Concept Questions for HW01

Question 1

Mathematical Difference:

1. vec4 operator*(const vec4 &v) const (Line 89): This multiplies a matrix (mat4) by a column vector (vec4), i.e., m * v. The matrix applies a transformation to the vector.
2. vec4 operator*(const vec4 &v, const mat4 &m) (Line 106): This multiplies a row vector (vec4) by a matrix (mat4), i.e., v * m. This may result in a different transformation, as the multiplication order is reversed.

Explanation of const:

1. const vec4 &v: The vector v is passed as a constant reference, meaning it cannot be modified inside the function.
2. const mat4 &m: The matrix m is passed as a constant reference, ensuring it isn't modified.
3. const after the function: Ensures that the matrix object calling the function is not modified.

Question 2

1. First function (line 25):

   float operator[](unsigned int index) const;

   This version can only be used when the vec4 object is const, as it provides read-only access to the vector's elements.

   Situation:

   • If you have a const vec4 object, you can only use this version to access its elements because the vector cannot be modified. For example:

     const vec4 v(1.0f, 2.0f, 3.0f, 4.0f);
     float x = v[0];  // Accesses the first element, but cannot modify it.

2. Second function (line 28):

   float& operator[](unsigned int index);

   This version can only be used with non-const vec4 objects, as it provides modifiable access to the elements.

   Situation:

   • When you want to modify an element of a vec4, you use this version. For instance:

     vec4 v(1.0f, 2.0f, 3.0f, 4.0f);
     v[0] = 5.0f;  // Modifies the first element of the vector.

In summary:

• The first function is used when reading values from a const vec4.
• The second function is used when you need to modify elements in a non-const vec4.