Normalizing vectors

A vector with a length of 1 is called a normal vector (or unit vector). Generally, unit vectors are used to represent a direction without a magnitude. The dot product of two unit vectors will always fall in the -1 to 1 range.

Aside from the 0 vector, any vector can be normalized by scaling the vector by the inverse of its length:

1. Implement the normalize function in vec3.cpp. Don't forget to add the function declaration to vec3.h:

   void normalize(vec3 &v) {

       float lenSq = v.x * v.x + v.y * v.y + v.z * v.z;

       if (lenSq < VEC3_EPSILON) { return; }

       float invLen = 1.0f / sqrtf(lenSq);    

       v.x *= invLen;

       v.y *= invLen;

       v.z *= invLen;

   }

2. Implement the normalized function in vec3.cpp. Don't forget to add the function declaration to vec3.h:

   vec3 normalized(const vec3 &v) {

       float lenSq = v.x * v.x + v.y * v.y + v.z * v.z;

       if (lenSq < VEC3_EPSILON) { return v; }

       float invLen = 1.0f / sqrtf(lenSq);

       return vec3(

           v.x * invLen,

           v.y * invLen,

           v.z * invLen

       );

   }

The normalize function takes a reference to a vector and normalizes it in place. The normalized function, on the other hand, takes a constant reference and does not modify the input vector. Instead, it returns a new vector.