godot-cpp/include/godot/core/Transform2D.h

#ifndef TRANSFORM2D_H
#define TRANSFORM2D_H

#include "Vector2.h"

// @Todo
// error handling plllls

#ifndef ERR_FAIL_INDEX_V
#define ERR_FAIL_INDEX_V(a, b, c)
#endif

#ifndef ERR_FAIL_INDEX
#define ERR_FAIL_INDEX(a, b)
#endif

#ifndef ERR_FAIL_COND
#define ERR_FAIL_COND(a)
#endif

namespace godot {

typedef Vector2 Size2;

class Rect2;

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];

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

	Vector2 get_axis(int p_axis) const { ERR_FAIL_INDEX_V(p_axis,3,Vector2()); return elements[p_axis]; }
	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;
	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;

	const Vector2& get_origin() const { return elements[2]; }
	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;

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


}

#include "Rect2.h"

namespace godot {

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

void Transform2D::invert() {
	// FIXME: this function assumes the basis is a rotation matrix, with no scaling.
	// Transform2D::affine_inverse can handle matrices with scaling, so GDScript should eventually use that.
	std::swap(elements[0][1],elements[1][0]);
	elements[2] = basis_xform(-elements[2]);
}

Transform2D Transform2D::inverse() const {

	Transform2D inv=*this;
	inv.invert();
	return inv;

}

void Transform2D::affine_invert() {

	real_t det = basis_determinant();
	ERR_FAIL_COND(det==0);
	real_t idet = 1.0 / det;

	std::swap( elements[0][0],elements[1][1] );
	elements[0]*=Vector2(idet,-idet);
	elements[1]*=Vector2(-idet,idet);

	elements[2] = basis_xform(-elements[2]);

}

Transform2D Transform2D::affine_inverse() const {

	Transform2D inv=*this;
	inv.affine_invert();
	return inv;
}

void Transform2D::rotate(real_t p_phi) {
	*this = Transform2D(p_phi,Vector2()) * (*this);
}

real_t Transform2D::get_rotation() const {
	real_t det = basis_determinant();
	Transform2D m = orthonormalized();
	if (det < 0) {
		m.scale_basis(Size2(-1,-1));
	}
	return ::atan2(m[0].y,m[0].x);
}

void Transform2D::set_rotation(real_t p_rot) {

	real_t cr = ::cos(p_rot);
	real_t sr = ::sin(p_rot);
	elements[0][0]=cr;
	elements[0][1]=sr;
	elements[1][0]=-sr;
	elements[1][1]=cr;
}

Transform2D::Transform2D(real_t p_rot, const Vector2& p_pos) {

	real_t cr = ::cos(p_rot);
	real_t sr = ::sin(p_rot);
	elements[0][0]=cr;
	elements[0][1]=sr;
	elements[1][0]=-sr;
	elements[1][1]=cr;
	elements[2]=p_pos;
}

Size2 Transform2D::get_scale() const {
	real_t det_sign = basis_determinant() > 0 ? 1 : -1;
	return det_sign * Size2( elements[0].length(), elements[1].length() );
}

void Transform2D::scale(const Size2& p_scale) {
	scale_basis(p_scale);
	elements[2]*=p_scale;
}
void Transform2D::scale_basis(const Size2& p_scale) {

	elements[0][0]*=p_scale.x;
	elements[0][1]*=p_scale.y;
	elements[1][0]*=p_scale.x;
	elements[1][1]*=p_scale.y;

}
void Transform2D::translate( real_t p_tx, real_t p_ty) {

	translate(Vector2(p_tx,p_ty));
}
void Transform2D::translate( const Vector2& p_translation ) {

	elements[2]+=basis_xform(p_translation);
}

void Transform2D::orthonormalize() {

	// Gram-Schmidt Process

	Vector2 x=elements[0];
	Vector2 y=elements[1];

	x.normalize();
	y = (y-x*(x.dot(y)));
	y.normalize();

	elements[0]=x;
	elements[1]=y;
}
Transform2D Transform2D::orthonormalized() const {

	Transform2D on=*this;
	on.orthonormalize();
	return on;

}

bool Transform2D::operator==(const Transform2D& p_transform) const {

	for(int i=0;i<3;i++) {
		if (elements[i]!=p_transform.elements[i])
			return false;
	}

	return true;
}

bool Transform2D::operator!=(const Transform2D& p_transform) const {

	for(int i=0;i<3;i++) {
		if (elements[i]!=p_transform.elements[i])
			return true;
	}

	return false;

}

void Transform2D::operator*=(const Transform2D& p_transform) {

	elements[2] = xform(p_transform.elements[2]);

	real_t x0,x1,y0,y1;

	x0 = tdotx(p_transform.elements[0]);
	x1 = tdoty(p_transform.elements[0]);
	y0 = tdotx(p_transform.elements[1]);
	y1 = tdoty(p_transform.elements[1]);

	elements[0][0]=x0;
	elements[0][1]=x1;
	elements[1][0]=y0;
	elements[1][1]=y1;
}


Transform2D Transform2D::operator*(const Transform2D& p_transform) const {

	Transform2D t = *this;
	t*=p_transform;
	return t;

}

Transform2D Transform2D::scaled(const Size2& p_scale) const {

	Transform2D copy=*this;
	copy.scale(p_scale);
	return copy;

}

Transform2D Transform2D::basis_scaled(const Size2& p_scale) const {

	Transform2D copy=*this;
	copy.scale_basis(p_scale);
	return copy;

}

Transform2D Transform2D::untranslated() const {

	Transform2D copy=*this;
	copy.elements[2]=Vector2();
	return copy;
}

Transform2D Transform2D::translated(const Vector2& p_offset) const {

	Transform2D copy=*this;
	copy.translate(p_offset);
	return copy;

}

Transform2D Transform2D::rotated(real_t p_phi) const {

	Transform2D copy=*this;
	copy.rotate(p_phi);
	return copy;

}

real_t Transform2D::basis_determinant() const {

	return elements[0].x * elements[1].y - elements[0].y * elements[1].x;
}

Transform2D Transform2D::interpolate_with(const Transform2D& p_transform, real_t p_c) const {

	//extract parameters
	Vector2 p1 = get_origin();
	Vector2 p2 = p_transform.get_origin();

	real_t r1 = get_rotation();
	real_t r2 = p_transform.get_rotation();

	Size2 s1 = get_scale();
	Size2 s2 = p_transform.get_scale();

	//slerp rotation
	Vector2 v1(::cos(r1), ::sin(r1));
	Vector2 v2(::cos(r2), ::sin(r2));

	real_t dot = v1.dot(v2);

	dot = (dot < -1.0) ? -1.0 : ((dot > 1.0) ? 1.0 : dot); //clamp dot to [-1,1]

	Vector2 v;

	if (dot > 0.9995) {
		v = Vector2::linear_interpolate(v1, v2, p_c).normalized(); //linearly interpolate to avoid numerical precision issues
	} else {
		real_t angle = p_c*::acos(dot);
		Vector2 v3 = (v2 - v1*dot).normalized();
		v = v1*::cos(angle) + v3*::sin(angle);
	}

	//construct matrix
	Transform2D res(::atan2(v.y, v.x), Vector2::linear_interpolate(p1, p2, p_c));
	res.scale_basis(Vector2::linear_interpolate(s1, s2, p_c));
	return res;
}

Transform2D::operator String() const {

	//return String(String()+elements[0]+", "+elements[1]+", "+elements[2]);
	return String(); // @Todo
}

}

#endif // TRANSFORM2D_H