virtualx-engine/core/math/matrix3.h

/*************************************************************************/
/*  matrix3.h                                                            */
/*************************************************************************/
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/*                           GODOT ENGINE                                */
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/* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur.                 */
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#include "vector3.h"

#ifndef MATRIX3_H
#define MATRIX3_H

#include "quat.h"

/**
	@author Juan Linietsky <reduzio@gmail.com>
*/
class Basis {
public:

	Vector3 elements[3];

	_FORCE_INLINE_ const Vector3& operator[](int axis) const {

		return elements[axis];
	}
	_FORCE_INLINE_ Vector3& operator[](int axis) {

		return elements[axis];
	}

	void invert();
	void transpose();

	Basis inverse() const;
	Basis transposed() const;

	_FORCE_INLINE_ real_t determinant() const;

	void from_z(const Vector3& p_z);

	_FORCE_INLINE_ Vector3 get_axis(int p_axis) const {
		// get actual basis axis (elements is transposed for performance)
		return Vector3( elements[0][p_axis], elements[1][p_axis], elements[2][p_axis] );
	}
	_FORCE_INLINE_ void set_axis(int p_axis, const Vector3& p_value) {
		// get actual basis axis (elements is transposed for performance)
		elements[0][p_axis]=p_value.x;
		elements[1][p_axis]=p_value.y;
		elements[2][p_axis]=p_value.z;
	}

	void rotate(const Vector3& p_axis, real_t p_phi);
	Basis rotated(const Vector3& p_axis, real_t p_phi) const;

	void rotate(const Vector3& p_euler);
	Basis rotated(const Vector3& p_euler) const;
	Vector3 get_rotation() const;

	void scale( const Vector3& p_scale );
	Basis scaled( const Vector3& p_scale ) const;
	Vector3 get_scale() const;

	Vector3 get_euler() const;
	void set_euler(const Vector3& p_euler);

	// transposed dot products
	_FORCE_INLINE_ real_t tdotx(const Vector3& v) const  {
		return elements[0][0] * v[0] + elements[1][0] * v[1] + elements[2][0] * v[2];
	}
	_FORCE_INLINE_ real_t tdoty(const Vector3& v) const {
		return elements[0][1] * v[0] + elements[1][1] * v[1] + elements[2][1] * v[2];
	}
	_FORCE_INLINE_ real_t tdotz(const Vector3& v) const {
		return elements[0][2] * v[0] + elements[1][2] * v[1] + elements[2][2] * v[2];
	}

	bool isequal_approx(const Basis& a, const Basis& b) const;

	bool operator==(const Basis& p_matrix) const;
	bool operator!=(const Basis& p_matrix) const;

	_FORCE_INLINE_ Vector3 xform(const Vector3& p_vector) const;
	_FORCE_INLINE_ Vector3 xform_inv(const Vector3& p_vector) const;
	_FORCE_INLINE_ void operator*=(const Basis& p_matrix);
	_FORCE_INLINE_ Basis operator*(const Basis& p_matrix) const;
	_FORCE_INLINE_ void operator+=(const Basis& p_matrix);
	_FORCE_INLINE_ Basis operator+(const Basis& p_matrix) const;
	_FORCE_INLINE_ void operator-=(const Basis& p_matrix);
	_FORCE_INLINE_ Basis operator-(const Basis& p_matrix) const;
	_FORCE_INLINE_ void operator*=(real_t p_val);
	_FORCE_INLINE_ Basis operator*(real_t p_val) const;

	int get_orthogonal_index() const;
	void set_orthogonal_index(int p_index);

	bool is_orthogonal() const;
	bool is_rotation() const;

	operator String() const;

	void get_axis_and_angle(Vector3 &r_axis,real_t& r_angle) const;

	/* create / set */


	_FORCE_INLINE_ void set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {

		elements[0][0]=xx;
		elements[0][1]=xy;
		elements[0][2]=xz;
		elements[1][0]=yx;
		elements[1][1]=yy;
		elements[1][2]=yz;
		elements[2][0]=zx;
		elements[2][1]=zy;
		elements[2][2]=zz;
	}
	_FORCE_INLINE_ Vector3 get_column(int i) const {

		return Vector3(elements[0][i],elements[1][i],elements[2][i]);
	}

	_FORCE_INLINE_ Vector3 get_row(int i) const {

		return Vector3(elements[i][0],elements[i][1],elements[i][2]);
	}
	_FORCE_INLINE_ Vector3 get_main_diagonal() const {
		return Vector3(elements[0][0],elements[1][1],elements[2][2]);
	}

	_FORCE_INLINE_ void set_row(int i, const Vector3& p_row) {
		elements[i][0]=p_row.x;
		elements[i][1]=p_row.y;
		elements[i][2]=p_row.z;
	}

	_FORCE_INLINE_ void set_zero() {
		elements[0].zero();
		elements[1].zero();
		elements[2].zero();
	}

	_FORCE_INLINE_ Basis transpose_xform(const Basis& m) const
	{
		return Basis(
			elements[0].x * m[0].x + elements[1].x * m[1].x + elements[2].x * m[2].x,
			elements[0].x * m[0].y + elements[1].x * m[1].y + elements[2].x * m[2].y,
			elements[0].x * m[0].z + elements[1].x * m[1].z + elements[2].x * m[2].z,
			elements[0].y * m[0].x + elements[1].y * m[1].x + elements[2].y * m[2].x,
			elements[0].y * m[0].y + elements[1].y * m[1].y + elements[2].y * m[2].y,
			elements[0].y * m[0].z + elements[1].y * m[1].z + elements[2].y * m[2].z,
			elements[0].z * m[0].x + elements[1].z * m[1].x + elements[2].z * m[2].x,
			elements[0].z * m[0].y + elements[1].z * m[1].y + elements[2].z * m[2].y,
			elements[0].z * m[0].z + elements[1].z * m[1].z + elements[2].z * m[2].z);
	}
	Basis(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {

		set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
	}

	void orthonormalize();
	Basis orthonormalized() const;

	bool is_symmetric() const;
	Basis diagonalize();

	operator Quat() const;

	Basis(const Quat& p_quat); // euler
	Basis(const Vector3& p_euler); // euler
	Basis(const Vector3& p_axis, real_t p_phi);

	_FORCE_INLINE_ Basis(const Vector3& row0, const Vector3& row1, const Vector3& row2)
	{
		elements[0]=row0;
		elements[1]=row1;
		elements[2]=row2;
	}

	_FORCE_INLINE_ Basis() {

		elements[0][0]=1;
		elements[0][1]=0;
		elements[0][2]=0;
		elements[1][0]=0;
		elements[1][1]=1;
		elements[1][2]=0;
		elements[2][0]=0;
		elements[2][1]=0;
		elements[2][2]=1;
	}


};

_FORCE_INLINE_ void Basis::operator*=(const Basis& p_matrix) {

	set(
		p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
		p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
		p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]));

}

_FORCE_INLINE_ Basis Basis::operator*(const Basis& p_matrix) const {

	return Basis(
		p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
		p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
		p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]) );

}


_FORCE_INLINE_ void Basis::operator+=(const Basis& p_matrix) {

	elements[0] += p_matrix.elements[0];
	elements[1] += p_matrix.elements[1];
	elements[2] += p_matrix.elements[2];
}

_FORCE_INLINE_ Basis Basis::operator+(const Basis& p_matrix) const {
	
	Basis ret(*this);
	ret += p_matrix;
	return ret;
}

_FORCE_INLINE_ void Basis::operator-=(const Basis& p_matrix) {

	elements[0] -= p_matrix.elements[0];
	elements[1] -= p_matrix.elements[1];
	elements[2] -= p_matrix.elements[2];
}

_FORCE_INLINE_ Basis Basis::operator-(const Basis& p_matrix) const {
	
	Basis ret(*this);
	ret -= p_matrix;
	return ret;
}

_FORCE_INLINE_ void Basis::operator*=(real_t p_val) {

	elements[0]*=p_val;
	elements[1]*=p_val;
	elements[2]*=p_val;
}

_FORCE_INLINE_ Basis Basis::operator*(real_t p_val) const {

		Basis ret(*this);
		ret *= p_val;
		return ret;
}

Vector3 Basis::xform(const Vector3& p_vector) const {

	return Vector3(
		elements[0].dot(p_vector),
		elements[1].dot(p_vector),
		elements[2].dot(p_vector)
	);
}

Vector3 Basis::xform_inv(const Vector3& p_vector) const {

	return Vector3(
		(elements[0][0]*p_vector.x ) + ( elements[1][0]*p_vector.y ) + ( elements[2][0]*p_vector.z ),
		(elements[0][1]*p_vector.x ) + ( elements[1][1]*p_vector.y ) + ( elements[2][1]*p_vector.z ),
		(elements[0][2]*p_vector.x ) + ( elements[1][2]*p_vector.y ) + ( elements[2][2]*p_vector.z )
	);
}

real_t Basis::determinant() const {

	return elements[0][0]*(elements[1][1]*elements[2][2] - elements[2][1]*elements[1][2]) -
	       elements[1][0]*(elements[0][1]*elements[2][2] - elements[2][1]*elements[0][2]) +
	       elements[2][0]*(elements[0][1]*elements[1][2] - elements[1][1]*elements[0][2]);
}
#endif