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• First thing
• Second thing
• Third thing

#include 
#include 
#include 

using namespace std;

struct Matrix
{
    float e[16];
};

struct Vector
{
    float e[4];

    float& operator[](int index)
    {
        return e[index];
    }

};

ostream& operator<<(ostream& out, const Matrix& m);
ostream& operator<<(ostream& out, const Vector& v);

Matrix buildidentitymatrix(void);
Matrix buildrotationmatrix(float theta, float x, float y, float z);
Matrix buildscalematrix(float x, float y, float z);
Matrix buildtranslationmatrix(float x, float y, float z);

Vector buildvector(float x, float y, float z);

Matrix operator*(const Matrix& a, const Matrix& b);
void operator*=(Matrix& a, const Matrix& b);
Vector operator*(const Matrix& a, const Vector& v);

ostream& operator<<(ostream& out, const Matrix& m)
{
    out << m.e[0] << " " << m.e[4] << " " << m.e[8] << " " << m.e[12] << endl;
    out << m.e[1] << " " << m.e[5] << " " << m.e[9] << " " << m.e[13] << endl;
    out << m.e[2] << " " << m.e[6] << " " << m.e[10] << " " << m.e[14] << endl;
    out << m.e[3] << " " << m.e[7] << " " << m.e[11] << " " << m.e[15];
    return out;
}

ostream& operator<<(ostream& out, const Vector& v)
{
    out << "(" << v.e[0] << ", " << v.e[1] << ", " << v.e[2] << ")";
    return out;
}

Matrix buildidentitymatrix(void)
{
    Matrix m;
    m.e[0] = 1;
    m.e[1] = 0;
    m.e[2] = 0;
    m.e[3] = 0;

    m.e[4] = 0;
    m.e[5] = 1;
    m.e[6] = 0;
    m.e[7] = 0;

    m.e[8] = 0;
    m.e[9] = 0;
    m.e[10] = 1;
    m.e[11] = 0;

    m.e[12] = 0;
    m.e[13] = 0;
    m.e[14] = 0;
    m.e[15] = 1;

    return m;
}

Matrix buildrotationmatrix(float theta, float x, float y, float z)
{
    Matrix m;
    float c = cos(theta);
    float s = sin(theta);
    float t = 1 - cos(theta);
    m.e[0] = t * x * x + c;
    m.e[1] = t * x * y + s * z;
    m.e[2] = t * x * z - s * y;
    m.e[3] = 0;

    m.e[4] = t * x * y - s * z;
    m.e[5] = t * y * y + c;
    m.e[6] = t * y * z + s * x;
    m.e[7] = 0;

    m.e[8] = t * x * z + s * y;
    m.e[9] = t * y * z - s * x;
    m.e[10] = t * z * z + c;
    m.e[11] = 0;

    m.e[12] = 0;
    m.e[13] = 0;
    m.e[14] = 0;
    m.e[15] = 1;

    return m;
}

Matrix buildscalematrix(float x, float y, float z)
{
    Matrix m;

    m.e[0] = x;
    m.e[1] = 0;
    m.e[2] = 0;
    m.e[3] = 0;

    m.e[4] = 0;
    m.e[5] = y;
    m.e[6] = 0;
    m.e[7] = 0;

    m.e[8] = 0;
    m.e[9] = 0;
    m.e[10] = z;
    m.e[11] = 0;

    m.e[12] = 0;
    m.e[13] = 0;
    m.e[14] = 0;
    m.e[15] = 1;

    return m;
}

Matrix buildtranslationmatrix(float x, float y, float z)
{
    Matrix m;
    m.e[0] = 1;
    m.e[1] = 0;
    m.e[2] = 0;
    m.e[3] = 0;

    m.e[4] = 0;
    m.e[5] = 1;
    m.e[6] = 0;
    m.e[7] = 0;

    m.e[8] = 0;
    m.e[9] = 0;
    m.e[10] = 1;
    m.e[11] = 0;

    m.e[12] = x;
    m.e[13] = y;
    m.e[14] = z;
    m.e[15] = 1;
    return m;
}

Matrix operator*(const Matrix& a, const Matrix& b)
{
    Matrix m;

    m.e[0] = b.e[0] * a.e[0] + b.e[1] * a.e[4] + b.e[2] * a.e[8] + b.e[3] * a.e[12];
    m.e[1] = b.e[0] * a.e[1] + b.e[1] * a.e[5] + b.e[2] * a.e[9] + b.e[3] * a.e[13];
    m.e[2] = b.e[0] * a.e[2] + b.e[1] * a.e[6] + b.e[2] * a.e[10] + b.e[3] * a.e[14];
    m.e[3] = b.e[0] * a.e[3] + b.e[1] * a.e[7] + b.e[2] * a.e[11] + b.e[3] * a.e[15];

    m.e[4] = b.e[4] * a.e[0] + b.e[5] * a.e[4] + b.e[6] * a.e[8] + b.e[7] * a.e[12];
    m.e[5] = b.e[4] * a.e[1] + b.e[5] * a.e[5] + b.e[6] * a.e[9] + b.e[7] * a.e[13];
    m.e[6] = b.e[4] * a.e[2] + b.e[5] * a.e[6] + b.e[6] * a.e[10] + b.e[7] * a.e[14];
    m.e[7] = b.e[4] * a.e[3] + b.e[5] * a.e[7] + b.e[6] * a.e[11] + b.e[7] * a.e[15];

    m.e[8] = b.e[8] * a.e[0] + b.e[9] * a.e[4] + b.e[10] * a.e[8] + b.e[11] * a.e[12];
    m.e[9] = b.e[8] * a.e[1] + b.e[9] * a.e[5] + b.e[10] * a.e[9] + b.e[11] * a.e[13];
    m.e[10] = b.e[8] * a.e[2] + b.e[9] * a.e[6] + b.e[10] * a.e[10] + b.e[11] * a.e[14];
    m.e[11] = b.e[8] * a.e[3] + b.e[9] * a.e[7] + b.e[10] * a.e[11] + b.e[11] * a.e[15];

    m.e[12] = b.e[12] * a.e[0] + b.e[13] * a.e[4] + b.e[14] * a.e[8] + b.e[15] * a.e[12];
    m.e[13] = b.e[12] * a.e[1] + b.e[13] * a.e[5] + b.e[14] * a.e[9] + b.e[15] * a.e[13];
    m.e[14] = b.e[12] * a.e[2] + b.e[13] * a.e[6] + b.e[14] * a.e[10] + b.e[15] * a.e[14];
    m.e[15] = b.e[12] * a.e[3] + b.e[13] * a.e[7] + b.e[14] * a.e[11] + b.e[15] * a.e[15];

    return m;
}


void operator*=(Matrix& a, const Matrix& b)
{
    a = a * b;
}


Vector buildvector(float x, float y, float z)
{
    Vector v;
    v.e[0] = x;
    v.e[1] = y;
    v.e[2] = z;
    v.e[3] = 1;
    return v;
}

Vector operator*(const Matrix& a, const Vector& v)
{
    Vector vnew;

    vnew.e[0] = v.e[0] * a.e[0] + v.e[1] * a.e[4] + v.e[2] * a.e[8] + v.e[3] * a.e[12];
    vnew.e[1] = v.e[0] * a.e[1] + v.e[1] * a.e[5] + v.e[2] * a.e[9] + v.e[3] * a.e[13];
    vnew.e[2] = v.e[0] * a.e[2] + v.e[1] * a.e[6] + v.e[2] * a.e[10] + v.e[3] * a.e[14];
    vnew.e[3] = v.e[0] * a.e[3] + v.e[1] * a.e[7] + v.e[2] * a.e[11] + v.e[3] * a.e[15];

    return vnew;
}






    
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