text: /*************************************************************************/
  /*  basis.h                                                              */
  /*************************************************************************/
  /*                       This file is part of:                           */
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  /* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur.                 */
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  #ifndef BASIS_H
  #define BASIS_H
  
  #include "vector3.h"
  #include "quat.h"
  
  class Basis {
  public:
  	Vector3 elements[3] = {
  		Vector3(1, 0, 0),
  		Vector3(0, 1, 0),
  		Vector3(0, 0, 1)
  	};
  
  	inline const Vector3& operator[](int axis) const {
  		return elements[axis];
  	}
  	inline Vector3& operator[](int axis) {
  		return elements[axis];
  	}
  
  	void invert();
  	void transpose();
  
  	Basis inverse() const;
  	Basis transposed() const;
  
  	inline double determinant() const;
  
  	void from_z(const Vector3& p_z);
  
  	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]);
  	}
  	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, double p_phi);
  	Basis rotated(const Vector3& p_axis, double p_phi) const;
  
  	void rotate_local(const Vector3& p_axis, double p_phi);
  	Basis rotated_local(const Vector3& p_axis, double p_phi) const;
  
  	void rotate(const Vector3& p_euler);
  	Basis rotated(const Vector3& p_euler) const;
  
  	void rotate(const Quat& p_quat);
  	Basis rotated(const Quat& p_quat) const;
  
  	Vector3 get_rotation_euler() const;
  	void get_rotation_axis_angle(Vector3& p_axis, double& p_angle) const;
  	void get_rotation_axis_angle_local(Vector3& p_axis, double& p_angle) const;
  	Quat get_rotation_quat() const;
  	Vector3 get_rotation() const { return get_rotation_euler(); };
  
  	Vector3 rotref_posscale_decomposition(Basis& rotref) const;
  
  	Vector3 get_euler_xyz() const;
  	void set_euler_xyz(const Vector3& p_euler);
  
  	Vector3 get_euler_xzy() const;
  	void set_euler_xzy(const Vector3& p_euler);
  
  	Vector3 get_euler_yzx() const;
  	void set_euler_yzx(const Vector3& p_euler);
  
  	Vector3 get_euler_yxz() const;
  	void set_euler_yxz(const Vector3& p_euler);
  
  	Vector3 get_euler_zxy() const;
  	void set_euler_zxy(const Vector3& p_euler);
  
  	Vector3 get_euler_zyx() const;
  	void set_euler_zyx(const Vector3& p_euler);
  
  	Quat get_quat() const;
  	void set_quat(const Quat& p_quat);
  
  	Vector3 get_euler() const { return get_euler_yxz(); }
  	void set_euler(const Vector3& p_euler) { set_euler_yxz(p_euler); }
  
  	void get_axis_angle(Vector3& r_axis, double& r_angle) const;
  	void set_axis_angle(const Vector3& p_axis, double p_phi);
  
  	void scale(const Vector3& p_scale);
  	Basis scaled(const Vector3& p_scale) const;
  
  	void scale_local(const Vector3& p_scale);
  	Basis scaled_local(const Vector3& p_scale) const;
  
  	void make_scale_uniform();
  	float get_uniform_scale() const;
  
  	Vector3 get_scale() const;
  	Vector3 get_scale_abs() const;
  	Vector3 get_scale_local() const;
  
  	void set_axis_angle_scale(const Vector3& p_axis, double p_phi, const Vector3& p_scale);
  	void set_euler_scale(const Vector3& p_euler, const Vector3& p_scale);
  	void set_quat_scale(const Quat& p_quat, const Vector3& p_scale);
  
  	// transposed dot products
  	inline double tdotx(const Vector3& v) const {
  		return elements[0][0] * v[0] + elements[1][0] * v[1] + elements[2][0] * v[2];
  	}
  	inline double tdoty(const Vector3& v) const {
  		return elements[0][1] * v[0] + elements[1][1] * v[1] + elements[2][1] * v[2];
  	}
  	inline double tdotz(const Vector3& v) const {
  		return elements[0][2] * v[0] + elements[1][2] * v[1] + elements[2][2] * v[2];
  	}
  
  	bool is_equal_approx(const Basis& p_basis) const;
  
  	bool operator==(const Basis& p_matrix) const;
  	bool operator!=(const Basis& p_matrix) const;
  
  	inline Vector3 xform(const Vector3& p_vector) const;
  	inline Vector3 xform_inv(const Vector3& p_vector) const;
  	inline void operator*=(const Basis& p_matrix);
  	inline Basis operator*(const Basis& p_matrix) const;
  	inline void operator+=(const Basis& p_matrix);
  	inline Basis operator+(const Basis& p_matrix) const;
  	inline void operator-=(const Basis& p_matrix);
  	inline Basis operator-(const Basis& p_matrix) const;
  	inline void operator*=(double p_val);
  	inline Basis operator*(double p_val) const;
  
  	int get_orthogonal_index() const;
  	void set_orthogonal_index(int p_index);
  
  	void set_diagonal(const Vector3& p_diag);
  
  	bool is_orthogonal() const;
  	bool is_diagonal() const;
  	bool is_rotation() const;
  
  	Basis slerp(const Basis& target, const double& t) const;
  	void rotate_sh(double* p_values);
  
  	/* create / set */
  
  	inline void set(double xx, double xy, double xz, double yx, double yy, double yz, double zx, double zy, double 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;
  	}
  	inline void set(const Vector3& p_x, const Vector3& p_y, const Vector3& p_z) {
  		set_axis(0, p_x);
  		set_axis(1, p_y);
  		set_axis(2, p_z);
  	}
  	inline Vector3 get_column(int i) const {
  		return Vector3(elements[0][i], elements[1][i], elements[2][i]);
  	}
  
  	inline Vector3 get_row(int i) const {
  		return Vector3(elements[i][0], elements[i][1], elements[i][2]);
  	}
  	inline Vector3 get_main_diagonal() const {
  		return Vector3(elements[0][0], elements[1][1], elements[2][2]);
  	}
  
  	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;
  	}
  
  	inline void set_zero() {
  		elements[0].zero();
  		elements[1].zero();
  		elements[2].zero();
  	}
  
  	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(double xx, double xy, double xz, double yx, double yy, double yz, double zx, double zy, double zz) {
  		set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
  	}
  
  	void orthonormalize();
  	Basis orthonormalized() const;
  
  #ifdef MATH_CHECKS
  	bool is_symmetric() const;
  #endif
  	Basis diagonalize();
  
  	operator Quat() const { return get_quat(); }
  
  	Basis(const Quat& p_quat) { set_quat(p_quat); };
  	Basis(const Quat& p_quat, const Vector3& p_scale) { set_quat_scale(p_quat, p_scale); }
  
  	Basis(const Vector3& p_euler) { set_euler(p_euler); }
  	Basis(const Vector3& p_euler, const Vector3& p_scale) { set_euler_scale(p_euler, p_scale); }
  
  	Basis(const Vector3& p_axis, double p_phi) { set_axis_angle(p_axis, p_phi); }
  	Basis(const Vector3& p_axis, double p_phi, const Vector3& p_scale) { set_axis_angle_scale(p_axis, p_phi, p_scale); }
  
  	inline Basis(const Vector3& row0, const Vector3& row1, const Vector3& row2) {
  		elements[0] = row0;
  		elements[1] = row1;
  		elements[2] = row2;
  	}
  
  	inline Basis() {}
  };
  
  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]));
  }
  
  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]));
  }
  
  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];
  }
  
  inline Basis Basis::operator+(const Basis& p_matrix) const {
  	Basis ret(*this);
  	ret += p_matrix;
  	return ret;
  }
  
  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];
  }
  
  inline Basis Basis::operator-(const Basis& p_matrix) const {
  	Basis ret(*this);
  	ret -= p_matrix;
  	return ret;
  }
  
  inline void Basis::operator*=(double p_val) {
  	elements[0] *= p_val;
  	elements[1] *= p_val;
  	elements[2] *= p_val;
  }
  
  inline Basis Basis::operator*(double 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));
  }
  
  double 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