treehouse/content/programming/blog/tairu.tree

%% title = "tairu - an interactive exploration of 2D autotiling techniques"
scripts = [
    "components/literate-programming.js",
    "vendor/codejar.js",
]
styles = ["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
    ```

        % 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
        ```

        [`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 `<canvas>`.

            % 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 `<canvas>` 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
    ```

    % 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.

    <div class="horizontal-tile-strip">
    <span class="metal x-0 y-0"></span>
    <span class="metal x-1 y-0"></span>
    <span class="metal x-2 y-0"></span>
    <span class="metal x-3 y-0"></span>
    <span class="metal x-0 y-1"></span>
    <span class="metal x-1 y-1"></span>
    <span class="metal x-2 y-1"></span>
    <span class="metal x-3 y-1"></span>
    <span class="metal x-0 y-2"></span>
    <span class="metal x-1 y-2"></span>
    <span class="metal x-2 y-2"></span>
    <span class="metal x-3 y-2"></span>
    <span class="metal x-0 y-3"></span>
    <span class="metal x-1 y-3"></span>
    <span class="metal x-2 y-3"></span>
    <span class="metal x-3 y-3"></span>
    </div>

    % 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!

    <div class="horizontal-tile-strip">
    <span class="metal x-0 y-0"><span class="east">E</span><span class="south">S</span></span>
    <span class="metal x-1 y-0"><span class="east">E</span><span class="south">S</span><span class="west">W</span></span>
    <span class="metal x-2 y-0"><span class="south">S</span><span class="west">W</span></span>
    <span class="metal x-3 y-0"><span class="south">S</span></span>
    <span class="metal x-0 y-1"><span class="east">E</span><span class="south">S</span><span class="north">N</span></span>
    <span class="metal x-1 y-1"><span class="east">E</span><span class="south">S</span><span class="west">W</span><span class="north">N</span></span>
    <span class="metal x-2 y-1"><span class="south">S</span><span class="west">W</span><span class="north">N</span></span>
    <span class="metal x-3 y-1"><span class="south">S</span><span class="north">N</span></span>
    <span class="metal x-0 y-2"><span class="east">E</span><span class="north">N</span></span>
    <span class="metal x-1 y-2"><span class="east">E</span><span class="west">W</span><span class="north">N</span></span>
    <span class="metal x-2 y-2"><span class="west">W</span><span class="north">N</span></span>
    <span class="metal x-3 y-2"><span class="north">N</span></span>
    <span class="metal x-0 y-3"><span class="east">E</span></span>
    <span class="metal x-1 y-3"><span class="east">E</span><span class="west">W</span></span>
    <span class="metal x-2 y-3"><span class="west">W</span></span>
    <span class="metal x-3 y-3"></span>
    </div>

    % 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`):

        <div class="horizontal-tile-strip">
        <span class="metal x-3 y-3"></span>
        <span class="metal x-0 y-3"><span class="east">E</span></span>
        <span class="metal x-3 y-0"><span class="south">S</span></span>
        <span class="metal x-0 y-0"><span class="east">E</span><span class="south">S</span></span>
        <span class="metal x-2 y-3"><span class="west">W</span></span>
        <span class="metal x-1 y-3"><span class="east">E</span><span class="west">W</span></span>
        <span class="metal x-2 y-0"><span class="south">S</span><span class="west">W</span></span>
        <span class="metal x-1 y-0"><span class="east">E</span><span class="south">S</span><span class="west">W</span></span>
        <span class="metal x-3 y-2"><span class="north">N</span></span>
        <span class="metal x-0 y-2"><span class="east">E</span><span class="north">N</span></span>
        <span class="metal x-3 y-1"><span class="south">S</span><span class="north">N</span></span>
        <span class="metal x-0 y-1"><span class="east">E</span><span class="south">S</span><span class="north">N</span></span>
        <span class="metal x-2 y-2"><span class="west">W</span><span class="north">N</span></span>
        <span class="metal x-1 y-2"><span class="east">E</span><span class="west">W</span><span class="north">N</span></span>
        <span class="metal x-2 y-1"><span class="south">S</span><span class="west">W</span><span class="north">N</span></span>
        <span class="metal x-1 y-1"><span class="east">E</span><span class="south">S</span><span class="west">W</span><span class="north">N</span></span>
        </div>

        % 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
    ```

    % 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
    ```

    % 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
    ```

    % 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!

            <ul class="directions-square bend">
                <li class="east">E</li>
                <li class="south">S</li>
            </ul>

            % classes.branch = "tileset-four-to-eight-demo"
              id = "01HQ1K39ASC5WTR2A2AJN85JK2"
            - huh. interesting. it connects to the east and the south. so what about this tile -
            <ul class="directions-square e-s">
                <li class="east">E</li>
                <li class="south">S</li>
            </ul>
                % 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…

    <ul class="directions-square">
        <li class="east">E</li>
        <li class="south">S</li>
        <li class="west">W</li>
        <li class="north">N</li>
    </ul>

    into eight *ordinal* directions:

    <ul class="directions-square">
        <li class="east">E</li>
        <li class="south-east">SE</li>
        <li class="south">S</li>
        <li class="south-west">SW</li>
        <li class="west">W</li>
        <li class="north-west">NW</li>
        <li class="north">N</li>
        <li class="north-east"><a href="https://github.com/NoiseStudio/NoiseEngine/" title="NoiseEngine????">NE</a></li>
    </ul>

    % 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
        ```

        % 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!

        <ul class="directions-square e-s">
            <li class="east">E</li>
            <li class="south-east">SE</li>
            <li class="south">S</li>
        </ul>

            % id = "01HQ1K39ASQTR054W0VWEAV2FS"
            - in this case, if we remove the tile to the southeast, we get that bent tile from before:

            <ul class="directions-square bend">
                <li class="east">E</li>
                <li class="south">S</li>
            </ul>

            % 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:

            <ul class="directions-square e-s">
                <li class="east">E</li>
                <li class="south-east">SE</li>
                <li class="south">S</li>
                <li class="south-west">SW</li>
                <li class="north-west">NW</li>
                <li class="north-east">NE</li>
            </ul>

                % 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
    ```

    % 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
```

:nap:

% disabled = true
  id = "01HQ1M84GS3WKE2X6QV2SNQX46"
- TODO: next chapter! if you're reading this, you're in on it soon. that's quite sad, but YOU CAN STILL TURN BACK! I advise you to do that immediately.

You have been warned.








    % id = "01HPD4XQPWPN6HNA6M6EH507C6"
    + but one day I found a really cool project called [Tilekit](https://rxi.itch.io/tilekit)

        % id = "01HPD4XQPW11EQTBDQSGXW3S52"
        + (of course it's really cool, after all [rxi](https://github.com/rxi) made it)

            % id = "01HPD4XQPWYHS327BV586SB085"
            - for context rxi is the genius behind the Lua-powered, simple, and modular text editor [lite](https://github.com/rxi/lite) that I was using for quite a while

                % id = "01HPD4XQPWJ9QAQ5MF2J5JBB8M"
                - after a while I switched to a fork - [Lite XL](https://github.com/lite-xl/lite-xl), which had better font rendering and more features

                % id = "01HPD4XQPWB11TZSX5VAAJ6TCD"
                - I stopped using it because VS Code was just more feature packed and usable; no need to reinvent the wheel, rust-analyzer *just works.*

                    % id = "01HPD4XQPW3G7BXTBBTD05MB8V"
                    - the LSP plugin for Lite XL had some issues around autocompletions not filling in properly :pensive:

                    it's likely a lot better now, but back then I decided this is too much for my nerves.
                    while tinkering with your editor is something really cool, in my experience it's only cool up to a point.

    % id = "01HPD4XQPWV1BAPA27SNDFR93B"
    - the cool thing with Tilekit is that it's *more* than just your average bitwise autotiling - of course it *can* do basic autotiling, but it can also do so much more

        % id = "01HPD4XQPWM1JSAPXVT6NBHKYY"
          classes.branch_children = "branch-quote"
        - if I had to describe it, it's basically something of a *shader langauge for tilesets.* this makes it really powerful, as you can do little programs like

            % id = "01HPD4XQPWE7ZVR0SS67DHTGHQ"
            - autotile using this base tileset

            % id = "01HPD4XQPW2BFZYQQ920SYHM9M"
            - if the tile above is empty AND with a 50% chance

                % id = "01HPD4XQPWJB7V67TS1M3HFCYE"
                - then grass

            % id = "01HPD4XQPWF7K85Z0CEK4WDDBZ"
            - if the tile above is solid AND with a 10% chance

                % id = "01HPD4XQPW5J3N6MVT9Z2W00S9"
                - then vines

            % id = "01HPD4XQPWGCMCEAR5Z9EETSGP"
            - if the tile above is vines AND with a 50% chance

                % id = "01HPD4XQPWP847T0EAM0FJ88T4"
                - then vines

        % id = "01HPSY4Y19FA2HGYE4F3Y9NJ57"
        - well… it's even simpler than that in terms of graphical presentation, but we'll get to that.

        % id = "01HPD4XQPWK58Z63X6962STADR"
        - I mean, after all - bitwise autotiling is basically a clever solution to an `if` complexity problem, so why not extend that with more logic and rules and stuff to let you build more complex maps?

            % id = "01HPJ8GHDFRA2SPNHKJYD0SYPP"
            - of course Tilekit's solution is a lot more simple, streamlined, and user-friendly, but you get the gist.