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Scaling

The scale of a matrix is stored in the main diagonal of the matrix. The scale is stored as a vec3. Each element of the vec3 represents the scale on the corresponding axis. Row and Column major matrices store scale information in the same elements:

The interesting thing with storing scale inside a matrix is that it shares some of the same elements as the rotation part of the matrix. Because of this, extracting the scale of a matrix may not always yield the numbers you would expect.

Getting ready

We're going to implement three functions. One function will retrieve the scale stored inside a matrix. The other two will return a new matrix, containing only the specified scale.

How to do it…

Follow these steps to set and retrieve the scale of a matrix:

Add the declaration for all scaling functions to matrices.h:

mat4 Scale(float x, float y, float z);
mat4 Scale(const vec3& vec);
vec3 GetScale(const mat4& mat);

Implement the functions that create a 4 X 4 matrix out of scaling information in matrices.cpp:

mat4 Scale(float x, float y, float z) {
   return mat4(
       x,    0.0f, 0.0f, 0.0f,
       0.0f,    y, 0.0f, 0.0f,
       0.0f, 0.0f,    z, 0.0f,
       0.0f, 0.0f, 0.0f, 1.0f
   );
}

mat4 Scale(const vec3&vec) {
   return mat4(
       vec.x,  0.0f, 0.0f, 0.0f,
       0.0f, vec.y,0.0f, 0.0f,
       0.0f, 0.0f, vec.z,0.0f,
       0.0f, 0.0f, 0.0f, 1.0f
   );
}

Implement the function to retrieve scaling from a 4 X 4 matrix in matrices.cpp.
```
vec3 GetScale(const mat4& mat) {
   return vec3(mat._11, mat._22, mat._33);
}
```

How it works…

Both of the Scale functions create a new matrix by placing the scaling values into the main diagonal of the identity matrix. The GetScale function retrieves the main diagonal of the matrix packed into a vec3. If a matrix contains scale and rotation information, the result of the GetScale function might not be what you expect.