tile look like *this* instead: ![mockup showing that previous L-shape but with a real corner][pic:01HQ17GYEZSZCVRBFHP4HXAJV8] % id = "01HQ1K39ASMKRMTXFV93FRHZTG" - that sure as heck looks a lot nicer! but there's a problem: that tile, let's zoom in on it… ![that bent tile, and just *it* alone][pic:01HQ183RANGH4S7VZSG1ZGH0S5] % classes.branch = "tileset-four-to-eight-demo" id = "01HQ1K39ASR81NWMW8Q0MF8QMP" - enhance! % classes.branch = "tileset-four-to-eight-demo" id = "01HQ1K39ASC5WTR2A2AJN85JK2" - huh. interesting. it connects to the east and the south. so what about this tile - % id = "01HQ1K39ASXYBH9QJH5Q0C45JZ" - because it *also* connects to the east and the south :thinking: % id = "01HQ1K39ASW5PWS52NGA2X3M0P" - seems like we'll need something to disambiguate the two cases - and what better thing to disambiguate with than *more bits*! % classes.branch = "tileset-four-to-eight-demo" id = "01HPQCCV4R5N97FJ1GS36HZJZ7" - to represent the corners, we'll turn our four cardinal directions… into eight *ordinal* directions: % id = "01HQ1K39ASFN94YDY1RWQYS12K" - at this point with the four extra corners we'll need 8 bits to represent our tiles, and that would make… ***256 tiles!?*** nobody in their right mind would actually draw 256 separate tiles, right? ***RIGHT???*** % template = true id = "01HQ1K39AS11M1M4GQQ60NXTY6" - …right! let's stick with the 16 tile version for a moment. if we arrange the tiles in a diagnonal cross like this, notice how the tile in the center would have the bits `SE | SW | NW | NE` set, which upon first glance would suggest us needing a different tile - but it looks correct! ```javascript tairu import { Tilemap } from "tairu/tilemap.js"; new TilesetTileEditor({ tilemap: Tilemap.parse(" x", [ " ", " x x ", " x ", " x x ", " ", ]), tileSize: 40, tilesets: [heavyMetalTileset], }); ``` ```output tairu 01HQ4A01MPE6JT5ZZFEN9S635W ``` % id = "01HQ1K39AS7CRBZ67N1VVHCVME" - therefore there must be *some* bit combinations that are redundant to others. let's find them! % classes.branch = "tileset-four-to-eight-demo" id = "01HQ1K39ASZPJ4E23EZ1XJ5J7K" - let's pick one corner first, then generalize to all the other ones. I pick southeast! % id = "01HQ1K39ASQTR054W0VWEAV2FS" - in this case, if we remove the tile to the southeast, we get that bent tile from before: % id = "01HQ1K39AS6RGE6Z83T8MH1R0M" - what we can learn from this is that for `E | S`, `ES` affects the result! % id = "01HQ1K39ASVSAQ6F8ANEZE1WQ4" - but if we add any other corner, nothing changes. heck, let's add all of them: % id = "01HQ1K39AST8RQTVSCDV7FSH62" - this combination is definitely redundant! % id = "01HQ1K39AS8VHKHANJFKA4PQJ5" - so it seems like for any two cardinal directions such as `E` and `S`, the ordinal direction that's a combination of the two - in this case `ES` - only matters if both the cardinal direction bits are set! % id = "01HPQCCV4R557T2SN7ES7Z4EJ7" - we can verify this logic with a bit of code; with a bit of luck, we should be able to narrow down our tileset into something a lot more manageable. % id = "01HPSY4Y19NQ6DZN10BP1KQEZN" + we'll start off by redefining our bits to be ordinal directions instead. I still want to keep the [nice orderliness][branch:01HQ162WWAM5YYQCEXH791T0E9] that comes with arranging the bits clockwise starting from east, so if we want that we can't just extend the indices with an extra four bits at the top. ```javascript tairu export const E = 0b0000_0001; export const SE = 0b0000_0010; export const S = 0b0000_0100; export const SW = 0b0000_1000; export const W = 0b0001_0000; export const NW = 0b0010_0000; export const N = 0b0100_0000; export const NE = 0b1000_0000; ``` % id = "01HPSY4Y19HPNXC54VP6TFFHXN" - I don't know about you, but I find the usual C-style way of checking whether a bit is set extremely hard to read, so let's take care of that: ```javascript tairu export function isSet(integer, bit) { return (integer & bit) == bit; } ``` % id = "01HPSY4Y1984H2FX6QY6K2KHKF" - now we can write a function that will remove the aforementioned redundancies. the logic is quite simple - for southeast, we only allow it to be set if both south and east are also set, and so on and so forth. ```javascript tairu // t is an existing tile index; variable name is short for brevity export function removeRedundancies(t) { if (isSet(t, SE) && (!isSet(t, S) || !isSet(t, E))) { t &= ~SE; } if (isSet(t, SW) && (!isSet(t, S) || !isSet(t, W))) { t &= ~SW; } if (isSet(t, NW) && (!isSet(t, N) || !isSet(t, W))) { t &= ~NW; } if (isSet(t, NE) && (!isSet(t, N) || !isSet(t, E))) { t &= ~NE; } return t; } ``` % id = "01HPSY4Y19HWQQ9XBW1DDGW68T" - with that, we can find a set of all unique non-redundant combinations: ```javascript tairu export function ordinalDirections() { let unique = new Set(); for (let i = 0; i <= 0b1111_1111; ++i) { unique.add(removeRedundancies(i)); } return Array.from(unique).sort((a, b) => a - b); } ``` % id = "01HPSY4Y19KG8DC4SYXR1DJJ5F" - by the way, I find it quite funny how JavaScript's [`Array.prototype.sort`] defaults to ASCII ordering *for all types.* even numbers! ain't that silly? [`Array.prototype.sort`]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/sort % id = "01HPSY4Y19V62YKTGK3TTKEB38" - and with all the ingredients in the pot, we now _Let It Cook™_: ```javascript tairu let dirs = ordinalDirections(); console.log(dirs.length); ``` ```output tairu 47 ``` % id = "01HPSY4Y194DYYDGSAT83MPQFR" - forty seven! that's how many unique tiles we actually need. % id = "01HPSY4Y19C303Z595KNVXYYVS" - you may find pixel art tutorials saying you need forty *eight* and not forty *seven*, but that is not quite correct - the forty eighth tile is actually just the empty tile! saying it's part of the tileset is quite misleading IMO. % id = "01HPSY4Y19TM2K2WN06HHEM3D0" - phew… the nesting's getting quite unwieldy, let's wrap up this tangent and return back to doing some bitwise autotiling! % id = "01HPSY4Y192FZ37K3KXZM90K9J" - so in reality we actually only need 47 tiles and not 256 - that's a whole lot less, that's 81.640625% less tiles we have to draw! % id = "01HPSY4Y19HEBWBTNMDMM0AZSC" - and it's even possible to autogenerate most of them given just a few smaller 4x4 pieces - but for now, let's not go down that path.\ maybe another time. % id = "01HPWJB4Y047YGYAP6XQXJ3576" - so we only need to draw 47 tiles, but to actually display them in a game we still need to pack them into an image. % id = "01HPWJB4Y0QX6YR6TQKZ7T1C2E" - we *could* use a similar approach to the 16 tile version, but that would leave us with lots of wasted space! % id = "01HPWJB4Y0HKGSDABB56CNFP9H" - think that with this redundancy elimination approach most of the tiles will never even be looked up by the renderer, because the bit combinations will be collapsed into a more canonical form before the lookup. % id = "01HQ1K39ASM53P1E74HKRZ1T24" - so instead of wasting space, we can compress the tiles into a compact strip, and use a lookup table from sparse tile indices to dense tile *positions* within the strip. % id = "01HPWJB4Y0F9JGXQDAAVC3ERG1" - I don't want to write the lookup table by hand, so let's generate it! % id = "01HPWJB4Y0HTV32T4WMKCKWTVA" - we'll start by obtaining our ordinal directions array again: ```javascript tairu export let xToConnectionBitSet = ordinalDirections(); ``` % id = "01HPWJB4Y03WYYZ3VTW27GP7Z3" - then we'll turn that array upside down… in other words, invert the index-value relationship, so that we can look up which X position in the tile strip to use for a specific connection combination. remember that our array has only 256 values, so it should be pretty cheap to represent using a [`Uint8Array`]: ```javascript tairu export let connectionBitSetToX = new Uint8Array(256); for (let i = 0; i < xToConnectionBitSet.length; ++i) { connectionBitSetToX[xToConnectionBitSet[i]] = i; } ``` [`Uint8Array`]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Uint8Array % id = "01HPWJB4Y0CWQB9EZG6C91A0H0" - and there we go! we now have a mapping from our bitset to positions within the tile strip. try to play around with the code example to see which bitsets correspond to which position! ```javascript tairu console.log(connectionBitSetToX[E | SE | S]); ``` ```output tairu 4 ``` % id = "01HPWJB4Y09P9Q3NGN59XWX2X9" + for my own (and your) convenience, here's a complete list of *all* the possible combinations in order. % id = "01HPWJB4Y01VJFMHYEC1WZ353W" - ```javascript tairu function toString(bitset) { if (bitset == 0) return "0"; let directions = []; if (isSet(bitset, E)) directions.push("E"); if (isSet(bitset, SE)) directions.push("SE"); if (isSet(bitset, S)) directions.push("S"); if (isSet(bitset, SW)) directions.push("SW"); if (isSet(bitset, W)) directions.push("W"); if (isSet(bitset, NW)) directions.push("NW"); if (isSet(bitset, N)) directions.push("N"); if (isSet(bitset, NE)) directions.push("NE"); return directions.join(" | "); } for (let x in xToConnectionBitSet) { console.log(`${x} => ${toString(xToConnectionBitSet[x])}`); } ``` ```output tairu 0 => 0 1 => E 2 => S 3 => E | S 4 => E | SE | S 5 => W 6 => E | W 7 => S | W 8 => E | S | W 9 => E | SE | S | W 10 => S | SW | W 11 => E | S | SW | W 12 => E | SE | S | SW | W 13 => N 14 => E | N 15 => S | N 16 => E | S | N 17 => E | SE | S | N 18 => W | N 19 => E | W | N 20 => S | W | N 21 => E | S | W | N 22 => E | SE | S | W | N 23 => S | SW | W | N 24 => E | S | SW | W | N 25 => E | SE | S | SW | W | N 26 => W | NW | N 27 => E | W | NW | N 28 => S | W | NW | N 29 => E | S | W | NW | N 30 => E | SE | S | W | NW | N 31 => S | SW | W | NW | N 32 => E | S | SW | W | NW | N 33 => E | SE | S | SW | W | NW | N 34 => E | N | NE 35 => E | S | N | NE 36 => E | SE | S | N | NE 37 => E | W | N | NE 38 => E | S | W | N | NE 39 => E | SE | S | W | N | NE 40 => E | S | SW | W | N | NE 41 => E | SE | S | SW | W | N | NE 42 => E | W | NW | N | NE 43 => E | S | W | NW | N | NE 44 => E | SE | S | W | NW | N | NE 45 => E | S | SW | W | NW | N | NE 46 => E | SE | S | SW | W | NW | N | NE ``` % id = "01HPWJB4Y0NMP35M9138DV3P8W" - with the lookup table generated, we are now able to prepare a tile strip like before - except now it's even more tedious work arranging the pieces together :ralsei_dead: anyways I spent like 20 minutes doing that by hand, and now we have a neat tile strip just like before, except way longer: ![horizontal tile strip of 47 8x8 pixel metal tiles][pic:01HPW47SHMSVAH7C0JR9HWXWCM] % id = "01HPWJB4Y0J3DHQV5F9GD3VNQ8" - now let's hook it up to our tileset renderer! % id = "01HQ1M84GS09M7PMXFYHDPRTMT" - since we already prepared the bulk of the framework before, it should be as simple as writing a new `tileIndex` function: ```javascript tairu export function tileIndexInBitwiseTileset47(tilemap, x, y) { let tile = tilemap.at(x, y); let tileBitset = 0; tileBitset |= shouldConnect(tile, tilemap.at(x + 1, y)) ? E : 0; tileBitset |= shouldConnect(tile, tilemap.at(x + 1, y + 1)) ? SE : 0; tileBitset |= shouldConnect(tile, tilemap.at(x, y + 1)) ? S : 0; tileBitset |= shouldConnect(tile, tilemap.at(x - 1, y + 1)) ? SW : 0; tileBitset |= shouldConnect(tile, tilemap.at(x - 1, y)) ? W : 0; tileBitset |= shouldConnect(tile, tilemap.at(x - 1, y - 1)) ? NW : 0; tileBitset |= shouldConnect(tile, tilemap.at(x, y - 1)) ? N : 0; tileBitset |= shouldConnect(tile, tilemap.at(x + 1, y - 1)) ? NE : 0; return connectionBitSetToX[removeRedundancies(tileBitset)]; } ``` % template = true id = "01HQ1M84GS4C99VQZC4150CMDS" - now we can write a new tileset descriptor that uses this indexing function and the larger tile strip: ```javascript tairu // Once again, use your own link here! let tilesetImage = new Image(); tilesetImage.src = "{% pic 01HPW47SHMSVAH7C0JR9HWXWCM %}"; export const heavyMetalTileset47 = { image: tilesetImage, tileSize: 8, tileIndex: tileIndexInBitwiseTileset47, }; ``` % id = "01HQ1M84GS9CC8VR1BVDC15W50" - and Drum Roll 2: Return of the Snare please… ```javascript tairu import { Tilemap } from "tairu/tilemap.js"; new TilesetTileEditor({ tilemap: Tilemap.parse(" x", [ " x ", " x x ", " xxx ", " xx ", " x ", ]), tileSize: 40, tilesets: [heavyMetalTileset47], }); ``` ```output tairu 01HQ4A11RRXEQ850598GFBJN0B ``` % id = "01HQ1M84GSCXTPGVPXY840WCQ6" - it works perfectly! % id = "01HQ1M84GSVBG9T94ZN9XTXX58" - but honestly, this is a bit *boring* if we're gonna build a game with procedural worlds. % id = "01HQ1M84GSH0KTFFZET6GZZ4V2" - heck, it's even boring for a level designer to have to lay out all the tiles manually - introducing variations and what not, such that the world doesn't look too bland… there has to be a better way! % id = "01HQ1M84GSE1N5WG88DGJZH0F8" - and a better way… there is! but I'll get to that once my nap is over. % id = "01HQ1M84GS0KJ9NA6GPS62RC95" - for now, have a big editor to play around with. it's a lot of fun arranging the tiles in various shapes! ```javascript tairu import { Tilemap } from "tairu/tilemap.js"; new TilesetTileEditor({ tilemap: new Tilemap(25, 16), tileSize: 40, tilesets: [heavyMetalTileset47], }); ``` ```output tairu 01HQ4A45WNAEJGCT2WDMQJHK14 ``` :nap: