# WebGPU - Point Lighting

In the previous article we covered directional lighting where the light is coming universally from the same direction. We set that direction before rendering.

What if instead of setting the direction for the light we picked a point in 3d space for the light and computed the direction from that point to each visible spot on the surface of our model in our shader? That would give us a point light.

If you rotate the surface above you’ll see how each point on the surface has a different surface to light vector. Getting the dot product of the surface normal and each individual surface to light vector gives us a different value at each point on the surface.

So, let’s do that.

First we need the light position

```struct Uniforms {
normalMatrix: mat3x3f,
worldViewProjection: mat4x4f,
color: vec4f,
-  lightDirection: vec3f,
+  lightPosition: vec3f,
};
```

And we need a way to compute the world position of the surface. For that we can multiply our positions by the world matrix so …

```struct Uniforms {
normalMatrix: mat3x3f,
worldViewProjection: mat4x4f,
+  world: mat4x4f,
color: vec4f,
lightDirection: vec3f,
lightPosition: vec3f,
};

....

// Compute the world position of the surface
let surfaceWorldPosition = (u_world * vert.position).xyz;

```

And we can compute a vector from the surface to the light which is similar to the light direction we had before except this time we’re computing it for every position on the surface to a light’s world position point.

```  struct VSOutput {
@builtin(position) position: vec4f,
@location(0) normal: vec3f,
@location(1) surfaceToLight: vec3f,
};

...

// Compute the vector of the surface to the light
// and pass it to the fragment shader
vsOut.surfaceToLight = uni.lightPosition - surfaceWorldPosition;
```

Here’s all that in context

```struct Uniforms {
normalMatrix: mat3x3f,
worldViewProjection: mat4x4f,
*  world: mat4x4f,
color: vec4f,
*  lightPosition: vec3f,
};

struct Vertex {
@location(0) position: vec4f,
@location(1) normal: vec3f,
};

struct VSOutput {
@builtin(position) position: vec4f,
@location(0) normal: vec3f,
*  @location(1) surfaceToLight: vec3f,
};

@group(0) @binding(0) var<uniform> uni: Uniforms;

@vertex fn vs(vert: Vertex) -> VSOutput {
var vsOut: VSOutput;
vsOut.position = uni.worldViewProjection * vert.position;

// Orient the normals and pass to the fragment shader
vsOut.normal = uni.normalMatrix * vert.normal;

*  // Compute the world position of the surface
*  let surfaceWorldPosition = (uni.world * vert.position).xyz;
*
*  // Compute the vector of the surface to the light
*  // and pass it to the fragment shader
*  vsOut.surfaceToLight = uni.lightPosition - surfaceWorldPosition;

return vsOut;
}
```

Now in the fragment shader we need to normalize the surface to light vector since it’s a not a unit vector. Note that we could normalize in the vertex shader but because it’s an inter-stage variable it will be linearly interpolated between our positions and so would not be a complete unit vector

```@fragment fn fs(vsOut: VSOutput) -> @location(0) vec4f {
// Because vsOut.normal is an inter-stage variable
// it's interpolated so it will not be a unit vector.
// Normalizing it will make it a unit vector again
let normal = normalize(vsOut.normal);

+  let surfaceToLightDirection = normalize(vsOut.surfaceToLight);

// Compute the light by taking the dot product
-  // of the normal to the light's reverse direction
-  let light = dot(normal, -uni.lightDirection);
+  // of the normal with the direction to the light
+  let light = dot(normal, surfaceToLightDirection);

// Lets multiply just the color portion (not the alpha)
// by the light
let color = uni.color.rgb * light;
return vec4f(color, uni.color.a);
}
```

Then we need to update our uniform buffer, offsets, and views

```-  const uniformBufferSize = (12 + 16 + 4 + 4) * 4;
+  const uniformBufferSize = (12 + 16 + 16 + 4 + 4) * 4;
const uniformBuffer = device.createBuffer({
label: 'uniforms',
size: uniformBufferSize,
usage: GPUBufferUsage.UNIFORM | GPUBufferUsage.COPY_DST,
});

const uniformValues = new Float32Array(uniformBufferSize / 4);

// offsets to the various uniform values in float32 indices
const kNormalMatrixOffset = 0;
const kWorldViewProjectionOffset = 12;
-  const kColorOffset = 28;
-  const kLightDirectionOffset = 32;
+  const kWorldOffset = 28;
+  const kColorOffset = 44;
+  const kLightPositionOffset = 48;

const normalMatrixValue = uniformValues.subarray(
kNormalMatrixOffset, kNormalMatrixOffset + 12);
const worldViewProjectionValue = uniformValues.subarray(
kWorldViewProjectionOffset, kWorldViewProjectionOffset + 16);
+  const worldValue = uniformValues.subarray(
+      kWorldOffset, kWorldOffset + 16);
const colorValue = uniformValues.subarray(kColorOffset, kColorOffset + 4);
-  const lightDirectionValue =
-      uniformValues.subarray(kLightDirectionOffset, kLightDirectionOffset + 3);
+  const lightPositionValue =
+      uniformValues.subarray(kLightPositionOffset, kLightPositionOffset + 3);
```

and we need to set them

```    const eye = [100, 150, 200];
const target = [0, 35, 0];
const up = [0, 1, 0];

// Compute a view matrix
const viewMatrix = mat4.lookAt(eye, target, up);

// Combine the view and projection matrixes
const viewProjectionMatrix = mat4.multiply(projection, viewMatrix);

// Compute a world matrix
-    const world = mat4.rotationY(settings.rotation);
+    const world = mat4.rotationY(settings.rotation, worldValue);

// Combine the viewProjection and world matrices
mat4.multiply(viewProjectionMatrix, world, worldViewProjectionValue);

// Inverse and transpose it into the worldInverseTranspose value
mat3.fromMat4(mat4.transpose(mat4.inverse(world)), normalMatrixValue);

colorValue.set([0.2, 1, 0.2, 1]);  // green
=    lightDirectionValue.set(vec3.normalize([-0.5, -0.7, -1]));
+    lightPositionValue.set([-10, 30, 100]);

// upload the uniform values to the uniform buffer
device.queue.writeBuffer(uniformBuffer, 0, uniformValues);

```

And here it is

# Specular Highlighting

Now that we have a point we can add something called specular highlighting.

If you look at on object in the real world, if it’s remotely shiny, then if it happens to reflect the light directly at you it’s almost like a mirror

We can simulate that effect by computing if the light reflects into our eyes. Again the dot-product comes to the rescue.

What do we need to check? Well let’s think about it. Light reflects at the same angle it hits a surface so if the direction of the surface to the light is the exact reflection of the surface to the eye then it’s at the perfect angle to reflect

If we know the direction from the surface of our model to the light (which we do since we just did that). And if we know the direction from the surface to view/eye/camera, which we can compute, then we can add those 2 vectors and normalize them to get the `halfVector` which is the vector that sits half way between them. If the halfVector and the surface normal match then it’s the perfect angle to reflect the light into the view/eye/camera. And how can we tell when they match? Take the dot product just like we did before. 1 = they match, same direction, 0 = they’re perpendicular, -1 = they’re opposite.

So first thing is we need to pass in the view/camera/eye position, compute the surface to view vector and pass it to the fragment shader.

```struct Uniforms {
normalMatrix: mat3x3f,
worldViewProjection: mat4x4f,
world: mat4x4f,
color: vec4f,
lightPosition: vec3f,
+  viewWorldPosition: vec3f,
};

struct Vertex {
@location(0) position: vec4f,
@location(1) normal: vec3f,
};

struct VSOutput {
@builtin(position) position: vec4f,
@location(0) normal: vec3f,
@location(1) surfaceToLight: vec3f,
+  @location(2) surfaceToView: vec3f,
};

@group(0) @binding(0) var<uniform> uni: Uniforms;

@vertex fn vs(vert: Vertex) -> VSOutput {
var vsOut: VSOutput;
vsOut.position = uni.worldViewProjection * vert.position;

// Orient the normals and pass to the fragment shader
vsOut.normal = uni.normalMatrix * vert.normal;

// Compute the world position of the surface
let surfaceWorldPosition = (uni.world * vert.position).xyz;

// Compute the vector of the surface to the light
// and pass it to the fragment shader
vsOut.surfaceToLight = uni.lightPosition - surfaceWorldPosition;

+  // Compute the vector of the surface to the light
+  // and pass it to the fragment shader
+  vsOut.surfaceToView = uni.viewWorldPosition - surfaceWorldPosition;

return vsOut;
}
```

Next in the fragment shader we need to compute the `halfVector` between the surface to view and surface to light vectors. Then we can take the dot product the `halfVector` and the normal to find out if the light is reflecting into the view.

```@fragment fn fs(vsOut: VSOutput) -> @location(0) vec4f {
// Because vsOut.normal is an inter-stage variable
// it's interpolated so it will not be a unit vector.
// Normalizing it will make it a unit vector again
let normal = normalize(vsOut.normal);

let surfaceToLightDirection = normalize(vsOut.surfaceToLight);

// Compute the light by taking the dot product
// of the normal with the direction to the light
let light = dot(normal, surfaceToLightDirection);

+  let surfaceToViewDirection = normalize(vsOut.surfaceToView);
+  let halfVector = normalize(
+    surfaceToLightDirection + surfaceToViewDirection);
+  let specular = dot(normal, halfVector);

// Lets multiply just the color portion (not the alpha)
// by the light
-  let color = uni.color.rgb * light;
+  let color = uni.color.rgb * light + specular;
return vec4f(color, uni.color.a);
}
```

Again we have add room for viewWorldPosition to our uniformBuffer.

```-  const uniformBufferSize = (12 + 16 + 16 + 4 + 4) * 4;
+  const uniformBufferSize = (12 + 16 + 16 + 4 + 4 + 4) * 4;
const uniformBuffer = device.createBuffer({
label: 'uniforms',
size: uniformBufferSize,
usage: GPUBufferUsage.UNIFORM | GPUBufferUsage.COPY_DST,
});

const uniformValues = new Float32Array(uniformBufferSize / 4);

// offsets to the various uniform values in float32 indices
const kNormalMatrixOffset = 0;
const kWorldViewProjectionOffset = 12;
const kWorldOffset = 28;
const kColorOffset = 44;
const kLightPositionOffset = 48;
+  const kViewWorldPositionOffset = 52;

const normalMatrixValue = uniformValues.subarray(
kNormalMatrixOffset, kNormalMatrixOffset + 12);
const worldViewProjectionValue = uniformValues.subarray(
kWorldViewProjectionOffset, kWorldViewProjectionOffset + 16);
const worldValue = uniformValues.subarray(
kWorldOffset, kWorldOffset + 16);
const colorValue = uniformValues.subarray(kColorOffset, kColorOffset + 4);
const lightPositionValue = uniformValues.subarray(
kLightPositionOffset, kLightPositionOffset + 3);
+  const viewWorldPositionValue = uniformValues.subarray(
+      kViewWorldPositionOffset, kViewWorldPositionOffset + 3);
```

and set it

```    const eye = [100, 150, 200];
const target = [0, 35, 0];
const up = [0, 1, 0];

...

viewWorldPositionValue.set(eye);
```

And here’s that

DANG THAT’S BRIGHT!

We can fix the brightness by raising the dot-product result to a power. This will scrunch up the specular highlight from a linear falloff to an exponential falloff.

The closer the red line is to the top of the graph the brighter our specular addition will be. By raising the power it scrunches the range where it goes bright to the right.

Let’s call that `shininess` and add it to our shader.

```struct Uniforms {
normalMatrix: mat3x3f,
worldViewProjection: mat4x4f,
world: mat4x4f,
color: vec4f,
lightWorldPosition: vec3f,
viewWorldPosition: vec3f,
+  shininess: f32,
};

...

@fragment fn fs(vsOut: VSOutput) -> @location(0) vec4f {

...

-  let specular = dot(normal, halfVector);
+  var specular = dot(normal, halfVector);
+  specular = select(
+      0.0,                           // value if condition false
+      pow(specular, uni.shininess),  // value if condition is true
+      specular > 0.0);               // condition
```

The dot product can go negative. Taking a negative number to a power is undefined in WebGPU (or is NaN?) which would be bad. So, if the dot product is negative then we just leave specular at 0.0.

Of course we need to set `shininess`.

```  const kNormalMatrixOffset = 0;
const kWorldViewProjectionOffset = 12;
const kWorldOffset = 28;
const kColorOffset = 44;
const kLightWorldPositionOffset = 48;
const kViewWorldPositionOffset = 52;
+  const kShininessOffset = 55;

const normalMatrixValue = uniformValues.subarray(
kNormalMatrixOffset, kNormalMatrixOffset + 12);
const worldViewProjectionValue = uniformValues.subarray(
kWorldViewProjectionOffset, kWorldViewProjectionOffset + 16);
const worldValue = uniformValues.subarray(
kWorldOffset, kWorldOffset + 16);
const colorValue = uniformValues.subarray(kColorOffset, kColorOffset + 4);
const lightWorldPositionValue = uniformValues.subarray(
kLightWorldPositionOffset, kLightWorldPositionOffset + 3);
const viewWorldPositionValue = uniformValues.subarray(
kViewWorldPositionOffset, kViewWorldPositionOffset + 3);
+  const shininessValue = uniformValues.subarray(
+      kShininessOffset, kShininessOffset + 1);

...

const settings = {
+    shininess: 30,
};

const radToDegOptions = { min: -360, max: 360, step: 1, converters: GUI.converters.radToDeg };

const gui = new GUI();
gui.onChange(render);
+  gui.add(settings, 'shininess', { min: 1, max: 250 });

...

function render() {

...

+    shininessValue[0] = settings.shininess;

```

And here’s that

Coming up next spot lighting.

### Why is `pow(negative, power)` undefined?

What does this mean?

`pow(5, 2)`

Well you can look at it as

`5 * 5 = 25`

`pow(5, 3)`

Well you can look at that as

`5 * 5 * 5 = 125`

`pow(-5, 2)`

Well that could be

`-5 * -5 = 25`

And

`pow(-5, 3)`

Well you can look at as

`-5 * -5 * -5 = -125`

As you know multiplying a negative by a negative makes a positive. Multiplying by a negative again makes it negative.

Well then what does this mean?

`pow(-5, 2.5)`

How do you decide whether the result of that positive or negative? That's the land of imaginary numbers.

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