#include <threevector.h>

The ThreeVector class represents a physical three-vector \( \mathbf{x} = (x_1,x_2,x_3)\) with the components \( x_1,x_2,x_3 \).

It is related to the classes FourVector and Angles, both of which can be converted into a ThreeVector using the 'threevec()' method.

Definition at line 31 of file threevector.h.

Public Types
using	iterator = std::array< double, 3 >::iterator
	iterates over the components More...

using	const_iterator = std::array< double, 3 >::const_iterator
	iterates over the components More...

Public Member Functions
	ThreeVector ()
	default constructor (nulls all components) More...

	ThreeVector (double y1, double y2, double y3)
	Constructor for ThreeVector that takes 3 doubles to set up a ThreeVector with desired values for the components. More...

double &	operator[] (std::size_t i)
	access the component at offset `i`. More...

double	operator[] (std::size_t i) const
	const overload of the above. More...

double	x1 () const

void	set_x1 (double x)
	set first component More...

double	x2 () const

void	set_x2 (double y)
	set second component More...

double	x3 () const

void	set_x3 (double z)
	set third component More...

double	sqr () const

double	abs () const

double	get_phi () const

double	get_theta () const

void	rotate (double phi, double theta, double psi)
	Rotate vector by the given Euler angles phi, theta, psi. More...

void	rotate_around_y (double theta)
	Rotate the vector around the y axis by the given angle theta. More...

void	rotate_around_z (double theta)
	Rotate the vector around the z axis by the given angle theta. More...

void	rotate_z_axis_to (ThreeVector &r)
	Rotate the z-axis onto the vector r. More...

ThreeVector	operator- () const
	Negation: Returns \(-\mathbf{x}\). More...

ThreeVector	operator+= (const ThreeVector &v)
	Increase this vector by \(\mathbf{v}\): \( \mathbf{x}^\prime = \mathbf{x} + \mathbf{v} \). More...

ThreeVector	operator-= (const ThreeVector &v)
	Decrease this vector by \(\mathbf{v}\): \( \mathbf{x}^\prime = \mathbf{x} - \mathbf{v} \). More...

ThreeVector	operator*= (const double &a)
	Scale this vector by \(a\): \( \mathbf{x}^\prime = a \cdot \mathbf{x} \). More...

ThreeVector	operator/= (const double &a)
	Divide this vector by \(a\): \( \mathbf x^\prime = \frac{1}{a} \cdot \mathbf{x}\). More...

bool	operator== (const ThreeVector &rhs) const

bool	operator!= (const ThreeVector &rhs) const

ThreeVector	cross_product (const ThreeVector &b) const

iterator	begin ()

iterator	end ()

const_iterator	begin () const
	const overload of the above More...

const_iterator	end () const
	const overload of the above More...

const_iterator	cbegin () const

const_iterator	cend () const

Private Attributes
std::array< double, 3 >	x_
	the internal storage of the components. More...

Member Typedef Documentation

◆ iterator

using smash::ThreeVector::iterator = std::array<double, 3>::iterator

iterates over the components

Definition at line 141 of file threevector.h.

◆ const_iterator

using smash::ThreeVector::const_iterator = std::array<double, 3>::const_iterator

iterates over the components

Definition at line 143 of file threevector.h.

Constructor & Destructor Documentation

◆ ThreeVector() [1/2]

smash::ThreeVector::ThreeVector ( )

inline

default constructor (nulls all components)

Definition at line 34 of file threevector.h.

34 : x_({0., 0., 0.}) {}

smash::ThreeVector::x_

std::array< double, 3 > x_

the internal storage of the components.

Definition: threevector.h:168

◆ ThreeVector() [2/2]

smash::ThreeVector::ThreeVector	(	double	y1,
		double	y2,
		double	y3
	)

inline

Constructor for ThreeVector that takes 3 doubles to set up a ThreeVector with desired values for the components.

Parameters

[in]	y1	value of the first component
[in]	y2	value of the second component
[in]	y3	value of the third component

Definition at line 44 of file threevector.h.

44 : x_({y1, y2, y3}) {}

Member Function Documentation

◆ operator[]() [1/2]

double& smash::ThreeVector::operator[] ( std::size_t i )

inline

access the component at offset i.

Definition at line 47 of file threevector.h.

47 { return x_[i]; }

◆ operator[]() [2/2]

double smash::ThreeVector::operator[] ( std::size_t i ) const

inline

const overload of the above.

Definition at line 49 of file threevector.h.

49 { return x_[i]; }

◆ x1()

double smash::ThreeVector::x1 ( ) const

inline

Returns: first component

Definition at line 177 of file threevector.h.

177 { return x_[0]; }

◆ set_x1()

void smash::ThreeVector::set_x1 ( double x )

inline

set first component

Definition at line 179 of file threevector.h.

179 { x_[0] = x; }

◆ x2()

double smash::ThreeVector::x2 ( ) const

inline

Returns: second component

Definition at line 181 of file threevector.h.

181 { return x_[1]; }

◆ set_x2()

void smash::ThreeVector::set_x2 ( double y )

inline

set second component

Definition at line 183 of file threevector.h.

183 { x_[1] = y; }

◆ x3()

double smash::ThreeVector::x3 ( ) const

inline

Returns: third component

Definition at line 185 of file threevector.h.

185 { return x_[2]; }

◆ set_x3()

void smash::ThreeVector::set_x3 ( double z )

inline

set third component

Definition at line 187 of file threevector.h.

187 { x_[2] = z; }

◆ sqr()

double smash::ThreeVector::sqr ( ) const

inline

Returns: the square of the vector (which is a scalar)

Definition at line 266 of file threevector.h.

266 { return (*this) * (*this); }

◆ abs()

double smash::ThreeVector::abs ( ) const

inline

Returns: the absolute value

Definition at line 268 of file threevector.h.

268 { return std::sqrt((*this) * (*this)); }

◆ get_phi()

double smash::ThreeVector::get_phi ( ) const

inline

Returns: the azimuthal angle phi

Definition at line 270 of file threevector.h.

                                          {
   if (std::abs(x1()) < really_small && std::abs(x2()) < really_small) {
     return 0.;
   } else {
     return std::atan2(x2(), x1());
   }
 }

◆ get_theta()

double smash::ThreeVector::get_theta ( ) const

inline

Returns: the polar angle theta

Definition at line 278 of file threevector.h.

                                            {
   double r = abs();
   return (r > 0.) ? std::acos(x3() / r) : 0.;
 }

◆ rotate()

void smash::ThreeVector::rotate	(	double	phi,
		double	theta,
		double	psi
	)

inline

Rotate vector by the given Euler angles phi, theta, psi.

If we assume the standard basis x, y, z, then this means applying the matrix for a rotation by phi about the z-axis, followed by the matrix for a rotation by theta about the rotated x-axis. Last, psi is a rotation about the rotated z-axis. To reverse the rotation one has to therefore exchange phi and psi and use the negative values for all angles.

Parameters

[in]	phi	angle by which the first rotation is done about the z-axis. Range: [0,2&pi]
[in]	theta	angle by which the second rotation is done about the rotated x-axis. Range: [0,&pi]
[in]	psi	angle by which the third rotation is done about the rotated z-axis. Range: [0,2&pi]

Euler angles are used to make rotation of several (different) position vectors belonging to one rigid body easy. A ThreeVector could be rotated via only two angles, but then the angles for rotating a rigid body consisting of multiple particles would require a different pair of rotation angles for every position.

Definition at line 283 of file threevector.h.

                                                                     {
   // Compute the cosine and sine for each angle.
   const double cos_phi = std::cos(phi);
   const double sin_phi = std::sin(phi);
   const double cos_theta = std::cos(theta);
   const double sin_theta = std::sin(theta);
   const double cos_psi = std::cos(psi);
   const double sin_psi = std::sin(psi);
   // Get original coordinates.
   std::array<double, 3> x_old = x_;
   // Compute new coordinates.
   x_[0] = (cos_phi * cos_psi - sin_phi * cos_theta * sin_psi) * x_old[0] +
           (-cos_phi * sin_psi - sin_phi * cos_theta * cos_psi) * x_old[1] +
           (sin_phi * sin_theta) * x_old[2];
   x_[1] = (sin_phi * cos_psi + cos_phi * cos_theta * sin_psi) * x_old[0] +
           (-sin_phi * sin_psi + cos_phi * cos_theta * cos_psi) * x_old[1] +
           (-cos_phi * sin_theta) * x_old[2];
   x_[2] = (sin_theta * sin_psi) * x_old[0] + (sin_theta * cos_psi) * x_old[1] +
           (cos_theta)*x_old[2];
 }

◆ rotate_around_y()

void smash::ThreeVector::rotate_around_y ( double theta )

inline

Rotate the vector around the y axis by the given angle theta.

Parameters

[in] theta angle by which the rotation is done about y axis.

Definition at line 304 of file threevector.h.

                                                      {
   const double cost = std::cos(theta);
   const double sint = std::sin(theta);
   // Get original coordinates.
   std::array<double, 3> x_old = x_;
   // Compute new coordinates.
   x_[0] = cost * x_old[0] + sint * x_old[2];
   // x_[1] is unchanged
   x_[2] = -sint * x_old[0] + cost * x_old[2];
 }

◆ rotate_around_z()

void smash::ThreeVector::rotate_around_z ( double theta )

inline

Rotate the vector around the z axis by the given angle theta.

Parameters

[in] theta angle by which the rotation is done about z axis.

Definition at line 315 of file threevector.h.

                                                      {
   const double cost = std::cos(theta);
   const double sint = std::sin(theta);
   // Get original coordinates.
   std::array<double, 3> x_old = x_;
   // Compute new coordinates.
   x_[0] = cost * x_old[0] - sint * x_old[1];
   x_[1] = sint * x_old[0] + cost * x_old[1];
   // x_[2] is unchanged
 }

◆ rotate_z_axis_to()

void smash::ThreeVector::rotate_z_axis_to ( ThreeVector & r )

inline

Rotate the z-axis onto the vector r.

Parameters

[in] r direction in which new z-axis is aligned

Definition at line 326 of file threevector.h.

                                                         {
   rotate_around_y(r.get_theta());
   rotate_around_z(r.get_phi());
 }

◆ operator-()

ThreeVector smash::ThreeVector::operator- ( ) const

inline

Negation: Returns \(-\mathbf{x}\).

Definition at line 189 of file threevector.h.

                                                 {
   ThreeVector neg(-x_[0], -x_[1], -x_[2]);
   return neg;
 }

◆ operator+=()

ThreeVector smash::ThreeVector::operator+= ( const ThreeVector & v )

inline

Increase this vector by \(\mathbf{v}\): \( \mathbf{x}^\prime = \mathbf{x} + \mathbf{v} \).

Definition at line 194 of file threevector.h.

                                                                {
   x_[0] += v.x_[0];
   x_[1] += v.x_[1];
   x_[2] += v.x_[2];
   return *this;
 }

◆ operator-=()

ThreeVector smash::ThreeVector::operator-= ( const ThreeVector & v )

inline

Decrease this vector by \(\mathbf{v}\): \( \mathbf{x}^\prime = \mathbf{x} - \mathbf{v} \).

Definition at line 207 of file threevector.h.

                                                                {
   x_[0] -= v.x_[0];
   x_[1] -= v.x_[1];
   x_[2] -= v.x_[2];
   return *this;
 }

◆ operator*=()

ThreeVector smash::ThreeVector::operator*= ( const double & a )

inline

Scale this vector by \(a\): \( \mathbf{x}^\prime = a \cdot \mathbf{x} \).

Definition at line 220 of file threevector.h.

                                                           {
   x_[0] *= a;
   x_[1] *= a;
   x_[2] *= a;
   return *this;
 }

◆ operator/=()

ThreeVector smash::ThreeVector::operator/= ( const double & a )

inline

Divide this vector by \(a\): \( \mathbf x^\prime = \frac{1}{a} \cdot \mathbf{x}\).

Definition at line 252 of file threevector.h.

                                                           {
   const double a_inv = 1.0 / a;
   x_[0] *= a_inv;
   x_[1] *= a_inv;
   x_[2] *= a_inv;
   return *this;
 }

◆ operator==()

bool smash::ThreeVector::operator== ( const ThreeVector & rhs ) const

inline

Returns: whether the vector is identical to another vector

Definition at line 131 of file threevector.h.

131 { return x_ == rhs.x_; }

◆ operator!=()

bool smash::ThreeVector::operator!= ( const ThreeVector & rhs ) const

inline

Returns: whether the vector is different from another vector

Definition at line 133 of file threevector.h.

133 { return x_ != rhs.x_; }

◆ cross_product()

ThreeVector smash::ThreeVector::cross_product ( const ThreeVector & b ) const

inline

Returns: cross product of this vector \(\mathbf{x}\) and another vector: \( \mathbf{x} \times \mathbf{b} \)

Definition at line 246 of file threevector.h.

                                                                         {
   return ThreeVector(x_[1] * b.x3() - x_[2] * b.x2(),
                      x_[2] * b.x1() - x_[0] * b.x3(),
                      x_[0] * b.x2() - x_[1] * b.x1());
 }

◆ begin() [1/2]

iterator smash::ThreeVector::begin ( )

inline

Returns: an iterator starting at the 0th component.

The iterator implements the randomIterator concept. Thus, you can simply write begin() + 1 to get an iterator that points to the 1st component.

Definition at line 151 of file threevector.h.

151 { return x_.begin(); }

◆ end() [1/2]

iterator smash::ThreeVector::end ( )

inline

Returns: an iterator pointing after the 4th component.

Definition at line 154 of file threevector.h.

154 { return x_.end(); }

◆ begin() [2/2]

const_iterator smash::ThreeVector::begin ( ) const

inline

const overload of the above

Definition at line 157 of file threevector.h.

157 { return x_.begin(); }

◆ end() [2/2]

const_iterator smash::ThreeVector::end ( ) const

inline

const overload of the above

Definition at line 159 of file threevector.h.

159 { return x_.end(); }

◆ cbegin()

const_iterator smash::ThreeVector::cbegin ( ) const

inline

See also: begin

Definition at line 162 of file threevector.h.

162 { return x_.cbegin(); }

◆ cend()

const_iterator smash::ThreeVector::cend ( ) const

inline

See also: end

Definition at line 164 of file threevector.h.

164 { return x_.cend(); }

Member Data Documentation

◆ x_

std::array<double, 3> smash::ThreeVector::x_

private

the internal storage of the components.

Definition at line 168 of file threevector.h.

The documentation for this class was generated from the following file:

src/include/smash/threevector.h

Public Types

Public Member Functions

Private Attributes

Member Typedef Documentation

◆ iterator

◆ const_iterator

Constructor & Destructor Documentation

◆ ThreeVector() [1/2]

◆ ThreeVector() [2/2]

Member Function Documentation

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ x1()

◆ set_x1()

◆ x2()

◆ set_x2()

◆ x3()

◆ set_x3()

◆ sqr()

◆ abs()

◆ get_phi()

◆ get_theta()

◆ rotate()

◆ rotate_around_y()

◆ rotate_around_z()

◆ rotate_z_axis_to()

◆ operator-()

◆ operator+=()

◆ operator-=()

◆ operator*=()

◆ operator/=()

◆ operator==()

◆ operator!=()

◆ cross_product()

◆ begin() [1/2]

◆ end() [1/2]

◆ begin() [2/2]

◆ end() [2/2]

◆ cbegin()

◆ cend()

Member Data Documentation

◆ x_