/*
 * matrix calculations for non-homogenous space..
 */
#ifndef MATRIX_H
#define MATRIX_H

#include <iostream>

#include "util.h"

using namespace std;

class vec {
  double data[3];
public:
  vec() t_no {};
  vec(double a, double b, double c) t_no
    { data[0] = a; data[1] = b; data[2] = c; };
  
        double &operator [](int idx)       t_no { return data[idx]; };
  const double &operator [](int idx) const t_no { return data[idx]; };
};

inline bool operator ==(const vec &a, const vec &b) t_no
  { return a[0] == b[0] && a[1] == b[1] && a[2] == b[2]; }

inline vec operator +(const vec &a, const vec &b) t_no
  { return vec(a[0] + b[0], a[1] + b[1], a[2] + b[2]); }

inline vec operator -(const vec &a, const vec &b) t_no
  { return vec(a[0] - b[0], a[1] - b[1], a[2] - b[2]); }

inline double operator *(const vec &a, const vec &b) t_no
  { return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]; }

inline vec operator *(double s, const vec &a) t_no
  { return vec(s * a[0], s * a[1], s * a[2]); }

double abs(const vec &a) t_no;
vec normalize(const vec &a) t_no;
vec cross(const vec &a, const vec &b) t_no;

class mat {
  vec data[3];
public:
  mat() t_no {};
  mat(vec a, vec b, vec c) t_no
    { data[0] = a; data[1] = b; data[2] = c; };
  
        vec &row(int y)       t_no { return data[y]; };
  const vec &row(int y) const t_no { return data[y]; };
        vec &operator [](int y)       t_no { return row(y); };
  const vec &operator [](int y) const t_no { return row(y); };
  
        vec col(int x)       t_no { return vec(data[0][x], data[1][x], data[2][x]); };
  const vec col(int x) const t_no { return vec(data[0][x], data[1][x], data[2][x]); };
        vec operator ()(int x)       t_no { return col(x); };
  const vec operator ()(int x) const t_no { return col(x); };
  
};

mat operator +(const mat &a, const mat &b) t_no;
mat operator -(const mat &a, const mat &b) t_no;
vec operator *(const mat &a, const vec &b) t_no;
vec operator *(const vec &a, const mat &b) t_no;
mat operator *(const mat &a, const mat &b) t_no;

ostream &operator <<(ostream &o, const vec &v) t_no;
ostream &operator <<(ostream &o, const mat &m) t_no;

#endif