In the previous article we put vertex data in a storage buffer and indexed it using the builtin vertex_index. While that technique is growing in popularity, the traditional way to provide vertex data to a vertex shader is via vertex buffers and attributes.

Vertex buffers are just like any other WebGPU buffer; they hold data. The difference is we don’t access them directly from the vertex shader. Instead, we tell WebGPU what kind of data is in the buffer and how it’s organized. It then pulls the data out of the buffer and provides it for us.

Let’s take the last example from the previous article and change it from using a storage buffer to using a vertex buffer.

The first thing to do is change the shader to get its vertex data from a vertex buffer.

struct OurStruct {
  color: vec4f,
  offset: vec2f,
};

struct OtherStruct {
  scale: vec2f,
};

struct Vertex {
-  position: vec2f,
+  @location(0) position: vec2f,
};

struct VSOutput {
  @builtin(position) position: vec4f,
  @location(0) color: vec4f,
};

@group(0) @binding(0) var<storage, read> ourStructs: array<OurStruct>;
@group(0) @binding(1) var<storage, read> otherStructs: array<OtherStruct>;
-@group(0) @binding(2) var<storage, read> pos: array<Vertex>;

@vertex fn vs(
-  @builtin(vertex_index) vertexIndex : u32,
+  vert: Vertex,
  @builtin(instance_index) instanceIndex: u32
) -> VSOutput {
  let otherStruct = otherStructs[instanceIndex];
  let ourStruct = ourStructs[instanceIndex];

  var vsOut: VSOutput;
  vsOut.position = vec4f(
-      pos[vertexIndex].position * otherStruct.scale + ourStruct.offset, 0.0, 1.0);
+      vert.position * otherStruct.scale + ourStruct.offset, 0.0, 1.0);
  vsOut.color = ourStruct.color;
  return vsOut;
}

...

As you can see, it’s a small change. The important part is declaring the position field with @location(0).

Next, we have to tell WebGPU how to supply data for @location(0) - for that, we use the render pipeline:

  const pipeline = device.createRenderPipeline({
    label: 'vertex buffer pipeline',
    layout: 'auto',
    vertex: {
      module,
+      buffers: [
+        {
+          arrayStride: 2 * 4, // 2 floats, 4 bytes each
+          attributes: [
+            {shaderLocation: 0, offset: 0, format: 'float32x2'},  // position
+          ],
+        },
+      ],
    },
    fragment: {
      module,
      targets: [{ format: presentationFormat }],
    },
  });

To the vertex entry of the pipeline descriptor we added a buffers array which is used to describe how to pull data out of 1 or more vertex buffers. For our first and only buffer, we set an arrayStride in number of bytes. A stride in this case is how many bytes to get from the data for one vertex in the buffer, to the next vertex in the buffer.

Since our data is vec2f, which is two float32 numbers, we set the arrayStride to 8.

Next we define an array of attributes. We only have one: shaderLocation: 0 corresponds to location(0) in our Vertex struct. offset: 0 says the data for this attribute starts at byte 0 in the vertex buffer. Finally format: 'float32x2' says we want WebGPU to pull the data out of the buffer as two 32bit floating point numbers. (Note: the attributes property is shown in the simplified draw diagram from the first article).

We need to change the usages of the buffer holding vertex data from STORAGE to VERTEX and remove it from the bind group.

-  const vertexStorageBuffer = device.createBuffer({
-    label: 'storage buffer vertices',
-    size: vertexData.byteLength,
-    usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_DST,
-  });
+  const vertexBuffer = device.createBuffer({
+    label: 'vertex buffer vertices',
+    size: vertexData.byteLength,
+    usage: GPUBufferUsage.VERTEX | GPUBufferUsage.COPY_DST,
+  });
+  device.queue.writeBuffer(vertexBuffer, 0, vertexData);

  const bindGroup = device.createBindGroup({
    label: 'bind group for objects',
    layout: pipeline.getBindGroupLayout(0),
    entries: [
      { binding: 0, resource: { buffer: staticStorageBuffer }},
      { binding: 1, resource: { buffer: changingStorageBuffer }},
-      { binding: 2, resource: { buffer: vertexStorageBuffer }},
    ],
  });

Then, at draw time we need to tell WebGPU which vertex buffer to use:

    pass.setPipeline(pipeline);
+    pass.setVertexBuffer(0, vertexBuffer);

The 0 here corresponds to first element of the render pipeline buffers array we specified above.

With that, we’ve switched from using a storage buffer for vertices to a vertex buffer.

The state when the draw command is executed would look something like this:

The attribute format field can be one of these types:

Instancing with Vertex Buffers

Attributes can advance per vertex or per instance. Advancing them per instance is effectively the same thing we’re doing when we index otherStructs[instanceIndex] and ourStructs[instanceIndex] where instanceIndex got its value from @builtin(instance_index).

Let’s get rid of the storage buffers and use vertex buffers to accomplish the same thing. First lets change the shader to use vertex attributes instead of storage buffers.

-struct OurStruct {
-  color: vec4f,
-  offset: vec2f,
-};
-
-struct OtherStruct {
-  scale: vec2f,
-};

struct Vertex {
  @location(0) position: vec2f,
+  @location(1) color: vec4f,
+  @location(2) offset: vec2f,
+  @location(3) scale: vec2f,
};

struct VSOutput {
  @builtin(position) position: vec4f,
  @location(0) color: vec4f,
};

-@group(0) @binding(0) var<storage, read> ourStructs: array<OurStruct>;
-@group(0) @binding(1) var<storage, read> otherStructs: array<OtherStruct>;

@vertex fn vs(
  vert: Vertex,
-  @builtin(instance_index) instanceIndex: u32
) -> VSOutput {
-  let otherStruct = otherStructs[instanceIndex];
-  let ourStruct = ourStructs[instanceIndex];

  var vsOut: VSOutput;
-  vsOut.position = vec4f(
-      vert.position * otherStruct.scale + ourStruct.offset, 0.0, 1.0);
-  vsOut.color = ourStruct.color;
+  vsOut.position = vec4f(
+      vert.position * vert.scale + vert.offset, 0.0, 1.0);
+  vsOut.color = vert.color;
  return vsOut;
}

@fragment fn fs(vsOut: VSOutput) -> @location(0) vec4f {
  return vsOut.color;
}

Now we need to update our render pipeline to tell it how we want to supply data to those attributes. To keep the changes to a minimum we’ll use the data we created for the storage buffers almost as is. We’ll use two buffers, one buffer will hold the color and offset per instance, the other will hold the scale.

  const pipeline = device.createRenderPipeline({
    label: 'flat colors',
    layout: 'auto',
    vertex: {
      module,
      buffers: [
        {
          arrayStride: 2 * 4, // 2 floats, 4 bytes each
          attributes: [
            {shaderLocation: 0, offset: 0, format: 'float32x2'},  // position
          ],
        },
+        {
+          arrayStride: 6 * 4, // 6 floats, 4 bytes each
+          stepMode: 'instance',
+          attributes: [
+            {shaderLocation: 1, offset:  0, format: 'float32x4'},  // color
+            {shaderLocation: 2, offset: 16, format: 'float32x2'},  // offset
+          ],
+        },
+        {
+          arrayStride: 2 * 4, // 2 floats, 4 bytes each
+          stepMode: 'instance',
+          attributes: [
+            {shaderLocation: 3, offset: 0, format: 'float32x2'},   // scale
+          ],
+        },
      ],
    },
    fragment: {
      module,
      targets: [{ format: presentationFormat }],
    },
  });

Above we added 2 entries to the buffers array on our pipeline description so now there are 3 buffer entries, meaning we’re telling WebGPU we’ll supply the data in 3 buffers.

For our 2 new entries we set the stepMode to instance. This means this attribute will only advance to next value once per instance. The default is stepMode: 'vertex' which advances once per vertex (and starts over for each instance).

We have 2 buffers. The one that holds just scale is simple. Just like our first buffer that holds position it’s 2 32 floats per vertex.

Our other buffer holds color and offset and they’re going to be interleaved in the data like this

So above we say the arrayStride to get from one set of data to the next is 6 * 4, 6 32bit floats each 4 bytes (24 bytes total). The color starts at offset 0 but the offset starts 16 bytes in.

Next we can change the code that sets up the buffers.

  // create 2 storage buffers
  const staticUnitSize =
    4 * 4 + // color is 4 32bit floats (4bytes each)
-    2 * 4 + // offset is 2 32bit floats (4bytes each)
-    2 * 4;  // padding
+    2 * 4;  // offset is 2 32bit floats (4bytes each)

  const changingUnitSize =
    2 * 4;  // scale is 2 32bit floats (4bytes each)
*  const staticVertexBufferSize = staticUnitSize * kNumObjects;
*  const changingVertexBufferSize = changingUnitSize * kNumObjects;

*  const staticVertexBuffer = device.createBuffer({
*    label: 'static vertex for objects',
*    size: staticVertexBufferSize,
-    usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_DST,
+    usage: GPUBufferUsage.VERTEX | GPUBufferUsage.COPY_DST,
  });

*  const changingVertexBuffer = device.createBuffer({
*    label: 'changing vertex for objects',
*    size: changingVertexBufferSize,
-    usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_DST,
+    usage: GPUBufferUsage.VERTEX | GPUBufferUsage.COPY_DST,
  });

Vertex attributes do not have the same padding restrictions as structures in storage buffers so we no longer need the padding. Otherwise all we did was change the usage from STORAGE to VERTEX (and we renamed all the variables from “storage” to “vertex”).

Since we’re no longer using the storage buffers we no longer need the bind group:

-  const bindGroup = device.createBindGroup({
-    label: 'bind group for objects',
-    layout: pipeline.getBindGroupLayout(0),
-    entries: [
-      { binding: 0, resource: { buffer: staticStorageBuffer }},
-      { binding: 1, resource: { buffer: changingStorageBuffer }},
-    ],
-  });

Finally, we don’t need to set the bind group but, we do need to set the vertex buffers:

    const encoder = device.createCommandEncoder();
    const pass = encoder.beginRenderPass(renderPassDescriptor);
    pass.setPipeline(pipeline);
    pass.setVertexBuffer(0, vertexBuffer);
+    pass.setVertexBuffer(1, staticVertexBuffer);
+    pass.setVertexBuffer(2, changingVertexBuffer);

    ...
-    pass.setBindGroup(0, bindGroup);
    pass.draw(numVertices, kNumObjects);

    pass.end();

Here the first parameter to setVertexBuffer corresponds to the elements of the buffers array in the pipeline we created above.

With that we have the same thing we had before, but we’re using all vertex buffers and no storage buffers.

Just for fun, let’s add another attribute for a per vertex color. First let’s change the shader:

struct Vertex {
  @location(0) position: vec2f,
  @location(1) color: vec4f,
  @location(2) offset: vec2f,
  @location(3) scale: vec2f,
+  @location(4) perVertexColor: vec3f,
};

struct VSOutput {
  @builtin(position) position: vec4f,
  @location(0) color: vec4f,
};

@vertex fn vs(
  vert: Vertex,
) -> VSOutput {
  var vsOut: VSOutput;
  vsOut.position = vec4f(
      vert.position * vert.scale + vert.offset, 0.0, 1.0);
-  vsOut.color = vert.color;
+  vsOut.color = vert.color * vec4f(vert.perVertexColor, 1);
  return vsOut;
}

@fragment fn fs(vsOut: VSOutput) -> @location(0) vec4f {
  return vsOut.color;
}

Then we need to update the pipeline to describe how we’ll supply the data. We’re going to interleave the perVertexColor data with the position like this:

So, the arrayStride needs to be changed to cover our new data and we need to add the new attribute. It starts after two 32bit floating point numbers so its offset into the buffer is 8 bytes.

  const pipeline = device.createRenderPipeline({
    label: 'per vertex color',
    layout: 'auto',
    vertex: {
      module,
      buffers: [
        {
-          arrayStride: 2 * 4, // 2 floats, 4 bytes each
+          arrayStride: 5 * 4, // 5 floats, 4 bytes each
          attributes: [
            {shaderLocation: 0, offset: 0, format: 'float32x2'},  // position
+            {shaderLocation: 4, offset: 8, format: 'float32x3'},  // perVertexColor
          ],
        },
        {
          arrayStride: 6 * 4, // 6 floats, 4 bytes each
          stepMode: 'instance',
          attributes: [
            {shaderLocation: 1, offset:  0, format: 'float32x4'},  // color
            {shaderLocation: 2, offset: 16, format: 'float32x2'},  // offset
          ],
        },
        {
          arrayStride: 2 * 4, // 2 floats, 4 bytes each
          stepMode: 'instance',
          attributes: [
            {shaderLocation: 3, offset: 0, format: 'float32x2'},   // scale
          ],
        },
      ],
    },
    fragment: {
      module,
      targets: [{ format: presentationFormat }],
    },
  });

We’ll update the circle vertex generation code to provide a dark color for vertices on the outer edge of the circle and a light color for the inner vertices.

function createCircleVertices({
  radius = 1,
  numSubdivisions = 24,
  innerRadius = 0,
  startAngle = 0,
  endAngle = Math.PI * 2,
} = {}) {
  // 2 triangles per subdivision, 3 verts per tri, 5 values (xyrgb) each.
  const numVertices = numSubdivisions * 3 * 2;
-  const vertexData = new Float32Array(numVertices * 2);
+  const vertexData = new Float32Array(numVertices * (2 + 3));

  let offset = 0;
-  const addVertex = (x, y, r, g, b) => {
+  const addVertex = (x, y, r, g, b) => {
    vertexData[offset++] = x;
    vertexData[offset++] = y;
+    vertexData[offset++] = r;
+    vertexData[offset++] = g;
+    vertexData[offset++] = b;
  };

+  const innerColor = [1, 1, 1];
+  const outerColor = [0.1, 0.1, 0.1];

  // 2 triangles per subdivision
  //
  // 0--1 4
  // | / /|
  // |/ / |
  // 2 3--5
  for (let i = 0; i < numSubdivisions; ++i) {
    const angle1 = startAngle + (i + 0) * (endAngle - startAngle) / numSubdivisions;
    const angle2 = startAngle + (i + 1) * (endAngle - startAngle) / numSubdivisions;

    const c1 = Math.cos(angle1);
    const s1 = Math.sin(angle1);
    const c2 = Math.cos(angle2);
    const s2 = Math.sin(angle2);

    // first triangle
-    addVertex(c1 * radius, s1 * radius);
-    addVertex(c2 * radius, s2 * radius);
-    addVertex(c1 * innerRadius, s1 * innerRadius);
+    addVertex(c1 * radius, s1 * radius, ...outerColor);
+    addVertex(c2 * radius, s2 * radius, ...outerColor);
+    addVertex(c1 * innerRadius, s1 * innerRadius, ...innerColor);

    // second triangle
-    addVertex(c1 * innerRadius, s1 * innerRadius);
-    addVertex(c2 * radius, s2 * radius);
-    addVertex(c2 * innerRadius, s2 * innerRadius);
+    addVertex(c1 * innerRadius, s1 * innerRadius, ...innerColor);
+    addVertex(c2 * radius, s2 * radius, ...outerColor);
+    addVertex(c2 * innerRadius, s2 * innerRadius, ...innerColor);
  }

  return {
    vertexData,
    numVertices,
  };
}

And with that we get shaded circles:

Attributes in WGSL do not have to match attributes in JavaScript

Above in WGSL we declared the perVertexColor attribute as a vec3f like this:

struct Vertex {
  @location(0) position: vec2f,
  @location(1) color: vec4f,
  @location(2) offset: vec2f,
  @location(3) scale: vec2f,
*  @location(4) perVertexColor: vec3f,
};

And used it like this:

@vertex fn vs(
  vert: Vertex,
) -> VSOutput {
  var vsOut: VSOutput;
  vsOut.position = vec4f(
      vert.position * vert.scale + vert.offset, 0.0, 1.0);
*  vsOut.color = vert.color * vec4f(vert.perVertexColor, 1);
  return vsOut;
}

We could also declare it as a vec4f and use it like this:

struct Vertex {
  @location(0) position: vec2f,
  @location(1) color: vec4f,
  @location(2) offset: vec2f,
  @location(3) scale: vec2f,
-  @location(4) perVertexColor: vec3f,
+  @location(4) perVertexColor: vec4f,
};

...

@vertex fn vs(
  vert: Vertex,
) -> VSOutput {
  var vsOut: VSOutput;
  vsOut.position = vec4f(
      vert.position * vert.scale + vert.offset, 0.0, 1.0);
-  vsOut.color = vert.color * vec4f(vert.perVertexColor, 1);
+  vsOut.color = vert.color * vert.perVertexColor;
  return vsOut;
}

And change nothing else. In JavaScript we’re still only supplying the data as 3 floats per vertex.

    {
      arrayStride: 5 * 4, // 5 floats, 4 bytes each
      attributes: [
        {shaderLocation: 0, offset: 0, format: 'float32x2'},  // position
*        {shaderLocation: 4, offset: 8, format: 'float32x3'},  // perVertexColor
      ],
    },

This works because attributes always have 4 values available in the shader. They default to 0, 0, 0, 1 so any values we don’t supply get these defaults.

Using normalized values to save space

We’re using 32bit floating point values for colors. Each perVertexColor has 3 values for a total of 12 bytes per color per vertex. Each color has 4 values for a total of 16 bytes per color per instance.

We could optimize that by using 8bit values and telling WebGPU they should be normalized from 0 ↔ 255 to 0.0 ↔ 1.0.

Looking at the list of valid attribute formats there is no 3 value 8bit format but there is 'unorm8x4' so let’s use that.

First let’s change the code that generates the vertices to store colors as 8bit values that will be normalized:

function createCircleVertices({
  radius = 1,
  numSubdivisions = 24,
  innerRadius = 0,
  startAngle = 0,
  endAngle = Math.PI * 2,
} = {}) {
-  // 2 triangles per subdivision, 3 verts per tri, 5 values (xyrgb) each.
+  // 2 triangles per subdivision, 3 verts per tri
  const numVertices = numSubdivisions * 3 * 2;
-  const vertexData = new Float32Array(numVertices * (2 + 3));
+  // 2 32-bit values for position (xy) and 1 32-bit value for color (rgb_)
+  // The 32-bit color value will be written/read as 4 8-bit values
+  const vertexData = new Float32Array(numVertices * (2 + 1));
+  const colorData = new Uint8Array(vertexData.buffer);

  let offset = 0;
+  let colorOffset = 8;
  const addVertex = (x, y, r, g, b) => {
    vertexData[offset++] = x;
    vertexData[offset++] = y;
-    vertexData[offset++] = r;
-    vertexData[offset++] = g;
-    vertexData[offset++] = b;
+    offset += 1;  // skip the color
+    colorData[colorOffset++] = r * 255;
+    colorData[colorOffset++] = g * 255;
+    colorData[colorOffset++] = b * 255;
+    colorOffset += 9;  // skip extra byte and the position
  };

Above we make colorData, which is a Uint8Array view of the same data as vertexData. Review the data memory layout article if this is unclear.

We then use colorData to insert the colors, expanding them from 0 ↔ 1 to 0 ↔ 255.

The memory layout of this (per vertex) data is like this:

We also need to update the per instance data.

  const kNumObjects = 100;
  const objectInfos = [];

  // create 2 vertex buffers
  const staticUnitSize =
-    4 * 4 + // color is 4 32bit floats (4bytes each)
+    4 +     // color is 4 bytes
    2 * 4;  // offset is 2 32bit floats (4bytes each)
  const changingUnitSize =
    2 * 4;  // scale is 2 32bit floats (4bytes each)
  const staticVertexBufferSize = staticUnitSize * kNumObjects;
  const changingVertexBufferSize = changingUnitSize * kNumObjects;

  const staticVertexBuffer = device.createBuffer({
    label: 'static vertex for objects',
    size: staticVertexBufferSize,
    usage: GPUBufferUsage.VERTEX | GPUBufferUsage.COPY_DST,
  });

  const changingVertexBuffer = device.createBuffer({
    label: 'changing storage for objects',
    size: changingVertexBufferSize,
    usage: GPUBufferUsage.VERTEX | GPUBufferUsage.COPY_DST,
  });

  // offsets to the various uniform values in float32 indices
  const kColorOffset = 0;
  const kOffsetOffset = 1;

  const kScaleOffset = 0;

  {
-    const staticVertexValues = new Float32Array(staticVertexBufferSize / 4);
+    const staticVertexValuesU8 = new Uint8Array(staticVertexBufferSize);
+    const staticVertexValuesF32 = new Float32Array(staticVertexValuesU8.buffer);
    for (let i = 0; i < kNumObjects; ++i) {
-      const staticOffset = i * (staticUnitSize / 4);
+      const staticOffsetU8 = i * staticUnitSize;
+      const staticOffsetF32 = staticOffsetU8 / 4;

      // These are only set once so set them now
-      staticVertexValues.set([rand(), rand(), rand(), 1], staticOffset + kColorOffset);        // set the color
-      staticVertexValues.set([rand(-0.9, 0.9), rand(-0.9, 0.9)], staticOffset + kOffsetOffset);      // set the offset
+      staticVertexValuesU8.set(        // set the color
+          [rand() * 255, rand() * 255, rand() * 255, 255],
+          staticOffsetU8 + kColorOffset);
+
+      staticVertexValuesF32.set(      // set the offset
+          [rand(-0.9, 0.9), rand(-0.9, 0.9)],
+          staticOffsetF32 + kOffsetOffset);

      objectInfos.push({
        scale: rand(0.2, 0.5),
      });
    }
    device.queue.writeBuffer(staticVertexBuffer, 0, staticVertexValuesF32);
  }

The layout for the per instance data is like this:

We then need to change the pipeline to pull out the data as 8bit unsigned values and to normalize them back to 0 ↔ 1, update the offsets, and update the stride to its new size.

  const pipeline = device.createRenderPipeline({
    label: 'per vertex color',
    layout: 'auto',
    vertex: {
      module,
      buffers: [
        {
-          arrayStride: 5 * 4, // 5 floats, 4 bytes each
+          arrayStride: 2 * 4 + 4, // 2 floats, 4 bytes each + 4 bytes
          attributes: [
            {shaderLocation: 0, offset: 0, format: 'float32x2'},  // position
-            {shaderLocation: 4, offset: 8, format: 'float32x3'},  // perVertexColor
+            {shaderLocation: 4, offset: 8, format: 'unorm8x4'},   // perVertexColor
          ],
        },
        {
-          arrayStride: 6 * 4, // 6 floats, 4 bytes each
+          arrayStride: 4 + 2 * 4, // 4 bytes + 2 floats, 4 bytes each
          stepMode: 'instance',
          attributes: [
-            {shaderLocation: 1, offset:  0, format: 'float32x4'},  // color
-            {shaderLocation: 2, offset: 16, format: 'float32x2'},  // offset
+            {shaderLocation: 1, offset: 0, format: 'unorm8x4'},   // color
+            {shaderLocation: 2, offset: 4, format: 'float32x2'},  // offset
          ],
        },
        {
          arrayStride: 2 * 4, // 2 floats, 4 bytes each
          stepMode: 'instance',
          attributes: [
            {shaderLocation: 3, offset: 0, format: 'float32x2'},   // scale
          ],
        },
      ],
    },
    fragment: {
      module,
      targets: [{ format: presentationFormat }],
    },
  });

And with that we’ve save a little space. We were using 20 bytes per vertex, now we’re using 12 bytes per vertex, a 40% savings. And we were using 24 bytes per instance, now we’re using 12, a 50% savings.

Note that we don’t have to use a struct. This would work just as well:

@vertex fn vs(
-  vert: Vertex,
+  @location(0) position: vec2f,
+  @location(1) color: vec4f,
+  @location(2) offset: vec2f,
+  @location(3) scale: vec2f,
+  @location(4) perVertexColor: vec3f,
) -> VSOutput {
  var vsOut: VSOutput;
-  vsOut.position = vec4f(
-      vert.position * vert.scale + vert.offset, 0.0, 1.0);
-  vsOut.color = vert.color * vec4f(vert.perVertexColor, 1);
+  vsOut.position = vec4f(
+      position * scale + offset, 0.0, 1.0);
+  vsOut.color = color * vec4f(perVertexColor, 1);
  return vsOut;
}

As again, all WebGPU cares about that we define locations in the shader and supply data to those locations via the API.

Index Buffers

One last thing to cover here are index buffers. Index buffers describe the order to process and use the vertices.

You can think of draw as going through the vertices in order:

0, 1, 2, 3, 4, 5, .....

With an index buffer we can change that order.

We were creating 6 vertices per subdivision of the circle even though 2 of them were identical.

Now instead, we’ll only create 4 but then use indices to use those 4 vertices 6 times by telling WebGPU to draw indices in this order:

0, 1, 2, 2, 1, 3, ...

function createCircleVertices({
  radius = 1,
  numSubdivisions = 24,
  innerRadius = 0,
  startAngle = 0,
  endAngle = Math.PI * 2,
} = {}) {
-  // 2 triangles per subdivision, 3 verts per tri
-  const numVertices = numSubdivisions * 3 * 2;
+  // 2 vertices at each subdivision, + 1 to wrap around the circle.
+  const numVertices = (numSubdivisions + 1) * 2;
  // 2 32-bit values for position (xy) and 1 32-bit value for color (rgb)
  // The 32-bit color value will be written/read as 4 8-bit values
  const vertexData = new Float32Array(numVertices * (2 + 1));
  const colorData = new Uint8Array(vertexData.buffer);

  let offset = 0;
  let colorOffset = 8;
  const addVertex = (x, y, r, g, b) => {
    vertexData[offset++] = x;
    vertexData[offset++] = y;
    offset += 1;  // skip the color
    colorData[colorOffset++] = r * 255;
    colorData[colorOffset++] = g * 255;
    colorData[colorOffset++] = b * 255;
    colorOffset += 9;  // skip extra byte and the position
  };
  const innerColor = [1, 1, 1];
  const outerColor = [0.1, 0.1, 0.1];

-  // 2 triangles per subdivision
-  //
-  // 0--1 4
-  // | / /|
-  // |/ / |
-  // 2 3--5
-  for (let i = 0; i < numSubdivisions; ++i) {
-    const angle1 = startAngle + (i + 0) * (endAngle - startAngle) / numSubdivisions;
-    const angle2 = startAngle + (i + 1) * (endAngle - startAngle) / numSubdivisions;
-
-    const c1 = Math.cos(angle1);
-    const s1 = Math.sin(angle1);
-    const c2 = Math.cos(angle2);
-    const s2 = Math.sin(angle2);
-
-    // first triangle
-    addVertex(c1 * radius, s1 * radius, ...outerColor);
-    addVertex(c2 * radius, s2 * radius, ...outerColor);
-    addVertex(c1 * innerRadius, s1 * innerRadius, ...innerColor);
-
-    // second triangle
-    addVertex(c1 * innerRadius, s1 * innerRadius, ...innerColor);
-    addVertex(c2 * radius, s2 * radius, ...outerColor);
-    addVertex(c2 * innerRadius, s2 * innerRadius, ...innerColor);
-  }
+  // 2 triangles per subdivision
+  //
+  // 0  2  4  6  8 ...
+  //
+  // 1  3  5  7  9 ...
+  for (let i = 0; i <= numSubdivisions; ++i) {
+    const angle = startAngle + (i + 0) * (endAngle - startAngle) / numSubdivisions;
+
+    const c1 = Math.cos(angle);
+    const s1 = Math.sin(angle);
+
+    addVertex(c1 * radius, s1 * radius, ...outerColor);
+    addVertex(c1 * innerRadius, s1 * innerRadius, ...innerColor);
+  }

+  const indexData = new Uint32Array(numSubdivisions * 6);
+  let ndx = 0;
+
+  // 1st tri  2nd tri  3rd tri  4th tri
+  // 0 1 2    2 1 3    2 3 4    4 3 5
+  //
+  // 0--2        2     2--4        4  .....
+  // | /        /|     | /        /|
+  // |/        / |     |/        / |
+  // 1        1--3     3        3--5  .....
+  for (let i = 0; i < numSubdivisions; ++i) {
+    const ndxOffset = i * 2;
+
+    // first triangle
+    indexData[ndx++] = ndxOffset;
+    indexData[ndx++] = ndxOffset + 1;
+    indexData[ndx++] = ndxOffset + 2;
+
+    // second triangle
+    indexData[ndx++] = ndxOffset + 2;
+    indexData[ndx++] = ndxOffset + 1;
+    indexData[ndx++] = ndxOffset + 3;
+  }

  return {
    vertexData,
+    indexData,
-    numVertices,
+    numVertices: indexData.length,
  };
}

Then we need to create an index buffer:

-  const { vertexData, numVertices } = createCircleVertices({
+  const { vertexData, indexData, numVertices } = createCircleVertices({
    radius: 0.5,
    innerRadius: 0.25,
  });
  const vertexBuffer = device.createBuffer({
    label: 'vertex buffer',
    size: vertexData.byteLength,
    usage: GPUBufferUsage.VERTEX | GPUBufferUsage.COPY_DST,
  });
  device.queue.writeBuffer(vertexBuffer, 0, vertexData);
+  const indexBuffer = device.createBuffer({
+    label: 'index buffer',
+    size: indexData.byteLength,
+    usage: GPUBufferUsage.INDEX | GPUBufferUsage.COPY_DST,
+  });
+  device.queue.writeBuffer(indexBuffer, 0, indexData);

Notice we set the usage to INDEX.

Then finally at draw time we need to specify the index buffer:

    pass.setPipeline(pipeline);
    pass.setVertexBuffer(0, vertexBuffer);
    pass.setVertexBuffer(1, staticVertexBuffer);
    pass.setVertexBuffer(2, changingVertexBuffer);
+    pass.setIndexBuffer(indexBuffer, 'uint32');

Because our buffer contains 32bit unsigned integer indices we need to pass 'uint32' here. We could also use 16 bit unsigned indices in which case we’d pass in 'uint16'.

And we need to call drawIndexed instead of draw:

-    pass.draw(numVertices, kNumObjects);
+    pass.drawIndexed(numVertices, kNumObjects);

With that we saved some space (33%) and, potentially a similar amount of processing when computing vertices in the vertex shader as it’s possible the GPU can reuse vertices it has already calculated.

Note that we could have also used an index buffer with the storage buffer example from the previous article. In that case the value from @builtin(vertex_index) that’s passed in matches the index from the index buffer.

Next up we’ll cover textures.