smash::Angles Class Reference

#include <angles.h>

Angles provides a common interface for generating directions: i.e., two angles that should be interpreted as azimuthal and polar angles.

Usage:

#include "Angles.h"
 
Angles direction;
 
direction.distribute_isotropically();
double azimuthal_angle = direction.phi();
double cosine_of_polar_angle = direction.costheta();
double x_projection_of_vector = direction.x();
direction.set_phi(0);
double new_azimuthal_angle = direction.phi();
// new_azimuthal_angle == 0.

Definition at line 59 of file angles.h.

Classes
struct	InvalidTheta
	Thrown for invalid values for theta. More...

Public Member Functions
	Angles ()
	Default constructor. More...
	Angles (double ph, double cost)
void	distribute_isotropically ()
	Populate the object with a new direction. More...
void	set_phi (const double phi)
	Sets the azimuthal angle. More...
void	set_psi (const double psi)
	Sets the euler angle psi. More...
void	set_costheta (const double cos)
	Set the polar angle from its cosine. More...
void	set_theta (const double theta)
	Set the polar angle. More...
bool	add_to_theta (const double delta)
	Advance polar angle. More...
bool	add_to_theta (const double delta, const bool reverse)
	Advance polar angle. More...
double	phi () const
double	psi () const
double	costheta () const
double	sintheta () const
double	x () const
double	y () const
double	z () const
ThreeVector	threevec () const
double	theta () const

Private Attributes
double	phi_
	Azimuthal angle \(\varphi\). More...
double	psi_
	Euler angle \(\psi\). More...
double	costheta_
	Cosine of polar angle \(\cos\vartheta\). More...

Constructor & Destructor Documentation

Angles() [1/2]

smash::Angles::Angles ( )

inline

Default constructor.

Returns

Angles pointing in x-direction.

Definition at line 65 of file angles.h.

: phi_(0), costheta_(0) {}

Angles() [2/2]

smash::Angles::Angles ( double  ph, double  cost  )

inline

Returns

Angles with given phi and cos(theta).

Parameters

[in]	ph	the azimuthal angle
[in]	cost	cosine of the polar angle

Definition at line 71 of file angles.h.

                                 {
    set_phi(ph);
    set_costheta(cost);
  }

Member Function Documentation

distribute_isotropically()

void smash::Angles::distribute_isotropically ( )

inline

Populate the object with a new direction.

the direction is taken randomly from a homogeneous distribution, i.e., each point on a unit sphere is equally likely.

Definition at line 199 of file angles.h.

                                             {
  /* Isotropic distribution: phi in [0, 2pi) and cos(theta) in [-1,1]. */
  phi_ = random::uniform(0.0, twopi);
  costheta_ = random::uniform(-1.0, 1.0);
}

set_phi()

void smash::Angles::set_phi ( const double  phi )

inline

Sets the azimuthal angle.

Parameters

[in]

phi

Any real number to set the azimuthal angle \(\varphi\) to.

Definition at line 205 of file angles.h.

                                               {
  /* Make sure that phi is in the range [0,2pi).  */
  phi_ = newphi;
  if (newphi < 0 || newphi >= twopi) {
    phi_ -= twopi * std::floor(newphi / twopi);
  }
}

set_psi()

void smash::Angles::set_psi ( const double  psi )

inline

Sets the euler angle psi.

Parameters

[in]

psi

Any real number to set the azimuthal angle \(\varphi\) to.

Definition at line 213 of file angles.h.

                                               {
  /* Make sure that phi is in the range [0,2pi).  */
  psi_ = newpsi;
  if (newpsi < 0 || newpsi >= twopi) {
    psi_ -= twopi * std::floor(newpsi / twopi);
  }
}

set_costheta()

void smash::Angles::set_costheta ( const double  cos )

inline

Set the polar angle from its cosine.

This is the preferred way of setting the polar information.

Parameters

[in]

cos

Cosine of the polar angle \(\cos\vartheta\).

Exceptions

InvalidTheta

If cos is not in range [-1 .. 1].

Definition at line 221 of file angles.h.

                                                    {
  costheta_ = newcos;
  /* check if costheta_ is in -1..1. If not, well. Error handling here
   * is a lot harder than in the above. Still, I will silently do the
   * same as above. Note, though, that costheta = 1 is allowed, even if
   * it cannot be generated by distribute_isotropically(). */
  if ((costheta_ < -1. - really_small) || (costheta_ > 1. + really_small)) {
    throw InvalidTheta("Wrong value for costheta (must be in [-1,1]): " +
                       std::to_string(costheta_));
  }
  if (costheta_ < -1.) {
    costheta_ = -1.;
  } else if (costheta_ > 1.) {
    costheta_ = 1.;
  }
}

set_theta()

void smash::Angles::set_theta ( const double  theta )

inline

Set the polar angle.

In the current implementation, costheta is stored inside the object. Don't convert the angle to and from cosine, use the set-function for the thing you have at hand.

Parameters

[in]

theta

Any real number to set the polar angle \(\vartheta\) to.

Definition at line 237 of file angles.h.

                                                   {
  /* no error handling necessary, because this gives a sensible answer
   * for every real number. */
  set_costheta(std::cos(newtheta));
}

add_to_theta() [1/2]

bool smash::Angles::add_to_theta ( const double  delta )

inline

Advance polar angle.

A positive addition means that we go towards the southpole.

See also

add_to_theta(const double& delta, const bool& reverse)

Parameters

[in]

delta

Angle increment.

Returns

true if pole has been crossed.

Exceptions

InvalidTheta

If delta is not in [ \(-\pi\) .. \(\pi\)].

Definition at line 243 of file angles.h.

                                                   {
  if (delta < -M_PI || delta > M_PI) {
    throw InvalidTheta("Cannot advance polar angle by " +
                       std::to_string(delta));
  }
  double theta_plus_delta = delta + theta();
  /* if sum is not in [0, PI], force it to be there:
   * "upper" overflow:
   * theta + delta + the_new_angle = 2*M_PI */
  if (theta_plus_delta > M_PI) {
    set_theta(twopi - theta_plus_delta);
    // set_phi takes care that phi_ is in [0 .. 2*M_PI]
    set_phi(phi() + M_PI);
    return true;  // meaning "we did change phi"
    // "lower" overflow: theta + delta switches sign
  } else if (theta_plus_delta < 0) {
    set_theta(-theta_plus_delta);
    set_phi(phi() + M_PI);
    return true;  // meaning "we did change phi"
    // no overflow: set theta, do not touch phi:
  } else {
    set_theta(theta_plus_delta);
  }
  return false;  // meaning "we did NOT change phi"
}

add_to_theta() [2/2]

bool smash::Angles::add_to_theta ( const double  delta, const bool  reverse  )

inline

Advance polar angle.

When crossing a pole, azimuthal angle is changed by 180 degrees.

Parameters

[in]	delta	Angle increment.
[in]	reverse	If true, we start in the "far" hemisphere, meaning a positive delta will shift the object towards the north pole.

Returns

true if we end up in the far hemisphere, false if we end up in the original hemisphere.

Exceptions

InvalidTheta

If delta is not in [ \(-\pi\) .. \(\pi\)].

Definition at line 268 of file angles.h.

                                                                       {
  double plusminus_one = reverse ? -1.0 : +1.0;
  bool this_reverse = add_to_theta(plusminus_one * delta);
  /* if we had to reverse first time and now reverse again OR if we
   * didn't reverse in either part, we do not reverse in total.
   * else: if we reverse in one, but not the other part, we reverse in
   * total. */
  return this_reverse ^ reverse;
}

phi()

double smash::Angles::phi ( ) const

inline

Returns

Azimuthal angle.

Definition at line 279 of file angles.h.

{ return phi_; }

psi()

double smash::Angles::psi ( ) const

inline

Returns

Euler angle.

Definition at line 280 of file angles.h.

{ return psi_; }

costheta()

double smash::Angles::costheta ( ) const

inline

Returns

Cosine of polar angle.

Definition at line 278 of file angles.h.

{ return costheta_; }

sintheta()

double smash::Angles::sintheta ( ) const

inline

Returns

Sine of polar angle.

Definition at line 281 of file angles.h.

                                     {
  return std::sqrt(1.0 - costheta_ * costheta_);
}

x()

double smash::Angles::x ( ) const

inline

Returns

\(x\) projection of the direction.

\(x = \sin\vartheta \cos\varphi\)

Definition at line 284 of file angles.h.

{ return sintheta() * std::cos(phi_); }

y()

double smash::Angles::y ( ) const

inline

Returns

\(y\) projection of the direction.

\(y = \sin\vartheta \sin\varphi\)

Definition at line 285 of file angles.h.

{ return sintheta() * std::sin(phi_); }

z()

double smash::Angles::z ( ) const

inline

Returns

\(z\) projection of the direction.

\(z = \cos\vartheta\)

Definition at line 286 of file angles.h.

{ return costheta_; }

threevec()

ThreeVector smash::Angles::threevec ( ) const

inline

Returns

The unit three-vector corresponding to the angles.

Definition at line 288 of file angles.h.

                                          {
  return ThreeVector(x(), y(), z());
}

theta()

double smash::Angles::theta ( ) const

inline

Returns

The polar angle.

Definition at line 292 of file angles.h.

{ return std::acos(costheta_); }

Member Data Documentation

phi_

double smash::Angles::phi_

private

Azimuthal angle \(\varphi\).

Definition at line 184 of file angles.h.

psi_

double smash::Angles::psi_

private

Euler angle \(\psi\).

Definition at line 186 of file angles.h.

costheta_

double smash::Angles::costheta_

private

Cosine of polar angle \(\cos\vartheta\).

Definition at line 188 of file angles.h.

---

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

• src/include/smash/angles.h