How should I represent matrices in C++?

Question

I'm teaching myself 3D mathematics and in the process building my own rudimentary engine (of sorts). I was wondering what would be the best way to structure my C++ matrix class. There are a few options:

1. Separate member variables:

   struct Mat4 {
       float
           m11, m12, m13, m14,
           m21, m22, m23, m24,
           m31, m32, m33, m34,
           m41, m42, m43, m44;
   
       // methods
   
   }
   

2. A multi-dimensional array:

   struct Mat4 {
       float[4][4] m;
   
       // methods
   
   }
   

3. An array of vectors

   struct Mat4 {
       Vec4[4] m;
   
       // methods
   
   }
   

I'm guessing there would be positives and negatives to each.

From 3D Math Primer for Graphics and Game Development, 2nd Edition p.155:

Matrices use 1-based indices, so the first row and column are numbered 1. For example, a12 (read “a one two,” not “a twelve”) is the element in the first row, second column. Notice that this is different from programming languages such as C++ and Java, which use 0-based array indices. A matrix does not have a column 0 or row 0. This difference in indexing can cause some confusion if matrices are stored using an actual array data type. For this reason, it’s common for classes that store small, fixed size matrices of the type used for geometric purposes to give each element its own named member variable, such as float a11, instead of using the language’s native array support with something like float elem[3][3].

So that's one vote for method one.

Is this really the accepted way to do things? It seems rather unwieldy if the only benefit would be sticking with the conventional math notation.

Answer 1

Why choose? You can have both. (Without any added complexity to logic and without any additional memory requirement thanks to unions.)

struct Mat4
{
    union
    {
        struct
        {
          float m11, m12, m13, m14,
                m21, m22, m23, m24,
                m31, m32, m33, m34,
                m41, m42, m43, m44;
        };
        float[4][4] m;
    };
// methods
}