smash::ThreeVector Class Reference

#include <threevector.h>

The ThreeVector class represents a physical three-vector \( \vec{x} = (x_1,x_2,x_3)\) 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 30 of file threevector.h.

Collaboration diagram for smash::ThreeVector:

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)
	copy constructor 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 \(-\vec x\) More...
ThreeVector	operator+= (const ThreeVector &v)
	increase this vector by \(\vec v: \vec x^\prime = \vec x + \vec v\) More...
ThreeVector	operator-= (const ThreeVector &v)
	decrease this vector by \(\vec v: \vec x^\prime = \vec x - \vec v\) More...
ThreeVector	operator*= (const double &a)
	scale this vector by \(a: \vec x^\prime = a \cdot \vec x\) More...
ThreeVector	operator/= (const double &a)
	divide this vector by \(a: \vec x^\prime = \frac{1}{a} \cdot \vec x\) More...
bool	operator== (const ThreeVector &rhs) const
bool	operator!= (const ThreeVector &rhs) const
ThreeVector	CrossProduct (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 119 of file threevector.h.

const_iterator

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

iterates over the components

Definition at line 121 of file threevector.h.

Constructor & Destructor Documentation

ThreeVector() [1/2]

smash::ThreeVector::ThreeVector ( )

inline

default constructor (nulls all components)

Definition at line 33 of file threevector.h.

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

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ThreeVector() [2/2]

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

inline

copy constructor

Definition at line 36 of file threevector.h.

: 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 39 of file threevector.h.

{ return x_[i]; }

operator[]() [2/2]

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

inline

const overload of the above.

Definition at line 41 of file threevector.h.

{ return x_[i]; }

x1()

double smash::ThreeVector::x1 ( ) const

inline

Returns

first component

Definition at line 155 of file threevector.h.

{ return x_[0]; }

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set_x1()

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

inline

set first component

Definition at line 157 of file threevector.h.

{ x_[0] = x; }

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x2()

double smash::ThreeVector::x2 ( ) const

inline

Returns

second component

Definition at line 159 of file threevector.h.

{ return x_[1]; }

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set_x2()

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

inline

set second component

Definition at line 161 of file threevector.h.

{ x_[1] = y; }

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x3()

double smash::ThreeVector::x3 ( ) const

inline

Returns

third component

Definition at line 163 of file threevector.h.

{ return x_[2]; }

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set_x3()

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

inline

set third component

Definition at line 165 of file threevector.h.

{ x_[2] = z; }

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sqr()

double smash::ThreeVector::sqr ( ) const

inline

Returns

the square of the vector (which is a scalar)

Definition at line 249 of file threevector.h.

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

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abs()

double smash::ThreeVector::abs ( ) const

inline

Returns

the absolute value

Definition at line 251 of file threevector.h.

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

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get_phi()

double smash::ThreeVector::get_phi ( ) const

inline

Returns

the azimuthal angle phi

Definition at line 253 of file threevector.h.

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

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get_theta()

double smash::ThreeVector::get_theta ( ) const

inline

Returns

the polar angle theta

Definition at line 261 of file threevector.h.

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

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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 of phi about z, followed by the matrix for a rotation theta about the rotated x axis. Last, psi is a rotation about the rotated z axis.

Parameters

[in]	phi	angle by which the first rotation is done about z axis.
[in]	theta	angle by which the second rotation is done about the rotated x axis.
[in]	psi	angle by which the third rotation is done about the rotated z axis.

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 266 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] +
          (sin_phi * cos_psi + cos_phi * cos_theta * sin_psi) * x_old[1] +
          sin_theta * sin_psi * x_old[2];
  x_[1] = (-cos_phi * sin_psi - sin_phi * cos_theta * cos_psi) * x_old[0] +
          (-sin_phi * sin_psi + cos_phi * cos_theta * cos_psi) * x_old[1] +
          sin_theta * cos_psi * x_old[2];
  x_[2] = sin_phi * sin_theta * x_old[0] - cos_phi * sin_theta * x_old[1] +
          cos_theta * x_old[2];
}

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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 287 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];
}

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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 298 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
}

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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 new z-axis is aligned

Definition at line 309 of file threevector.h.

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

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operator-()

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

inline

negation: Returns \(-\vec x\)

Definition at line 167 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 \(\vec v: \vec x^\prime = \vec x + \vec v\)

Definition at line 172 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 \(\vec v: \vec x^\prime = \vec x - \vec v\)

Definition at line 185 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 \(a: \vec x^\prime = a \cdot \vec x\)

Definition at line 198 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 \(a: \vec x^\prime = \frac{1}{a} \cdot \vec x\)

Definition at line 235 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 109 of file threevector.h.

{ 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 111 of file threevector.h.

{ return x_ != rhs.x_; }

CrossProduct()

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

inline

Returns

cross product of this vector and another vector \( \vec{this} \times \vec{b} \)

cross product of two three-vectors \( \vec{a} \times \vec{b} \)

Definition at line 229 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());
}

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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 129 of file threevector.h.

{ return x_.begin(); }

end() [1/2]

iterator smash::ThreeVector::end ( )

inline

Returns

an iterator pointing after the 4th component.

Definition at line 132 of file threevector.h.

{ return x_.end(); }

begin() [2/2]

const_iterator smash::ThreeVector::begin ( ) const

inline

const overload of the above

Definition at line 135 of file threevector.h.

{ return x_.begin(); }

end() [2/2]

const_iterator smash::ThreeVector::end ( ) const

inline

const overload of the above

Definition at line 137 of file threevector.h.

{ return x_.end(); }

cbegin()

const_iterator smash::ThreeVector::cbegin ( ) const

inline

See also

begin

Definition at line 140 of file threevector.h.

{ return x_.cbegin(); }

cend()

const_iterator smash::ThreeVector::cend ( ) const

inline

See also

end

Definition at line 142 of file threevector.h.

{ return x_.cend(); }

Member Data Documentation

x_

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

private

the internal storage of the components.

Definition at line 146 of file threevector.h.

---

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

• src/include/smash/threevector.h