# Voxel(Minecraft Like) Geometry

I've seen this topic come up more than once in various places. That is basically, "How do I make a voxel display like Minecraft".

Most people first attempt this by making a cube geometry and then making a mesh at each voxel position. Just for fun I tried this. I made a 16777216 element `Uint8Array` to represent a 256x256x256 cube of voxels.

    const cellSize = 256;
    const cell = new Uint8Array(cellSize * cellSize * cellSize);

I then made a single layer with a kind of hills of sine waves like this

    for (let y = 0; y < cellSize; ++y) {
      for (let z = 0; z < cellSize; ++z) {
        for (let x = 0; x < cellSize; ++x) {
          const height = (Math.sin(x / cellSize * Math.PI * 4) + Math.sin(z / cellSize * Math.PI * 6)) * 20 + cellSize / 2;
          if (height > y && height < y + 1) {
            const offset = y * cellSize * cellSize +
                           z * cellSize +
                           x;
            cell[offset] = 1;
          }
        }
      }
    }

I then walked through all the cells and if they were not 0 I created a mesh with a cube.

    const geometry = new THREE.BoxGeometry(1, 1, 1);
    const material = new THREE.MeshPhongMaterial({color: 'green'});

    for (let y = 0; y < cellSize; ++y) {
      for (let z = 0; z < cellSize; ++z) {
        for (let x = 0; x < cellSize; ++x) {
          const offset = y * cellSize * cellSize +
                         z * cellSize +
                         x;
          const block = cell[offset];
          const mesh = new THREE.Mesh(geometry, material);
          mesh.position.set(x, y, z);
          scene.add(mesh);
        }
      }
    }

The rest of the code is based on the example from the article on rendering on demand.

click here to open in a separate window

It takes a while to start and if you try to move the camera it's likely too slow. Like the article on how to optimize lots of objects the problem is there are just way too many objects. 256x256 is 65536 boxes!

Using the technique of merging the geometry will fix the issue for this example but what if instead of just making a single layer we filled in everything below the ground with voxel. In other words change the loop filling in the voxels to this

    for (let y = 0; y < cellSize; ++y) {
      for (let z = 0; z < cellSize; ++z) {
        for (let x = 0; x < cellSize; ++x) {
          const height = (Math.sin(x / cellSize * Math.PI * 4) + Math.sin(z / cellSize * Math.PI * 6)) * 20 + cellSize / 2;
    -      if (height > y && height < y + 1) {
    +      if (height < y + 1) {
            const offset = y * cellSize * cellSize +
                           z * cellSize +
                           x;
            cell[offset] = 1;
          }
        }
      }
    }

I tried it once just to see the results. It churned for about a minute and then crashed with out of memory 😅

There are several issues but the biggest issue is we're making all these faces inside the cubes that we can actually never see.

In other words lets say we have a box of voxels 3x2x2. By merging cubes we're getting this

but we really want this

In the top box there are faces between the voxels. Faces that are a waste since they can't be seen. It's not just one face between each voxel, there are 2 faces, one for each voxel facing its neighbor that are a waste. All these extra faces, especially for a large volume of voxels will kill performance.

It should be clear that we can't just merge geometry. We need to build it ourselves, taking into account that if a voxel has an adjacent neighbor it doesn't need the face facing that neighbor.

The next issue is that 256x256x256 is just too big. 16meg is a lot of memory and if nothing else in much of the space nothing is there so that's a lot of wasted memory. It's also a huge number of voxels, 16 million! That's too much to consider at once.

A solution is to divide the area into smaller areas. Any area that has nothing in it needs no storage. Let's use 32x32x32 areas (that's 32k) and only create an area if something is in it. We'll call one of these larger 32x32x32 areas a "cell".

Let's break this into pieces. First let's make a class to manage the voxel data.

    class VoxelWorld {
      constructor(cellSize) {
        this.cellSize = cellSize;
      }
    }

Let's make the function that makes geometry for a cell. Let's assume you pass in a cell position. In other words if you want the geometry for the cell that covers voxels (0-31x, 0-31y, 0-31z) then you'd pass in 0,0,0. For the cell that covers voxels (32-63x, 0-31y, 0-31z) you'd pass in 1,0,0.

We need to be able to check the neighboring voxels so let's assume our class has a function `getVoxel` that given a voxel position returns the value of the voxel there. In other words if you pass it 35,0,0 and the cellSize is 32 it's going to look at cell 1,0,0 and in that cell it will look at voxel 3,0,0. Using this function we can look at a voxel's neighboring voxels even if they happen to be in neighboring cells.

    class VoxelWorld {
      constructor(cellSize) {
        this.cellSize = cellSize;
      }
    +  generateGeometryDataForCell(cellX, cellY, cellZ) {
    +    const {cellSize} = this;
    +    const startX = cellX * cellSize;
    +    const startY = cellY * cellSize;
    +    const startZ = cellZ * cellSize;
    +
    +    for (let y = 0; y < cellSize; ++y) {
    +      const voxelY = startY + y;
    +      for (let z = 0; z < cellSize; ++z) {
    +        const voxelZ = startZ + z;
    +        for (let x = 0; x < cellSize; ++x) {
    +          const voxelX = startX + x;
    +          const voxel = this.getVoxel(voxelX, voxelY, voxelZ);
    +          if (voxel) {
    +            for (const {dir} of VoxelWorld.faces) {
    +              const neighbor = this.getVoxel(
    +                  voxelX + dir[0],
    +                  voxelY + dir[1],
    +                  voxelZ + dir[2]);
    +              if (!neighbor) {
    +                // this voxel has no neighbor in this direction so we need a face
    +                // here.
    +              }
    +            }
    +          }
    +        }
    +      }
    +    }
    +  }
    }

    +VoxelWorld.faces = [
    +  { // left
    +    dir: [ -1,  0,  0, ],
    +  },
    +  { // right
    +    dir: [  1,  0,  0, ],
    +  },
    +  { // bottom
    +    dir: [  0, -1,  0, ],
    +  },
    +  { // top
    +    dir: [  0,  1,  0, ],
    +  },
    +  { // back
    +    dir: [  0,  0, -1, ],
    +  },
    +  { // front
    +    dir: [  0,  0,  1, ],
    +  },
    +];

So using the code above we know when we need a face. Let's generate the faces.

    class VoxelWorld {
      constructor(cellSize) {
        this.cellSize = cellSize;
      }
      generateGeometryDataForCell(cellX, cellY, cellZ) {
        const {cellSize} = this;
    +    const positions = [];
    +    const normals = [];
    +    const indices = [];
        const startX = cellX * cellSize;
        const startY = cellY * cellSize;
        const startZ = cellZ * cellSize;

        for (let y = 0; y < cellSize; ++y) {
          const voxelY = startY + y;
          for (let z = 0; z < cellSize; ++z) {
            const voxelZ = startZ + z;
            for (let x = 0; x < cellSize; ++x) {
              const voxelX = startX + x;
              const voxel = this.getVoxel(voxelX, voxelY, voxelZ);
              if (voxel) {
    -            for (const {dir} of VoxelWorld.faces) {
    +            for (const {dir, corners} of VoxelWorld.faces) {
                  const neighbor = this.getVoxel(
                      voxelX + dir[0],
                      voxelY + dir[1],
                      voxelZ + dir[2]);
                  if (!neighbor) {
                    // this voxel has no neighbor in this direction so we need a face.
    +                const ndx = positions.length / 3;
    +                for (const pos of corners) {
    +                  positions.push(pos[0] + x, pos[1] + y, pos[2] + z);
    +                  normals.push(...dir);
    +                }
    +                indices.push(
    +                  ndx, ndx + 1, ndx + 2,
    +                  ndx + 2, ndx + 1, ndx + 3,
    +                );
                  }
                }
              }
            }
          }
        }
    +    return {
    +      positions,
    +      normals,
    +      indices,
        };
      }
    }

    VoxelWorld.faces = [
      { // left
        dir: [ -1,  0,  0, ],
    +    corners: [
    +      [ 0, 1, 0 ],
    +      [ 0, 0, 0 ],
    +      [ 0, 1, 1 ],
    +      [ 0, 0, 1 ],
    +    ],
      },
      { // right
        dir: [  1,  0,  0, ],
    +    corners: [
    +      [ 1, 1, 1 ],
    +      [ 1, 0, 1 ],
    +      [ 1, 1, 0 ],
    +      [ 1, 0, 0 ],
    +    ],
      },
      { // bottom
        dir: [  0, -1,  0, ],
    +    corners: [
    +      [ 1, 0, 1 ],
    +      [ 0, 0, 1 ],
    +      [ 1, 0, 0 ],
    +      [ 0, 0, 0 ],
    +    ],
      },
      { // top
        dir: [  0,  1,  0, ],
    +    corners: [
    +      [ 0, 1, 1 ],
    +      [ 1, 1, 1 ],
    +      [ 0, 1, 0 ],
    +      [ 1, 1, 0 ],
    +    ],
      },
      { // back
        dir: [  0,  0, -1, ],
    +    corners: [
    +      [ 1, 0, 0 ],
    +      [ 0, 0, 0 ],
    +      [ 1, 1, 0 ],
    +      [ 0, 1, 0 ],
    +    ],
      },
      { // front
        dir: [  0,  0,  1, ],
    +    corners: [
    +      [ 0, 0, 1 ],
    +      [ 1, 0, 1 ],
    +      [ 0, 1, 1 ],
    +      [ 1, 1, 1 ],
    +    ],
      },
    ];

The code above would make basic geometry data for us. We just need to supply the `getVoxel` function. Let's start with just one hard coded cell.

    class VoxelWorld {
      constructor(cellSize) {
        this.cellSize = cellSize;
    +    this.cell = new Uint8Array(cellSize * cellSize * cellSize);
      }
    +  getCellForVoxel(x, y, z) {
    +    const {cellSize} = this;
    +    const cellX = Math.floor(x / cellSize);
    +    const cellY = Math.floor(y / cellSize);
    +    const cellZ = Math.floor(z / cellSize);
    +    if (cellX !== 0 || cellY !== 0 || cellZ !== 0) {
    +      return null
    +    }
    +    return this.cell;
    +  }
    +  getVoxel(x, y, z) {
    +    const cell = this.getCellForVoxel(x, y, z);
    +    if (!cell) {
    +      return 0;
    +    }
    +    const {cellSize} = this;
    +    const voxelX = THREE.MathUtils.euclideanModulo(x, cellSize) | 0;
    +    const voxelY = THREE.MathUtils.euclideanModulo(y, cellSize) | 0;
    +    const voxelZ = THREE.MathUtils.euclideanModulo(z, cellSize) | 0;
    +    const voxelOffset = voxelY * cellSize * cellSize +
    +                        voxelZ * cellSize +
    +                        voxelX;
    +    return cell[voxelOffset];
    +  }
      generateGeometryDataForCell(cellX, cellY, cellZ) {

      ...
    }

This seems like it would work. Let's make a `setVoxel` function so we can set some data.

    class VoxelWorld {
      constructor(cellSize) {
        this.cellSize = cellSize;
        this.cell = new Uint8Array(cellSize * cellSize * cellSize);
      }
      getCellForVoxel(x, y, z) {
        const {cellSize} = this;
        const cellX = Math.floor(x / cellSize);
        const cellY = Math.floor(y / cellSize);
        const cellZ = Math.floor(z / cellSize);
        if (cellX !== 0 || cellY !== 0 || cellZ !== 0) {
          return null
        }
        return this.cell;
      }
    +  setVoxel(x, y, z, v) {
    +    let cell = this.getCellForVoxel(x, y, z);
    +    if (!cell) {
    +      return;  // TODO: add a new cell?
    +    }
    +    const {cellSize} = this;
    +    const voxelX = THREE.MathUtils.euclideanModulo(x, cellSize) | 0;
    +    const voxelY = THREE.MathUtils.euclideanModulo(y, cellSize) | 0;
    +    const voxelZ = THREE.MathUtils.euclideanModulo(z, cellSize) | 0;
    +    const voxelOffset = voxelY * cellSize * cellSize +
    +                        voxelZ * cellSize +
    +                        voxelX;
    +    cell[voxelOffset] = v;
    +  }
      getVoxel(x, y, z) {
        const cell = this.getCellForVoxel(x, y, z);
        if (!cell) {
          return 0;
        }
        const {cellSize} = this;
        const voxelX = THREE.MathUtils.euclideanModulo(x, cellSize) | 0;
        const voxelY = THREE.MathUtils.euclideanModulo(y, cellSize) | 0;
        const voxelZ = THREE.MathUtils.euclideanModulo(z, cellSize) | 0;
        const voxelOffset = voxelY * cellSize * cellSize +
                            voxelZ * cellSize +
                            voxelX;
        return cell[voxelOffset];
      }
      generateGeometryDataForCell(cellX, cellY, cellZ) {

      ...
    }

Hmmm, I see a lot of repeated code. Let's fix that up

    class VoxelWorld {
      constructor(cellSize) {
        this.cellSize = cellSize;
    +    this.cellSliceSize = cellSize * cellSize;
        this.cell = new Uint8Array(cellSize * cellSize * cellSize);
      }
      getCellForVoxel(x, y, z) {
        const {cellSize} = this;
        const cellX = Math.floor(x / cellSize);
        const cellY = Math.floor(y / cellSize);
        const cellZ = Math.floor(z / cellSize);
        if (cellX !== 0 || cellY !== 0 || cellZ !== 0) {
          return null;
        }
        return this.cell;
      }
    +  computeVoxelOffset(x, y, z) {
    +    const {cellSize, cellSliceSize} = this;
    +    const voxelX = THREE.MathUtils.euclideanModulo(x, cellSize) | 0;
    +    const voxelY = THREE.MathUtils.euclideanModulo(y, cellSize) | 0;
    +    const voxelZ = THREE.MathUtils.euclideanModulo(z, cellSize) | 0;
    +    return voxelY * cellSliceSize +
    +           voxelZ * cellSize +
    +           voxelX;
    +  }
      setVoxel(x, y, z, v) {
        const cell = this.getCellForVoxel(x, y, z);
        if (!cell) {
          return;  // TODO: add a new cell?
        }
    -    const {cellSize} = this;
    -    const voxelX = THREE.MathUtils.euclideanModulo(x, cellSize) | 0;
    -    const voxelY = THREE.MathUtils.euclideanModulo(y, cellSize) | 0;
    -    const voxelZ = THREE.MathUtils.euclideanModulo(z, cellSize) | 0;
    -    const voxelOffset = voxelY * cellSize * cellSize +
    -                        voxelZ * cellSize +
    -                        voxelX;
    +    const voxelOffset = this.computeVoxelOffset(x, y, z);
        cell[voxelOffset] = v;
      }
      getVoxel(x, y, z) {
        const cell = this.getCellForVoxel(x, y, z);
        if (!cell) {
          return 0;
        }
    -    const {cellSize} = this;
    -    const voxelX = THREE.MathUtils.euclideanModulo(x, cellSize) | 0;
    -    const voxelY = THREE.MathUtils.euclideanModulo(y, cellSize) | 0;
    -    const voxelZ = THREE.MathUtils.euclideanModulo(z, cellSize) | 0;
    -    const voxelOffset = voxelY * cellSize * cellSize +
    -                        voxelZ * cellSize +
    -                        voxelX;
    +    const voxelOffset = this.computeVoxelOffset(x, y, z);
        return cell[voxelOffset];
      }
      generateGeometryDataForCell(cellX, cellY, cellZ) {

      ...
    }

Now let's make some code to fill out the first cell with voxels.

    const cellSize = 32;

    const world = new VoxelWorld(cellSize);

    for (let y = 0; y < cellSize; ++y) {
      for (let z = 0; z < cellSize; ++z) {
        for (let x = 0; x < cellSize; ++x) {
          const height = (Math.sin(x / cellSize * Math.PI * 2) + Math.sin(z / cellSize * Math.PI * 3)) * (cellSize / 6) + (cellSize / 2);
          if (y < height) {
            world.setVoxel(x, y, z, 1);
          }
        }
      }
    }

and some code to actually generate geometry like we covered in the article on custom BufferGeometry.

    const {positions, normals, indices} = world.generateGeometryDataForCell(0, 0, 0);
    const geometry = new THREE.BufferGeometry();
    const material = new THREE.MeshLambertMaterial({color: 'green'});

    const positionNumComponents = 3;
    const normalNumComponents = 3;
    geometry.setAttribute(
        'position',
        new THREE.BufferAttribute(new Float32Array(positions), positionNumComponents));
    geometry.setAttribute(
        'normal',
        new THREE.BufferAttribute(new Float32Array(normals), normalNumComponents));
    geometry.setIndex(indices);
    const mesh = new THREE.Mesh(geometry, material);
    scene.add(mesh);

let's try it

click here to open in a separate window

That seems to be working! Okay, let's add in textures.

Searching on the net I found this set of CC-BY-NC-SA licensed minecraft textures by Joshtimus. I picked a few at random and built this texture atlas.

To make things simple they are arranged a voxel type per column where the top row is the side of a voxel. The 2nd row is the top of voxel, and the 3rd row is the bottom of the voxel.

Knowing that we can add info to our `VoxelWorld.faces` data to specify for each face which row to use and the UVs to use for that face.

    VoxelWorld.faces = [
      { // left
    +    uvRow: 0,
        dir: [ -1,  0,  0, ],
        corners: [
    -      [ 0, 1, 0 ],
    -      [ 0, 0, 0 ],
    -      [ 0, 1, 1 ],
    -      [ 0, 0, 1 ],
    +      { pos: [ 0, 1, 0 ], uv: [ 0, 1 ], },
    +      { pos: [ 0, 0, 0 ], uv: [ 0, 0 ], },
    +      { pos: [ 0, 1, 1 ], uv: [ 1, 1 ], },
    +      { pos: [ 0, 0, 1 ], uv: [ 1, 0 ], },
        ],
      },
      { // right
    +    uvRow: 0,
        dir: [  1,  0,  0, ],
        corners: [
    -      [ 1, 1, 1 ],
    -      [ 1, 0, 1 ],
    -      [ 1, 1, 0 ],
    -      [ 1, 0, 0 ],
    +      { pos: [ 1, 1, 1 ], uv: [ 0, 1 ], },
    +      { pos: [ 1, 0, 1 ], uv: [ 0, 0 ], },
    +      { pos: [ 1, 1, 0 ], uv: [ 1, 1 ], },
    +      { pos: [ 1, 0, 0 ], uv: [ 1, 0 ], },
        ],
      },
      { // bottom
    +    uvRow: 1,
        dir: [  0, -1,  0, ],
        corners: [
    -      [ 1, 0, 1 ],
    -      [ 0, 0, 1 ],
    -      [ 1, 0, 0 ],
    -      [ 0, 0, 0 ],
    +      { pos: [ 1, 0, 1 ], uv: [ 1, 0 ], },
    +      { pos: [ 0, 0, 1 ], uv: [ 0, 0 ], },
    +      { pos: [ 1, 0, 0 ], uv: [ 1, 1 ], },
    +      { pos: [ 0, 0, 0 ], uv: [ 0, 1 ], },
        ],
      },
      { // top
    +    uvRow: 2,
        dir: [  0,  1,  0, ],
        corners: [
    -      [ 0, 1, 1 ],
    -      [ 1, 1, 1 ],
    -      [ 0, 1, 0 ],
    -      [ 1, 1, 0 ],
    +      { pos: [ 0, 1, 1 ], uv: [ 1, 1 ], },
    +      { pos: [ 1, 1, 1 ], uv: [ 0, 1 ], },
    +      { pos: [ 0, 1, 0 ], uv: [ 1, 0 ], },
    +      { pos: [ 1, 1, 0 ], uv: [ 0, 0 ], },
        ],
      },
      { // back
    +    uvRow: 0,
        dir: [  0,  0, -1, ],
        corners: [
    -      [ 1, 0, 0 ],
    -      [ 0, 0, 0 ],
    -      [ 1, 1, 0 ],
    -      [ 0, 1, 0 ],
    +      { pos: [ 1, 0, 0 ], uv: [ 0, 0 ], },
    +      { pos: [ 0, 0, 0 ], uv: [ 1, 0 ], },
    +      { pos: [ 1, 1, 0 ], uv: [ 0, 1 ], },
    +      { pos: [ 0, 1, 0 ], uv: [ 1, 1 ], },
        ],
      },
      { // front
    +    uvRow: 0,
        dir: [  0,  0,  1, ],
        corners: [
    -      [ 0, 0, 1 ],
    -      [ 1, 0, 1 ],
    -      [ 0, 1, 1 ],
    -      [ 1, 1, 1 ],
    +      { pos: [ 0, 0, 1 ], uv: [ 0, 0 ], },
    +      { pos: [ 1, 0, 1 ], uv: [ 1, 0 ], },
    +      { pos: [ 0, 1, 1 ], uv: [ 0, 1 ], },
    +      { pos: [ 1, 1, 1 ], uv: [ 1, 1 ], },
        ],
      },
    ];

And we can update the code to use that data. We need to know the size of a tile in the texture atlas and the dimensions of the texture.

    class VoxelWorld {
    -  constructor(cellSize) {
    -    this.cellSize = cellSize;
    +  constructor(options) {
    +    this.cellSize = options.cellSize;
    +    this.tileSize = options.tileSize;
    +    this.tileTextureWidth = options.tileTextureWidth;
    +    this.tileTextureHeight = options.tileTextureHeight;
    +    const {cellSize} = this;
    +    this.cellSliceSize = cellSize * cellSize;
    +    this.cell = new Uint8Array(cellSize * cellSize * cellSize);
      }

      ...

      generateGeometryDataForCell(cellX, cellY, cellZ) {
    -    const {cellSize} = this;
    +    const {cellSize, tileSize, tileTextureWidth, tileTextureHeight} = this;
        const positions = [];
        const normals = [];
    +    const uvs = [];
        const indices = [];
        const startX = cellX * cellSize;
        const startY = cellY * cellSize;
        const startZ = cellZ * cellSize;

        for (let y = 0; y < cellSize; ++y) {
          const voxelY = startY + y;
          for (let z = 0; z < cellSize; ++z) {
            const voxelZ = startZ + z;
            for (let x = 0; x < cellSize; ++x) {
              const voxelX = startX + x;
              const voxel = this.getVoxel(voxelX, voxelY, voxelZ);
              if (voxel) {
                const uvVoxel = voxel - 1;  // voxel 0 is sky so for UVs we start at 0
                // There is a voxel here but do we need faces for it?
    -            for (const {dir, corners} of VoxelWorld.faces) {
    +            for (const {dir, corners, uvRow} of VoxelWorld.faces) {
                  const neighbor = this.getVoxel(
                      voxelX + dir[0],
                      voxelY + dir[1],
                      voxelZ + dir[2]);
                  if (!neighbor) {
                    // this voxel has no neighbor in this direction so we need a face.
                    const ndx = positions.length / 3;
    -                for (const pos of corners) {
    +                for (const {pos, uv} of corners) {
                      positions.push(pos[0] + x, pos[1] + y, pos[2] + z);
                      normals.push(...dir);
    +                  uvs.push(
    +                        (uvVoxel +   uv[0]) * tileSize / tileTextureWidth,
    +                    1 - (uvRow + 1 - uv[1]) * tileSize / tileTextureHeight);
                    }
                    indices.push(
                      ndx, ndx + 1, ndx + 2,
                      ndx + 2, ndx + 1, ndx + 3,
                    );
                  }
                }
              }
            }
          }
        }

        return {
          positions,
          normals,
          uvs,
          indices,
        };
      }
    }

We then need to load the texture

    const loader = new THREE.TextureLoader();
    const texture = loader.load('resources/images/minecraft/flourish-cc-by-nc-sa.png', render);
    texture.magFilter = THREE.NearestFilter;
    texture.minFilter = THREE.NearestFilter;
    texture.colorSpace = THREE.SRGBColorSpace;

and pass the settings to the `VoxelWorld` class

    +const tileSize = 16;
    +const tileTextureWidth = 256;
    +const tileTextureHeight = 64;
    -const world = new VoxelWorld(cellSize);
    +const world = new VoxelWorld({
    +  cellSize,
    +  tileSize,
    +  tileTextureWidth,
    +  tileTextureHeight,
    +});

Let's actually use the UVs when we create the geometry and the texture when we make the material

    -const {positions, normals, indices} = world.generateGeometryDataForCell(0, 0, 0);
    +const {positions, normals, uvs, indices} = world.generateGeometryDataForCell(0, 0, 0);
    const geometry = new THREE.BufferGeometry();
    -const material = new THREE.MeshLambertMaterial({color: 'green'});
    +const material = new THREE.MeshLambertMaterial({
    +  map: texture,
    +  side: THREE.DoubleSide,
    +  alphaTest: 0.1,
    +  transparent: true,
    +});

    const positionNumComponents = 3;
    const normalNumComponents = 3;
    +const uvNumComponents = 2;
    geometry.setAttribute(
        'position',
        new THREE.BufferAttribute(new Float32Array(positions), positionNumComponents));
    geometry.setAttribute(
        'normal',
        new THREE.BufferAttribute(new Float32Array(normals), normalNumComponents));
    +geometry.setAttribute(
    +    'uv',
    +    new THREE.BufferAttribute(new Float32Array(uvs), uvNumComponents));
    geometry.setIndex(indices);
    const mesh = new THREE.Mesh(geometry, material);
    scene.add(mesh);

One last thing, we actually need to set some voxels to use different textures.

    for (let y = 0; y < cellSize; ++y) {
      for (let z = 0; z < cellSize; ++z) {
        for (let x = 0; x < cellSize; ++x) {
          const height = (Math.sin(x / cellSize * Math.PI * 2) + Math.sin(z / cellSize * Math.PI * 3)) * (cellSize / 6) + (cellSize / 2);
          if (y < height) {
    -        world.setVoxel(x, y, z, 1);
    +        world.setVoxel(x, y, z, randInt(1, 17));
          }
        }
      }
    }

    +function randInt(min, max) {
    +  return Math.floor(Math.random() * (max - min) + min);
    +}

and with that we get textures!

click here to open in a separate window

Let's make it support more than one cell.

To do this lets store cells in an object using cell ids. A cell id will just be a cell's coordinates separated by a comma. In other words if we ask for voxel 35,0,0 that is in cell 1,0,0 so its id is `"1,0,0"`.

    class VoxelWorld {
      constructor(options) {
        this.cellSize = options.cellSize;
        this.tileSize = options.tileSize;
        this.tileTextureWidth = options.tileTextureWidth;
        this.tileTextureHeight = options.tileTextureHeight;
        const {cellSize} = this;
        this.cellSliceSize = cellSize * cellSize;
    -    this.cell = new Uint8Array(cellSize * cellSize * cellSize);
    +    this.cells = {};
      }
    +  computeCellId(x, y, z) {
    +    const {cellSize} = this;
    +    const cellX = Math.floor(x / cellSize);
    +    const cellY = Math.floor(y / cellSize);
    +    const cellZ = Math.floor(z / cellSize);
    +    return `${cellX},${cellY},${cellZ}`;
    +  }
    +  getCellForVoxel(x, y, z) {
    -    const cellX = Math.floor(x / cellSize);
    -    const cellY = Math.floor(y / cellSize);
    -    const cellZ = Math.floor(z / cellSize);
    -    if (cellX !== 0 || cellY !== 0 || cellZ !== 0) {
    -      return null;
    -    }
    -    return this.cell;
    +    return this.cells[this.computeCellId(x, y, z)];
      }

       ...
    }

and now we can make `setVoxel` add new cells if we try to set a voxel in a cell that does not yet exist

      setVoxel(x, y, z, v) {
    -    const cell = this.getCellForVoxel(x, y, z);
    +    let cell = this.getCellForVoxel(x, y, z);
        if (!cell) {
    -      return 0;
    +      cell = this.addCellForVoxel(x, y, z);
        }
        const voxelOffset = this.computeVoxelOffset(x, y, z);
        cell[voxelOffset] = v;
      }
    +  addCellForVoxel(x, y, z) {
    +    const cellId = this.computeCellId(x, y, z);
    +    let cell = this.cells[cellId];
    +    if (!cell) {
    +      const {cellSize} = this;
    +      cell = new Uint8Array(cellSize * cellSize * cellSize);
    +      this.cells[cellId] = cell;
    +    }
    +    return cell;
    +  }

Let's make this editable.

First we`ll add a UI. Using radio buttons we can make an 8x2 array of tiles

    <body>
      <canvas id="c"></canvas>
    +  <div id="ui">
    +    <div class="tiles">
    +      <input type="radio" name="voxel" id="voxel1" value="1"><label for="voxel1" style="background-position:   -0% -0%"></label>
    +      <input type="radio" name="voxel" id="voxel2" value="2"><label for="voxel2" style="background-position: -100% -0%"></label>
    +      <input type="radio" name="voxel" id="voxel3" value="3"><label for="voxel3" style="background-position: -200% -0%"></label>
    +      <input type="radio" name="voxel" id="voxel4" value="4"><label for="voxel4" style="background-position: -300% -0%"></label>
    +      <input type="radio" name="voxel" id="voxel5" value="5"><label for="voxel5" style="background-position: -400% -0%"></label>
    +      <input type="radio" name="voxel" id="voxel6" value="6"><label for="voxel6" style="background-position: -500% -0%"></label>
    +      <input type="radio" name="voxel" id="voxel7" value="7"><label for="voxel7" style="background-position: -600% -0%"></label>
    +      <input type="radio" name="voxel" id="voxel8" value="8"><label for="voxel8" style="background-position: -700% -0%"></label>
    +    </div>
    +    <div class="tiles">
    +      <input type="radio" name="voxel" id="voxel9"  value="9" ><label for="voxel9"  style="background-position:  -800% -0%"></label>
    +      <input type="radio" name="voxel" id="voxel10" value="10"><label for="voxel10" style="background-position:  -900% -0%"></label>
    +      <input type="radio" name="voxel" id="voxel11" value="11"><label for="voxel11" style="background-position: -1000% -0%"></label>
    +      <input type="radio" name="voxel" id="voxel12" value="12"><label for="voxel12" style="background-position: -1100% -0%"></label>
    +      <input type="radio" name="voxel" id="voxel13" value="13"><label for="voxel13" style="background-position: -1200% -0%"></label>
    +      <input type="radio" name="voxel" id="voxel14" value="14"><label for="voxel14" style="background-position: -1300% -0%"></label>
    +      <input type="radio" name="voxel" id="voxel15" value="15"><label for="voxel15" style="background-position: -1400% -0%"></label>
    +      <input type="radio" name="voxel" id="voxel16" value="16"><label for="voxel16" style="background-position: -1500% -0%"></label>
    +    </div>
    +  </div>
    </body>

And add some CSS to style it, display the tiles and highlight the current selection

    body {
        margin: 0;
    }
    #c {
        width: 100%;
        height: 100%;
        display: block;
    }
    +#ui {
    +    position: absolute;
    +    left: 10px;
    +    top: 10px;
    +    background: rgba(0, 0, 0, 0.8);
    +    padding: 5px;
    +}
    +#ui input[type=radio] {
    +  width: 0;
    +  height: 0;
    +  display: none;
    +}
    +#ui input[type=radio] + label {
    +  background-image: url('resources/images/minecraft/flourish-cc-by-nc-sa.png');
    +  background-size: 1600% 400%;
    +  image-rendering: pixelated;
    +  width: 64px;
    +  height: 64px;
    +  display: inline-block;
    +}
    +#ui input[type=radio]:checked + label {
    +  outline: 3px solid red;
    +}
    +@media (max-width: 600px), (max-height: 600px) {
    +  #ui input[type=radio] + label {
    +    width: 32px;
    +    height: 32px;
    +  }
    +}

The UX will be as follows. If no tile is selected and you click a voxel that voxel will be erased or if you click a voxel and are holding the shift key it will be erased. Otherwise if a tiles is selected it will be added. You can deselect the selected tile type by clicking it again.

This code will let the user unselect the highlighted radio button.

    let currentVoxel = 0;
    let currentId;

    document.querySelectorAll('#ui .tiles input[type=radio][name=voxel]').forEach((elem) => {
      elem.addEventListener('click', allowUncheck);
    });

    function allowUncheck() {
      if (this.id === currentId) {
        this.checked = false;
        currentId = undefined;
        currentVoxel = 0;
      } else {
        currentId = this.id;
        currentVoxel = parseInt(this.value);
      }
    }

And this below code will let us set a voxel based on where the user clicks. It uses code similar to the code we made in the article on picking but it's not using the built in `RayCaster`. Instead it's using `VoxelWorld.intersectRay` which returns the position of intersection and the normal of the face hit.

    function getCanvasRelativePosition(event) {
      const rect = canvas.getBoundingClientRect();
      return {
        x: (event.clientX - rect.left) * canvas.width  / rect.width,
        y: (event.clientY - rect.top ) * canvas.height / rect.height,
      };
    }

    function placeVoxel(event) {
      const pos = getCanvasRelativePosition(event);
      const x = (pos.x / canvas.width ) *  2 - 1;
      const y = (pos.y / canvas.height) * -2 + 1;  // note we flip Y

      const start = new THREE.Vector3();
      const end = new THREE.Vector3();
      start.setFromMatrixPosition(camera.matrixWorld);
      end.set(x, y, 1).unproject(camera);

      const intersection = world.intersectRay(start, end);
      if (intersection) {
        const voxelId = event.shiftKey ? 0 : currentVoxel;
        // the intersection point is on the face. That means
        // the math imprecision could put us on either side of the face.
        // so go half a normal into the voxel if removing (currentVoxel = 0)
        // our out of the voxel if adding (currentVoxel  > 0)
        const pos = intersection.position.map((v, ndx) => {
          return v + intersection.normal[ndx] * (voxelId > 0 ? 0.5 : -0.5);
        });
        world.setVoxel(...pos, voxelId);
        updateVoxelGeometry(...pos);
        requestRenderIfNotRequested();
      }
    }

    const mouse = {
      x: 0,
      y: 0,
    };

    function recordStartPosition(event) {
      mouse.x = event.clientX;
      mouse.y = event.clientY;
      mouse.moveX = 0;
      mouse.moveY = 0;
    }
    function recordMovement(event) {
      mouse.moveX += Math.abs(mouse.x - event.clientX);
      mouse.moveY += Math.abs(mouse.y - event.clientY);
    }
    function placeVoxelIfNoMovement(event) {
      if (mouse.moveX < 5 && mouse.moveY < 5) {
        placeVoxel(event);
      }
      window.removeEventListener('pointermove', recordMovement);
      window.removeEventListener('pointerup', placeVoxelIfNoMovement);
    }
    canvas.addEventListener('pointerdown', (event) => {
      event.preventDefault();
      recordStartPosition(event);
      window.addEventListener('pointermove', recordMovement);
      window.addEventListener('pointerup', placeVoxelIfNoMovement);
    }, {passive: false});
    canvas.addEventListener('touchstart', (event) => {
      // stop scrolling
      event.preventDefault();
    }, {passive: false});

There's a lot going on in the code above. Basically the mouse has a dual purpose. One is to move the camera. The other is to edit the world. Placing/Erasing a voxel happen when you let off the mouse but only if you have not moved the mouse since you first pressed down. This is just a guess that if you did move the mouse you were trying to move the camera, not place a block. `moveX` and `moveY` are in absolute movement so if you move to the left 10 and then back to the right 10 you'll have moved 20 units. In that case the user likely was just rotating the model back and forth and does not want to place a block. I didn't do any testing to see if `5` is a good range or not.

In the code we call `world.setVoxel` to set a voxel and then `updateVoxelGeometry` to update the three.js geometry based on what's changed.

Let's make that now. If the user clicks a voxel on the edge of a cell then the geometry for the voxel in the adjacent cell might need new geometry. This means we need to check the cell for the voxel we just edited as well as in all 6 directions from that cell.

    const neighborOffsets = [
      [ 0,  0,  0], // self
      [-1,  0,  0], // left
      [ 1,  0,  0], // right
      [ 0, -1,  0], // down
      [ 0,  1,  0], // up
      [ 0,  0, -1], // back
      [ 0,  0,  1], // front
    ];
    function updateVoxelGeometry(x, y, z) {
      const updatedCellIds = {};
      for (const offset of neighborOffsets) {
        const ox = x + offset[0];
        const oy = y + offset[1];
        const oz = z + offset[2];
        const cellId = world.computeCellId(ox, oy, oz);
        if (!updatedCellIds[cellId]) {
          updatedCellIds[cellId] = true;
          updateCellGeometry(ox, oy, oz);
        }
      }
    }

I thought about checking for adjacent cells like

    const voxelX = THREE.MathUtils.euclideanModulo(x, cellSize) | 0;
    if (voxelX === 0) {
      // update cell to the left
    } else if (voxelX === cellSize - 1) {
      // update cell to the right
    }

and there would be 4 more checks for the other 4 directions but it occurred to me the code would be much simpler with just an array of offsets and saving off the cell ids of the cells we already updated. If the updated voxel is not on the edge of a cell then the test will quickly reject updating the same cell.

For `updateCellGeometry` we're just going to take the code we had before that was generating the geometry for one cell and make it handle multiple cells.

    const cellIdToMesh = {};
    function updateCellGeometry(x, y, z) {
      const cellX = Math.floor(x / cellSize);
      const cellY = Math.floor(y / cellSize);
      const cellZ = Math.floor(z / cellSize);
      const cellId = world.computeCellId(x, y, z);
      let mesh = cellIdToMesh[cellId];
      const geometry = mesh ? mesh.geometry : new THREE.BufferGeometry();

      const {positions, normals, uvs, indices} = world.generateGeometryDataForCell(cellX, cellY, cellZ);
      const positionNumComponents = 3;
      geometry.setAttribute('position', new THREE.BufferAttribute(new Float32Array(positions), positionNumComponents));
      const normalNumComponents = 3;
      geometry.setAttribute('normal', new THREE.BufferAttribute(new Float32Array(normals), normalNumComponents));
      const uvNumComponents = 2;
      geometry.setAttribute('uv', new THREE.BufferAttribute(new Float32Array(uvs), uvNumComponents));
      geometry.setIndex(indices);
      geometry.computeBoundingSphere();

      if (!mesh) {
        mesh = new THREE.Mesh(geometry, material);
        mesh.name = cellId;
        cellIdToMesh[cellId] = mesh;
        scene.add(mesh);
        mesh.position.set(cellX * cellSize, cellY * cellSize, cellZ * cellSize);
      }
    }

The code above checks a map of cell ids to meshes. If we ask for a cell that doesn't exist a new `Mesh` is made and added to the correct place in world space. At the end we update the attributes and indices with the new data.

click here to open in a separate window

Some notes:

`RayCaster` might have worked just fine. I didn't try it. Instead I found a voxel specific raycaster. that is optimized for voxels.

I made `intersectRay` part of VoxelWorld because it seemed like if it gets too slow we could raycast against cells before raycasting on voxels as a simple speed up if it becomes too slow.

You might want to change the length of the raycast as currently it's all the way to Z-far. I expect if the user clicks something too far way they don't really want to be placing blocks on the other side of the world that are 1 or 2 pixel large.

Calling `geometry.computeBoundingSphere` might be slow. We could just manually set the bounding sphere to the fit the entire cell.

Do we want remove cells if all voxels in that cell are 0? That would probably be reasonable change if we wanted to ship this.

Thinking about how this works it's clear the absolute worst case is a checkerboard of on and off voxels. I don't know off the top of my head what other strategies to use if things get too slow. Maybe getting too slow would just encourage the user not to make giant checkerboard areas.

To keep it simple the texture atlas is just 1 column per voxel type. It would be better to make something more flexible where we have a table of voxel types and each type can specify where its face textures are in the atlas. As it is lots of space is wasted.

Looking at real minecraft there are tiles that are not voxels, not cubes. Like a fence tile or flowers. To do that we'd again need some table of voxel types and for each voxel whether it's a cube or some other geometry. If it's not a cube the neighbor check when generating the geometry would also need to change. A flower voxel next to another voxel should not remove the faces between them.

If you want to make some minecraft like thing using three.js I hope this has given you some ideas where to start and how to generate some what efficient geometry.