godot/core/math/math_2d.h

/*************************************************************************/
/*  math_2d.h                                                            */
/*************************************************************************/
/*                       This file is part of:                           */
/*                           GODOT ENGINE                                */
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/* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur.                 */
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#ifndef MATH_2D_H
#define MATH_2D_H

#include "math_funcs.h"
#include "ustring.h"
/**
	@author Juan Linietsky <reduzio@gmail.com>
*/
enum Margin {

	MARGIN_LEFT,
	MARGIN_TOP,
	MARGIN_RIGHT,
	MARGIN_BOTTOM
};

enum Orientation {

	HORIZONTAL,
	VERTICAL
};

enum HAlign {

	HALIGN_LEFT,
	HALIGN_CENTER,
	HALIGN_RIGHT
};

enum VAlign {

	VALIGN_TOP,
	VALIGN_CENTER,
	VALIGN_BOTTOM
};

struct Vector2 {

	union {
		real_t x;
		real_t width;
	};
	union {
		real_t y;
		real_t height;
	};


	_FORCE_INLINE_ real_t& operator[](int p_idx) {
		return p_idx?y:x;
	}
	_FORCE_INLINE_ const real_t& operator[](int p_idx) const {
		return p_idx?y:x;
	}

	void normalize();
	Vector2 normalized() const;

	real_t length() const;
	real_t length_squared() const;

	real_t distance_to(const Vector2& p_vector2) const;
	real_t distance_squared_to(const Vector2& p_vector2) const;
	real_t angle_to(const Vector2& p_vector2) const;
	real_t angle_to_point(const Vector2& p_vector2) const;

	real_t dot(const Vector2& p_other) const;
	real_t cross(const Vector2& p_other) const;
	Vector2 cross(real_t p_other) const;
	Vector2 project(const Vector2& p_vec) const;

	Vector2 plane_project(real_t p_d, const Vector2& p_vec) const;

	Vector2 clamped(real_t p_len) const;

	_FORCE_INLINE_ static Vector2 linear_interpolate(const Vector2& p_a, const Vector2& p_b,real_t p_t);
	_FORCE_INLINE_ Vector2 linear_interpolate(const Vector2& p_b,real_t p_t) const;
	Vector2 cubic_interpolate(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,real_t p_t) const;
	Vector2 cubic_interpolate_soft(const Vector2& p_b,const Vector2& p_pre_a, const Vector2& p_post_b,real_t p_t) const;

	Vector2 slide(const Vector2& p_vec) const;
	Vector2 reflect(const Vector2& p_vec) const;

	Vector2 operator+(const Vector2& p_v) const;
	void operator+=(const Vector2& p_v);
	Vector2 operator-(const Vector2& p_v) const;
	void operator-=(const Vector2& p_v);
	Vector2 operator*(const Vector2 &p_v1) const;

	Vector2 operator*(const real_t &rvalue) const;
	void operator*=(const real_t &rvalue);
	void operator*=(const Vector2 &rvalue) { *this = *this * rvalue; }

	Vector2 operator/(const Vector2 &p_v1) const;

	Vector2 operator/(const real_t &rvalue) const;

	void operator/=(const real_t &rvalue);

	Vector2 operator-() const;

	bool operator==(const Vector2& p_vec2) const;
	bool operator!=(const Vector2& p_vec2) const;

	bool operator<(const Vector2& p_vec2) const { return (x==p_vec2.x)?(y<p_vec2.y):(x<p_vec2.x); }
	bool operator<=(const Vector2& p_vec2) const { return (x==p_vec2.x)?(y<=p_vec2.y):(x<=p_vec2.x); }

	bool nan_equals(const Vector2& p_vec2) const;
	real_t angle() const;

	void set_rotation(real_t p_radians) {

		x=Math::cos(p_radians);
		y=Math::sin(p_radians);
	}

	_FORCE_INLINE_ Vector2 abs() const {

		return Vector2( Math::abs(x), Math::abs(y) );
	}

	Vector2 rotated(real_t p_by) const;
	Vector2 tangent() const {

		return Vector2(y,-x);
	}

	Vector2 floor() const;
	Vector2 snapped(const Vector2& p_by) const;
	real_t aspect() const { return width/height; }


	operator String() const { return String::num(x)+", "+String::num(y); }

	_FORCE_INLINE_ Vector2(real_t p_x,real_t p_y) { x=p_x; y=p_y; }
	_FORCE_INLINE_ Vector2() { x=0; y=0; }
};

_FORCE_INLINE_ Vector2 Vector2::plane_project(real_t p_d, const Vector2& p_vec) const {

	return  p_vec - *this * ( dot(p_vec) -p_d);
}


_FORCE_INLINE_ Vector2 operator*(real_t p_scalar, const Vector2& p_vec)  {

	return p_vec*p_scalar;
}

Vector2 Vector2::linear_interpolate(const Vector2& p_b,real_t p_t) const {

	Vector2 res=*this;

	res.x+= (p_t * (p_b.x-x));
	res.y+= (p_t * (p_b.y-y));

	return res;

}

Vector2 Vector2::linear_interpolate(const Vector2& p_a, const Vector2& p_b,real_t p_t)  {

	Vector2 res=p_a;

	res.x+= (p_t * (p_b.x-p_a.x));
	res.y+= (p_t * (p_b.y-p_a.y));

	return res;
}

typedef Vector2 Size2;
typedef Vector2 Point2;

struct Transform2D;


struct Rect2 {

	Point2 pos;
	Size2 size;

	const Vector2& get_pos() const { return pos; }
	void set_pos(const Vector2& p_pos) { pos=p_pos; }
	const Vector2& get_size() const { return size; }
	void set_size(const Vector2& p_size) { size=p_size; }

	real_t get_area() const { return size.width*size.height; }

	inline bool intersects(const Rect2& p_rect) const {
		if ( pos.x >= (p_rect.pos.x + p_rect.size.width) )
			return false;
		if ( (pos.x+size.width) <= p_rect.pos.x  )
			return false;
		if ( pos.y >= (p_rect.pos.y + p_rect.size.height) )
			return false;
		if ( (pos.y+size.height) <= p_rect.pos.y  )
			return false;

		return true;
	}

	inline real_t distance_to(const Vector2& p_point) const {

		real_t dist = 1e20;

		if (p_point.x < pos.x) {
			dist=MIN(dist,pos.x-p_point.x);
		}
		if (p_point.y < pos.y) {
			dist=MIN(dist,pos.y-p_point.y);
		}
		if (p_point.x >= (pos.x+size.x) ) {
			dist=MIN(p_point.x-(pos.x+size.x),dist);
		}
		if (p_point.y >= (pos.y+size.y) ) {
			dist=MIN(p_point.y-(pos.y+size.y),dist);
		}

		if (dist==1e20)
			return 0;
		else
			return dist;
	}

	_FORCE_INLINE_ bool intersects_transformed(const Transform2D& p_xform, const Rect2& p_rect) const;

	bool intersects_segment(const Point2& p_from, const Point2& p_to, Point2* r_pos=NULL, Point2* r_normal=NULL) const;

	inline bool encloses(const Rect2& p_rect) const {

		return 	(p_rect.pos.x>=pos.x) && (p_rect.pos.y>=pos.y) &&
			((p_rect.pos.x+p_rect.size.x)<(pos.x+size.x)) &&
			((p_rect.pos.y+p_rect.size.y)<(pos.y+size.y));

	}

	inline bool has_no_area() const {

		return (size.x<=0 || size.y<=0);

	}
	inline Rect2 clip(const Rect2& p_rect) const { /// return a clipped rect

		Rect2 new_rect=p_rect;

		if (!intersects( new_rect ))
			return Rect2();

		new_rect.pos.x = MAX( p_rect.pos.x , pos.x );
		new_rect.pos.y = MAX( p_rect.pos.y , pos.y );

		Point2 p_rect_end=p_rect.pos+p_rect.size;
		Point2 end=pos+size;

		new_rect.size.x=MIN(p_rect_end.x,end.x) - new_rect.pos.x;
		new_rect.size.y=MIN(p_rect_end.y,end.y) - new_rect.pos.y;

		return new_rect;
	}

	inline Rect2 merge(const Rect2& p_rect) const { ///< return a merged rect

		Rect2 new_rect;

		new_rect.pos.x=MIN( p_rect.pos.x , pos.x );
		new_rect.pos.y=MIN( p_rect.pos.y , pos.y );


		new_rect.size.x = MAX( p_rect.pos.x+p_rect.size.x , pos.x+size.x );
		new_rect.size.y = MAX( p_rect.pos.y+p_rect.size.y , pos.y+size.y );

		new_rect.size = new_rect.size - new_rect.pos; //make relative again

		return new_rect;
	};
	inline bool has_point(const Point2& p_point) const {
		if (p_point.x < pos.x)
			return false;
		if (p_point.y < pos.y)
			return false;

		if (p_point.x >= (pos.x+size.x) )
			return false;
		if (p_point.y >= (pos.y+size.y) )
			return false;

		return true;
	}

	inline bool no_area() const { return (size.width<=0 || size.height<=0 ); }

	bool operator==(const Rect2& p_rect) const { return pos==p_rect.pos && size==p_rect.size; }
	bool operator!=(const Rect2& p_rect) const { return pos!=p_rect.pos || size!=p_rect.size; }

	bool nan_equals(const Rect2& p_rect) const { return pos.nan_equals(p_rect.pos) && size == p_rect.size; }

	inline Rect2 grow(real_t p_by) const {

		Rect2 g=*this;
		g.pos.x-=p_by;
		g.pos.y-=p_by;
		g.size.width+=p_by*2;
		g.size.height+=p_by*2;
		return g;
	}

	inline Rect2 expand(const Vector2& p_vector) const {

		Rect2 r = *this;
		r.expand_to(p_vector);
		return r;
	}

	inline void expand_to(const Vector2& p_vector) { //in place function for speed

		Vector2 begin=pos;
		Vector2 end=pos+size;

		if (p_vector.x<begin.x)
			begin.x=p_vector.x;
		if (p_vector.y<begin.y)
			begin.y=p_vector.y;

		if (p_vector.x>end.x)
			end.x=p_vector.x;
		if (p_vector.y>end.y)
			end.y=p_vector.y;

		pos=begin;
		size=end-begin;
	}


	operator String() const { return String(pos)+", "+String(size); }

	Rect2() {}
	Rect2( real_t p_x, real_t p_y, real_t p_width, real_t p_height) { pos=Point2(p_x,p_y); size=Size2( p_width, p_height ); }
	Rect2( const Point2& p_pos, const Size2& p_size ) { pos=p_pos; size=p_size; }
};


/* INTEGER STUFF */

struct Point2i {

	union {
		int x;
		int width;
	};
	union {
		int y;
		int height;
	};


	_FORCE_INLINE_ int& operator[](int p_idx) {
		return p_idx?y:x;
	}
	_FORCE_INLINE_ const int& operator[](int p_idx) const {
		return p_idx?y:x;
	}

	Point2i operator+(const Point2i& p_v) const;
	void operator+=(const Point2i& p_v);
	Point2i operator-(const Point2i& p_v) const;
	void operator-=(const Point2i& p_v);
	Point2i operator*(const Point2i &p_v1) const;

	Point2i operator*(const int &rvalue) const;
	void operator*=(const int &rvalue);

	Point2i operator/(const Point2i &p_v1) const;

	Point2i operator/(const int &rvalue) const;

	void operator/=(const int &rvalue);

	Point2i operator-() const;
	bool operator<(const Point2i& p_vec2) const { return (x==p_vec2.x)?(y<p_vec2.y):(x<p_vec2.x); }
	bool operator>(const Point2i& p_vec2) const { return (x==p_vec2.x)?(y>p_vec2.y):(x>p_vec2.x); }

	bool operator==(const Point2i& p_vec2) const;
	bool operator!=(const Point2i& p_vec2) const;

	real_t get_aspect() const { return width/(real_t)height; }

	operator String() const { return String::num(x)+", "+String::num(y); }

	operator Vector2() const { return Vector2(x,y); }
	inline Point2i(const Vector2& p_vec2) { x=(int)p_vec2.x; y=(int)p_vec2.y; }
	inline Point2i(int p_x,int p_y) { x=p_x; y=p_y; }
	inline Point2i() { x=0; y=0; }
};

typedef Point2i Size2i;

struct Rect2i {

	Point2i pos;
	Size2i size;

	const Point2i& get_pos() const { return pos; }
	void set_pos(const Point2i& p_pos) { pos=p_pos; }
	const Point2i& get_size() const { return size; }
	void set_size(const Point2i& p_size) { size=p_size; }

	int get_area() const { return size.width*size.height; }

	inline bool intersects(const Rect2i& p_rect) const {
		if ( pos.x > (p_rect.pos.x + p_rect.size.width) )
			return false;
		if ( (pos.x+size.width) < p_rect.pos.x  )
			return false;
		if ( pos.y > (p_rect.pos.y + p_rect.size.height) )
			return false;
		if ( (pos.y+size.height) < p_rect.pos.y  )
			return false;

		return true;
	}

	inline bool encloses(const Rect2i& p_rect) const {

		return 	(p_rect.pos.x>=pos.x) && (p_rect.pos.y>=pos.y) &&
			((p_rect.pos.x+p_rect.size.x)<(pos.x+size.x)) &&
			((p_rect.pos.y+p_rect.size.y)<(pos.y+size.y));

	}

	inline bool has_no_area() const {

		return (size.x<=0 || size.y<=0);

	}
	inline Rect2i clip(const Rect2i& p_rect) const { /// return a clipped rect

		Rect2i new_rect=p_rect;

		if (!intersects( new_rect ))
			return Rect2i();

		new_rect.pos.x = MAX( p_rect.pos.x , pos.x );
		new_rect.pos.y = MAX( p_rect.pos.y , pos.y );

		Point2 p_rect_end=p_rect.pos+p_rect.size;
		Point2 end=pos+size;

		new_rect.size.x=(int)(MIN(p_rect_end.x,end.x) - new_rect.pos.x);
		new_rect.size.y=(int)(MIN(p_rect_end.y,end.y) - new_rect.pos.y);

		return new_rect;
	}

	inline Rect2i merge(const Rect2i& p_rect) const { ///< return a merged rect

		Rect2i new_rect;

		new_rect.pos.x=MIN( p_rect.pos.x , pos.x );
		new_rect.pos.y=MIN( p_rect.pos.y , pos.y );


		new_rect.size.x = MAX( p_rect.pos.x+p_rect.size.x , pos.x+size.x );
		new_rect.size.y = MAX( p_rect.pos.y+p_rect.size.y , pos.y+size.y );

		new_rect.size = new_rect.size - new_rect.pos; //make relative again

		return new_rect;
	};
	bool has_point(const Point2& p_point) const {
		if (p_point.x < pos.x)
			return false;
		if (p_point.y < pos.y)
			return false;

		if (p_point.x >= (pos.x+size.x) )
			return false;
		if (p_point.y >= (pos.y+size.y) )
			return false;

		return true;
	}

	bool no_area() { return (size.width<=0 || size.height<=0 ); }

	bool operator==(const Rect2i& p_rect) const { return pos==p_rect.pos && size==p_rect.size; }
	bool operator!=(const Rect2i& p_rect) const { return pos!=p_rect.pos || size!=p_rect.size; }

	Rect2i grow(int p_by) const {

		Rect2i g=*this;
		g.pos.x-=p_by;
		g.pos.y-=p_by;
		g.size.width+=p_by*2;
		g.size.height+=p_by*2;
		return g;
	}

	inline void expand_to(const Point2i& p_vector) {

		Point2i begin=pos;
		Point2i end=pos+size;

		if (p_vector.x<begin.x)
			begin.x=p_vector.x;
		if (p_vector.y<begin.y)
			begin.y=p_vector.y;

		if (p_vector.x>end.x)
			end.x=p_vector.x;
		if (p_vector.y>end.y)
			end.y=p_vector.y;

		pos=begin;
		size=end-begin;
	}


	operator String() const { return String(pos)+", "+String(size); }

	operator Rect2() const { return Rect2(pos,size); }
	Rect2i(const Rect2& p_r2) { pos=p_r2.pos; size=p_r2.size; }
	Rect2i() {}
	Rect2i( int p_x, int p_y, int p_width, int p_height) { pos=Point2(p_x,p_y); size=Size2( p_width, p_height ); }
	Rect2i( const Point2& p_pos, const Size2& p_size ) { pos=p_pos; size=p_size; }
};



struct Transform2D {
	// Warning #1: basis of Transform2D is stored differently from Basis. In terms of elements array, the basis matrix looks like "on paper":
	// M = (elements[0][0] elements[1][0])
	//     (elements[0][1] elements[1][1])
	// This is such that the columns, which can be interpreted as basis vectors of the coordinate system "painted" on the object, can be accessed as elements[i].
	// Note that this is the opposite of the indices in mathematical texts, meaning: $M_{12}$ in a math book corresponds to elements[1][0] here.
	// This requires additional care when working with explicit indices.
 	// See https://en.wikipedia.org/wiki/Row-_and_column-major_order for further reading.

	// Warning #2: 2D be aware that unlike 3D code, 2D code uses a left-handed coordinate system: Y-axis points down,
	// and angle is measure from +X to +Y in a clockwise-fashion.

	Vector2 elements[3];

	_FORCE_INLINE_ real_t tdotx(const Vector2& v) const { return elements[0][0] * v.x + elements[1][0] * v.y; }
	_FORCE_INLINE_ real_t tdoty(const Vector2& v) const { return elements[0][1] * v.x + elements[1][1] * v.y; }

	const Vector2& operator[](int p_idx) const { return elements[p_idx]; }
	Vector2& operator[](int p_idx) { return elements[p_idx]; }

	_FORCE_INLINE_ Vector2 get_axis(int p_axis) const { ERR_FAIL_INDEX_V(p_axis,3,Vector2()); return elements[p_axis]; }
	_FORCE_INLINE_ void set_axis(int p_axis,const Vector2& p_vec) { ERR_FAIL_INDEX(p_axis,3); elements[p_axis]=p_vec; }

	void invert();
	Transform2D inverse() const;

	void affine_invert();
	Transform2D affine_inverse() const;

	void set_rotation(real_t p_phi);
	real_t get_rotation() const;
	_FORCE_INLINE_ void set_rotation_and_scale(real_t p_phi,const Size2& p_scale);
	void rotate(real_t p_phi);

	void scale(const Size2& p_scale);
	void scale_basis(const Size2& p_scale);
	void translate( real_t p_tx, real_t p_ty);
	void translate( const Vector2& p_translation );

	real_t basis_determinant() const;

	Size2 get_scale() const;

	_FORCE_INLINE_ const Vector2& get_origin() const { return elements[2]; }
	_FORCE_INLINE_ void set_origin(const Vector2& p_origin) { elements[2]=p_origin; }

	Transform2D scaled(const Size2& p_scale) const;
	Transform2D basis_scaled(const Size2& p_scale) const;
	Transform2D translated(const Vector2& p_offset) const;
	Transform2D rotated(real_t p_phi) const;

	Transform2D untranslated() const;

	void orthonormalize();
	Transform2D orthonormalized() const;

	bool operator==(const Transform2D& p_transform) const;
	bool operator!=(const Transform2D& p_transform) const;

	void operator*=(const Transform2D& p_transform);
	Transform2D operator*(const Transform2D& p_transform) const;

	Transform2D interpolate_with(const Transform2D& p_transform, real_t p_c) const;

	_FORCE_INLINE_ Vector2 basis_xform(const Vector2& p_vec) const;
	_FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2& p_vec) const;
	_FORCE_INLINE_ Vector2 xform(const Vector2& p_vec) const;
	_FORCE_INLINE_ Vector2 xform_inv(const Vector2& p_vec) const;
	_FORCE_INLINE_ Rect2 xform(const Rect2& p_vec) const;
	_FORCE_INLINE_ Rect2 xform_inv(const Rect2& p_vec) const;

	operator String() const;

	Transform2D(real_t xx, real_t xy, real_t yx, real_t yy, real_t ox, real_t oy) {

		elements[0][0] = xx;
		elements[0][1] = xy;
		elements[1][0] = yx;
		elements[1][1] = yy;
		elements[2][0] = ox;
		elements[2][1] = oy;
	}

	Transform2D(real_t p_rot, const Vector2& p_pos);
	Transform2D() { elements[0][0]=1.0; elements[1][1]=1.0; }
};

bool Rect2::intersects_transformed(const Transform2D& p_xform, const Rect2& p_rect) const {

	//SAT intersection between local and transformed rect2

	Vector2 xf_points[4]={
		p_xform.xform(p_rect.pos),
		p_xform.xform(Vector2(p_rect.pos.x+p_rect.size.x,p_rect.pos.y)),
		p_xform.xform(Vector2(p_rect.pos.x,p_rect.pos.y+p_rect.size.y)),
		p_xform.xform(Vector2(p_rect.pos.x+p_rect.size.x,p_rect.pos.y+p_rect.size.y)),
	};

	real_t low_limit;

	//base rect2 first (faster)

	if (xf_points[0].y>pos.y)
		goto next1;
	if (xf_points[1].y>pos.y)
		goto next1;
	if (xf_points[2].y>pos.y)
		goto next1;
	if (xf_points[3].y>pos.y)
		goto next1;

	return false;

	next1:

	low_limit=pos.y+size.y;

	if (xf_points[0].y<low_limit)
		goto next2;
	if (xf_points[1].y<low_limit)
		goto next2;
	if (xf_points[2].y<low_limit)
		goto next2;
	if (xf_points[3].y<low_limit)
		goto next2;

	return false;

	next2:

	if (xf_points[0].x>pos.x)
		goto next3;
	if (xf_points[1].x>pos.x)
		goto next3;
	if (xf_points[2].x>pos.x)
		goto next3;
	if (xf_points[3].x>pos.x)
		goto next3;

	return false;

	next3:

	low_limit=pos.x+size.x;

	if (xf_points[0].x<low_limit)
		goto next4;
	if (xf_points[1].x<low_limit)
		goto next4;
	if (xf_points[2].x<low_limit)
		goto next4;
	if (xf_points[3].x<low_limit)
		goto next4;

	return false;

	next4:

	Vector2 xf_points2[4]={
		pos,
		Vector2(pos.x+size.x,pos.y),
		Vector2(pos.x,pos.y+size.y),
		Vector2(pos.x+size.x,pos.y+size.y),
	};

	real_t maxa=p_xform.elements[0].dot(xf_points2[0]);
	real_t mina=maxa;

	real_t dp = p_xform.elements[0].dot(xf_points2[1]);
	maxa=MAX(dp,maxa);
	mina=MIN(dp,mina);

	dp = p_xform.elements[0].dot(xf_points2[2]);
	maxa=MAX(dp,maxa);
	mina=MIN(dp,mina);

	dp = p_xform.elements[0].dot(xf_points2[3]);
	maxa=MAX(dp,maxa);
	mina=MIN(dp,mina);

	real_t maxb=p_xform.elements[0].dot(xf_points[0]);
	real_t minb=maxb;

	dp = p_xform.elements[0].dot(xf_points[1]);
	maxb=MAX(dp,maxb);
	minb=MIN(dp,minb);

	dp = p_xform.elements[0].dot(xf_points[2]);
	maxb=MAX(dp,maxb);
	minb=MIN(dp,minb);

	dp = p_xform.elements[0].dot(xf_points[3]);
	maxb=MAX(dp,maxb);
	minb=MIN(dp,minb);


	if ( mina > maxb )
		return false;
	if ( minb > maxa  )
		return false;

	maxa=p_xform.elements[1].dot(xf_points2[0]);
	mina=maxa;

	dp = p_xform.elements[1].dot(xf_points2[1]);
	maxa=MAX(dp,maxa);
	mina=MIN(dp,mina);

	dp = p_xform.elements[1].dot(xf_points2[2]);
	maxa=MAX(dp,maxa);
	mina=MIN(dp,mina);

	dp = p_xform.elements[1].dot(xf_points2[3]);
	maxa=MAX(dp,maxa);
	mina=MIN(dp,mina);

	maxb=p_xform.elements[1].dot(xf_points[0]);
	minb=maxb;

	dp = p_xform.elements[1].dot(xf_points[1]);
	maxb=MAX(dp,maxb);
	minb=MIN(dp,minb);

	dp = p_xform.elements[1].dot(xf_points[2]);
	maxb=MAX(dp,maxb);
	minb=MIN(dp,minb);

	dp = p_xform.elements[1].dot(xf_points[3]);
	maxb=MAX(dp,maxb);
	minb=MIN(dp,minb);


	if ( mina > maxb )
		return false;
	if ( minb > maxa  )
		return false;


	return true;

}

Vector2 Transform2D::basis_xform(const Vector2& v) const {

	return Vector2(
		tdotx(v),
		tdoty(v)
	);
}

Vector2 Transform2D::basis_xform_inv(const Vector2& v) const{

	return Vector2(
		elements[0].dot(v),
		elements[1].dot(v)
	);
}

Vector2 Transform2D::xform(const Vector2& v) const {

	return Vector2(
		tdotx(v),
		tdoty(v)
	) + elements[2];
}
Vector2 Transform2D::xform_inv(const Vector2& p_vec) const {

	Vector2 v = p_vec - elements[2];

	return Vector2(
		elements[0].dot(v),
		elements[1].dot(v)
	);

}
Rect2 Transform2D::xform(const Rect2& p_rect) const {

	Vector2 x=elements[0]*p_rect.size.x;
	Vector2 y=elements[1]*p_rect.size.y;
	Vector2 pos = xform( p_rect.pos );

	Rect2 new_rect;
	new_rect.pos=pos;
	new_rect.expand_to( pos+x );
	new_rect.expand_to( pos+y );
	new_rect.expand_to( pos+x+y );
	return new_rect;
}

void Transform2D::set_rotation_and_scale(real_t p_rot,const Size2& p_scale) {

	elements[0][0]=Math::cos(p_rot)*p_scale.x;
	elements[1][1]=Math::cos(p_rot)*p_scale.y;
	elements[1][0]=-Math::sin(p_rot)*p_scale.y;
	elements[0][1]=Math::sin(p_rot)*p_scale.x;

}

Rect2 Transform2D::xform_inv(const Rect2& p_rect) const {

	Vector2 ends[4]={
		xform_inv( p_rect.pos ),
		xform_inv( Vector2(p_rect.pos.x,p_rect.pos.y+p_rect.size.y ) ),
		xform_inv( Vector2(p_rect.pos.x+p_rect.size.x,p_rect.pos.y+p_rect.size.y ) ),
		xform_inv( Vector2(p_rect.pos.x+p_rect.size.x,p_rect.pos.y ) )
	};

	Rect2 new_rect;
	new_rect.pos=ends[0];
	new_rect.expand_to(ends[1]);
	new_rect.expand_to(ends[2]);
	new_rect.expand_to(ends[3]);

	return new_rect;
}


#endif