With just lighting, our scene is already looking pretty good. Still, our models are still overly smooth. This is understandable because we are using a very simple model. If we were using a texture that was supposed to be smooth, this wouldn't be a problem, but our brick texture is supposed to be rougher. We could solve this by adding more geometry, but that would slow our scene down, and it be would hard to know where to add new polygons. This is were normal mapping comes in.
Remember in [the instancing tutorial](/beginner/tutorial7-instancing/#a-different-way-textures), we experimented with storing instance data in a texture? A normal map is doing just that with normal data! We'll use the normals in the normal map in our lighting calculation in addition to the vertex normal.
The brick texture I found came with a normal map. Let's take a look at it!
The r, g, and b components of the texture correspond to the x, y, and z components or the normals. All the z values should be positive, that's why the normal map has a bluish tint.
We'll need to modify our `Material` struct in `model.rs` to include a `normal_texture`.
```rust
pub struct Material {
pub name: String,
pub diffuse_texture: texture::Texture,
pub normal_texture: texture::Texture,
pub bind_group: wgpu::BindGroup,
}
```
We'll have to update the `texture_bind_group_layout` to include the normal map as well.
```rust
let texture_bind_group_layout = device.create_bind_group_layout(&wgpu::BindGroupLayoutDescriptor {
* Note: I duplicated and moved the `command_buffers.push(cmds);` line. This means we can reuse the `cmds` variable for both the normal map and diffuse/color map.
If we run the code now, you'll notice things don't look quite right. Let's compare our results with the last tutorial.
Parts of the scene are dark when they should be lit up, and vice versa.
## Tangent Space to World Space
I mentioned it briefly in the [lighting tutorial](/intermediate/tutorial10-lighting/#the-normal-matrix), that we were doing our lighting calculation in "world space". This meant that the entire scene was oriented with respect to the *world's* coordinate system. When we pull the normal data from our normal texture, all the normals are in what's known as pointing roughly in the positive z direction. That means that our lighting calculation thinks all of the surfaces of our models are facing in roughly the same direction. This is referred to as `tangent space`.
If we remember the [lighting-tutorial](/intermediate/tutorial10-lighting/#), we used the vertex normal to indicate the direction of the surface. It turns out we can use that to transform our normals from `tangent space` into `world space`. In order to do that we need to draw from the depths of linear algebra.
We can create a matrix that represents a coordinate system using 3 vectors that are perpendicular (or orthonormal) to each other. Basically we define the x, y, and z axes of our coordinate system.
We're going to create a matrix that will represent the coordinate space relative to our vertex normals. We're then going to use that to transform our normal map data to be in world space.
## The tangent, and the bitangent
We have one of the 3 vectors we need, the normal. What about the others? These are the tangent, and bitangent vectors. A tangent represents any vector that is parallel with a surface (aka. doesn't intersect with it). The tangent is always perpendicular to the normal vector. The bitangent is a tangent vector that is perpendicular to the other tangent vector. Together the tangent, bitangent, and normal represent the x, y, and z axes respectively.
Some model formats include the tanget and bitangent (sometimes called the binormal) in the vertex data, but OBJ does not. We'll have to calculate them manually. Luckily we can derive our tangent, and bitangent from our existing vertex data. Take a look at the following diagram.
Basically we can use the edges of our triangles, and our normal to calculate the tangent and bitangent. But first, we need to update our `ModelVertex` struct in `model.rs`.
Since the normal map by default is in tangent space, we need to transform all the other variables used in that calculation to tangent space as well. We'll need to construct the tangent matrix in the vertex shader. First we need our `VertexInput` to include the tangent and bitangents we calculated earlier.
We've been using `Rgba8UnormSrgb` for all our textures. The `Srgb` bit specifies that we will be using [standard red green blue color space](https://en.wikipedia.org/wiki/SRGB). This is also known as linear color space. Linear color space has less color density. Even so, it is often used for diffuse textures, as they are typically made in `Srgb` color space.
Normal textures aren't made with `Srgb`. Using `Rgba8UnormSrgb` can changes how the GPU samples the texture. This can make the resulting simulation [less accurate](https://medium.com/@bgolus/generating-perfect-normal-maps-for-unity-f929e673fc57#b86c). We can avoid these issues by using `Rgba8Unorm` when we create the texture. Let's add an `is_normal_map` method to our `Texture` struct.
let diffuse_texture = texture::Texture::load(device, queue, containing_folder.join(diffuse_path), false)?;
let normal_path = mat.normal_texture;
// UPDATED!
let normal_texture = texture::Texture::load(device, queue, containing_folder.join(normal_path), true)?;
```
That gives us the following.
## Unrelated stuff
While I was debugging the normal mapping code, I made a few changes to `model.rs` that I haven't mentioned. I wanted to be able to see the model with different textures, so I modified the `Material` struct to have a `new()` method.
```rust
impl Material {
pub fn new(
device: &wgpu::Device,
name: &str,
diffuse_texture: texture::Texture,
normal_texture: texture::Texture,
layout: &wgpu::BindGroupLayout,
) -> Self {
let bind_group = device.create_bind_group(&wgpu::BindGroupDescriptor {
