#ifndef SEEN_Geom_TRANSFORMS_H

#define SEEN_Geom_TRANSFORMS_H

#include "matrix.h"

#include <cmath>

namespace Geom {

template <typename T>

struct TransformConcept {

T t;

Matrix m;

Point p;

void constraints() {

m = t; //implicit conversion

t = t.inverse();

p = p * t;

t = t * t;

}

};

class Rotate;

class Translate {

private:

Translate();

Point vec;

public:

explicit Translate(Point const &p) : vec(p) {}

explicit Translate(Coord const x, Coord const y) : vec(x, y) {}

inline operator Matrix() const { return Matrix(1, 0, 0, 1, vec[X], vec[Y]); }

inline Coord operator[](Dim2 const dim) const { return vec[dim]; }

inline Coord operator[](unsigned const dim) const { return vec[dim]; }

inline bool operator==(Translate const &o) const { return vec == o.vec; }

inline bool operator!=(Translate const &o) const { return vec != o.vec; }

inline Translate inverse() const { return Translate(-vec); }

friend Point operator*(Point const &v, Translate const &t);

inline Translate operator*(Translate const &b) const { return Translate(vec + b.vec); }

friend Matrix operator*(Translate const &t, Rotate const &r);

};

inline Point operator*(Point const &v, Translate const &t) { return v + t.vec; }

class Scale {

private:

Point vec;

Scale();

public:

explicit Scale(Point const &p) : vec(p) {}

Scale(Coord const x, Coord const y) : vec(x, y) {}

explicit Scale(Coord const s) : vec(s, s) {}

inline operator Matrix() const { return Matrix(vec[X], 0, 0, vec[Y], 0, 0); }

inline Coord operator[](Dim2 const d) const { return vec[d]; }

inline Coord operator[](unsigned const d) const { return vec[d]; }

//TODO: should we keep these mutators? add them to the other transforms?

inline Coord &operator[](Dim2 const d) { return vec[d]; }

inline Coord &operator[](unsigned const d) { return vec[d]; }

inline bool operator==(Scale const &o) const { return vec == o.vec; }

inline bool operator!=(Scale const &o) const { return vec != o.vec; }

inline Scale inverse() const { return Scale(1./vec[0], 1./vec[1]); }

friend Point operator*(Point const &v, Translate const &t);

inline Scale operator*(Scale const &b) const { return Scale(vec[X]*b[X], vec[Y]*b[Y]); }

};

inline Point operator*(Point const &p, Scale const &s) { return Point(p[X] * s[X], p[Y] * s[Y]); }

class Rotate {

private:

Rotate();

Point vec;

public:

explicit Rotate(Coord theta) : vec(std::cos(theta), std::sin(theta)) {}

Rotate(Point const &p) {Point v = p; v.normalize(); vec = v;} //TODO: UGLY!

explicit Rotate(Coord x, Coord y) { Rotate(Point(x, y)); }

inline operator Matrix() const { return Matrix(vec[X], vec[Y], -vec[Y], vec[X], 0, 0); }

inline Coord operator[](Dim2 const dim) const { return vec[dim]; }

inline Coord operator[](unsigned const dim) const { return vec[dim]; }

inline bool operator==(Rotate const &o) const { return vec == o.vec; }

inline bool operator!=(Rotate const &o) const { return vec != o.vec; }

Rotate inverse() const { return Rotate( Point(vec[X], -vec[Y]) ); }

static Rotate from_degrees(Coord deg) {

Coord rad = (deg / 180.0) * M_PI;

return Rotate(rad);

}

friend Point operator*(Point const &v, Rotate const &r);

inline Rotate operator*(Rotate const &b) const { return Rotate(vec * b); }

};

inline Point operator*(Point const &v, Rotate const &r) { return v ^ r.vec; }

Matrix operator*(Translate const &t, Scale const &s);

Matrix operator*(Translate const &t, Rotate const &r);

Matrix operator*(Scale const &s, Translate const &t);

Matrix operator*(Scale const &s, Matrix const &m);

Matrix operator*(Matrix const &m, Translate const &t);

Matrix operator*(Matrix const &m, Scale const &s);

Matrix operator*(Matrix const &m, Rotate const &r);

Matrix operator*(Matrix const &m1, Matrix const &m2);

Translate pow(Translate const &t, int n);

Scale pow(Scale const &t, int n);

Rotate pow(Rotate t, int n);

Matrix pow(Matrix t, int n);

} /* namespace Geom */

#endif /* !SEEN_Geom_TRANSFORMS_H */