geometry.h

#ifndef __GEOMETRY_H__
#define __GEOMETRY_H__

#include <cmath>
#include <iostream>

///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

template <class t> struct Vec2 {
  union {
    struct {t u, v;};
    struct {t x, y;};
    t raw[2];
  };
  Vec2() : u(0), v(0) {}
  Vec2(t _u, t _v) : u(_u),v(_v) {}
  inline Vec2<t> operator +(const Vec2<t> &V) const { return Vec2<t>(u+V.u, v+V.v); }
  inline Vec2<t> operator -(const Vec2<t> &V) const { return Vec2<t>(u-V.u, v-V.v); }
  inline Vec2<t> operator *(float f)          const { return Vec2<t>(u*f, v*f); }
  template <class > friend std::ostream& operator<<(std::ostream& s, Vec2<t>& v);
};

template <class t> struct Vec3 {
  union {
    struct {t x, y, z;};
    struct { t ivert, iuv, inorm; };
    t raw[3];
  };
  Vec3() : x(0), y(0), z(0) {}
  Vec3(t _x, t _y, t _z) : x(_x),y(_y),z(_z) {}
  inline Vec3<t> operator ^(const Vec3<t> &v) const { return Vec3<t>(y*v.z-z*v.y, z*v.x-x*v.z, x*v.y-y*v.x); }
  inline Vec3<t> operator +(const Vec3<t> &v) const { return Vec3<t>(x+v.x, y+v.y, z+v.z); }
  inline Vec3<t> operator -(const Vec3<t> &v) const { return Vec3<t>(x-v.x, y-v.y, z-v.z); }
  inline Vec3<t> operator *(float f)          const { return Vec3<t>(x*f, y*f, z*f); }
  inline t       operator *(const Vec3<t> &v) const { return x*v.x + y*v.y + z*v.z; }
  float norm () const { return std::sqrt(x*x+y*y+z*z); }
  Vec3<t> & normalize(t l=1) { *this = (*this)*(l/norm()); return *this; }
  template <class > friend std::ostream& operator<<(std::ostream& s, Vec3<t>& v);
};

typedef Vec2<float> Vec2f;
typedef Vec2<int>   Vec2i;
typedef Vec3<float> Vec3f;
typedef Vec3<int>   Vec3i;

template <class t> std::ostream& operator<<(std::ostream& s, Vec2<t>& v) {
  s << "(" << v.x << ", " << v.y << ")\n";
  return s;
}

template <class t> std::ostream& operator<<(std::ostream& s, Vec3<t>& v) {
  s << "(" << v.x << ", " << v.y << ", " << v.z << ")\n";
  return s;
};


///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

const int DEFAULT_ALLOC = 4;

class Matrix {
  std::vector<std::vector<float>> m;
  int rows, cols;
public:
  Matrix(int r=DEFAULT_ALLOC, int c=DEFAULT_ALLOC);
  Matrix(Vec3f v); // cartesian to homogeneous coordinates
  inline int nrows();
  inline int ncols();

  static Matrix identity(int dimensions);
  std::vector<float>& operator[](const int i);
  Matrix operator*(const Matrix& a);
  Matrix transpose();
  Matrix inverse();

  Vec3f to_Vec3f(); // convert homogenous 4d vec/mat to 3d vec;

  friend std::ostream& operator<<(std::ostream& s, Matrix& m);
};

#endif //__GEOMETRY_H__