General symmetry functions. More...

#include "symmetry.h"
#include "random_numbers.h"
#include "Euler.h"
#include "linked_list.h"
#include "utilities.h"

Functions
string	symmetry_helical_label (double helix_rise, double helix_angle, int dyad_axis, int cyclic, double seam_shift)
	Returns the label for helical symmetry. More...

View	view_symmetry_reference (Bsymmetry &sym)
	Returns an asymmetric unit reference point. More...

Matrix3	symmetry_rotate_to_axis (Bsymmetry &sym, long axis, long axis_flag)
	Rotation matrix to orient a symmetry axis on the z axis. More...

vector< Vector3< double > >	symmetry_get_axes (Bsymmetry &sym)
	Get all symmetry axes. More...

View *	symmetry_get_all_views (Bsymmetry &sym, View asu_view)
	Get all symmetry-related views of one given view. More...

View *	symmetry_get_all_views (Bsymmetry &sym, View *views)

vector< Matrix3 >	symmetry_get_all_matrices (Bsymmetry &sym)
	Get all symmetry-related views of one given view. More...

View *	asymmetric_unit_views (Bsymmetry &sym, double theta_step, double phi_step, int flag)
	Initializes a well-distributed set of views in an asymmetric unit. More...

View *	asymmetric_unit_views (Bsymmetry &sym, double theta_step, double phi_step, double alpha_step, int flag)

View *	side_views (Bsymmetry &sym, double side_ang, double theta_step, double phi_step)
	Initializes a set of views around the z-axis for helical projection. More...

View *	side_views (Bsymmetry &sym, double side_ang, double theta_step, double phi_step, double alpha_step)

int	change_views_to_asymmetric_unit (Bsymmetry &sym, View *view)
	Change the views to those in the asymmetric unit. More...

View	find_asymmetric_unit_view (Bsymmetry &sym, View theview)
	Finds the corresponding view in the asymmetric unit. More...

View	find_closest_symmetric_view (Bsymmetry &sym, View view_ref, View view)
	Finds the closest symmetric match between two views. More...

View *	reference_asymmetric_unit_views (Bsymmetry &sym)
	Returns a reference view for each asymmetric unit. More...

View	random_symmetric_view (View &asu_view, Bsymmetry &sym)
	Returns a randomly picked symmetry view. More...

int	test_asymmetric_unit_view (View theview, Bsymmetry &sym)
	Returns an asymmetric unit index number. More...

int	sym_show_matrices (Bsymmetry &sym)
	Show symmetry matrices. More...

int	sym_show_operational_matrices (Bsymmetry &sym)
	Show symmetry matrices associated with each symmetry operator. More...

int	sym_show_pdb_matrices (Bsymmetry &sym)
	Show PDB format symmetry matrices associated with each symmetry operator. More...

Variables
int	verbose

Detailed Description

General symmetry functions.

Author: Bernard Heymann

Date: Created: 20010420; Modified: 20210116

Function Documentation

◆ asymmetric_unit_views() [1/2]

View * asymmetric_unit_views	(	Bsymmetry &	sym,
		double	theta_step,
		double	phi_step,
		double	alpha_step,
		int	flag
	)

◆ asymmetric_unit_views() [2/2]

View * asymmetric_unit_views	(	Bsymmetry &	sym,
		double	theta_step,
		double	phi_step,
		int	flag
	)

Initializes a well-distributed set of views in an asymmetric unit.

Parameters

&sym	symmetry structure.
theta_step	angular step size from primary symmetry axis (radians).
phi_step	angular step size around primary symmetry axis (radians).
flag	flag: 0=half, 1=full, 2=no in-plane.

Returns

View* a linked list of views.

A set of views is calculated with tesselation within each asymmetric
unit such that the views are well-distributed.
Flag bits:
    1: both halves of the asymmetric unit are covered.
    2: no in-plane rotations are applied.

◆ change_views_to_asymmetric_unit()

int change_views_to_asymmetric_unit	(	Bsymmetry &	sym,
		View *	view
	)

Change the views to those in the asymmetric unit.

Parameters

&sym	symmetry structure.
*view	list of views (replaced).

Returns

int 0.

The view is replaced with the one in the standard asymmetric unit.

◆ find_asymmetric_unit_view()

View find_asymmetric_unit_view	(	Bsymmetry &	sym,
		View	theview
	)

Finds the corresponding view in the asymmetric unit.

Parameters

&sym	symmetry structure.
theview	view.

Returns

View the asymmetric unit view.

The asymmetric unit view is found and the the new view with the 
link from the old view is returned.

◆ find_closest_symmetric_view()

View find_closest_symmetric_view	(	Bsymmetry &	sym,
		View	view_ref,
		View	view
	)

Finds the closest symmetric match between two views.

Parameters

&sym	symmetry structure.
view_ref	reference view.
view	test view.

Returns

View matched symmetric version of test view.

A list of symmetry-related views of the test view is searched
for the closest to the reference view.
The matched view is returned.

◆ random_symmetric_view()

View random_symmetric_view	(	View &	asu_view,
		Bsymmetry &	sym
	)

Returns a randomly picked symmetry view.

Parameters

&asu_view	asymmetric unit view.
&sym	symmetry structure.

Returns: View picked view.

◆ reference_asymmetric_unit_views()

View * reference_asymmetric_unit_views ( Bsymmetry & sym )

Returns a reference view for each asymmetric unit.

Parameters

&sym	symmetry structure.

Returns: View* reference views.

◆ side_views() [1/2]

View * side_views	(	Bsymmetry &	sym,
		double	side_ang,
		double	theta_step,
		double	phi_step
	)

Initializes a set of views around the z-axis for helical projection.

Parameters

&sym	symmetry structure.
side_ang	starting angle (radians).
theta_step	angular step size perpendicular to equator (radians).
phi_step	angular step size around equator (radians).

Returns

View* a set of 4-value views.

A set of views is calculated corresponding to views around the z-axis
including some tilting to account for oblique views.

◆ side_views() [2/2]

View * side_views	(	Bsymmetry &	sym,
		double	side_ang,
		double	theta_step,
		double	phi_step,
		double	alpha_step
	)

◆ sym_show_matrices()

int sym_show_matrices ( Bsymmetry & sym )

Show symmetry matrices.

Parameters

&sym	symmetry structure.

Returns: int number of symmetry matrices.

◆ sym_show_operational_matrices()

int sym_show_operational_matrices ( Bsymmetry & sym )

Show symmetry matrices associated with each symmetry operator.

Parameters

&sym	symmetry structure.

Returns: int number of symmetry matrices.

◆ sym_show_pdb_matrices()

int sym_show_pdb_matrices ( Bsymmetry & sym )

Show PDB format symmetry matrices associated with each symmetry operator.

Parameters

&sym	symmetry structure.

Returns: int number of symmetry matrices.

◆ symmetry_get_all_matrices()

vector< Matrix3 > symmetry_get_all_matrices ( Bsymmetry & sym )

Get all symmetry-related views of one given view.

Parameters

&sym	symmetry structure.

Returns

vector<Matrix3> array of matrices.

The number of views generated for a point group symmetry is
calculated as the product of the order fields in the symmetry
structure.

◆ symmetry_get_all_views() [1/2]

View * symmetry_get_all_views	(	Bsymmetry &	sym,
		View *	views
	)

◆ symmetry_get_all_views() [2/2]

View * symmetry_get_all_views	(	Bsymmetry &	sym,
		View	asu_view
	)

Get all symmetry-related views of one given view.

Parameters

&sym	symmetry structure.
asu_view	asymmetric unit vector and rotation angle.

Returns

View* linked list of views.

The number of views generated for a point group symmetry is
calculated as the product of the order fields in the symmetry
structure.

◆ symmetry_get_axes()

vector< Vector3< double > > symmetry_get_axes ( Bsymmetry & sym )

Get all symmetry axes.

Parameters

&sym	symmetry structure.

Returns: vector<Vector3<double>> array of axes.

◆ symmetry_helical_label()

string symmetry_helical_label	(	double	helix_rise,
		double	helix_angle,
		int	dyad_axis,
		int	cyclic,
		double	seam_shift
	)

Returns the label for helical symmetry.

Parameters

helix_rise	helical rise (angstroms).
helix_angle	helical rotation angle (radians).
dyad_axis	presence of dyad axis (1/2).
cyclic	cyclic symmetry.
seam_shift	fractional shift for seamed helices.

Returns

string label.

Thge symmetry order is defined as the product of all the individual
orders of the symmetry operations, or alternatively, the number of views.

◆ symmetry_rotate_to_axis()

Matrix3 symmetry_rotate_to_axis	(	Bsymmetry &	sym,
		long	axis,
		long	axis_flag
	)

Rotation matrix to orient a symmetry axis on the z axis.

Parameters

&sym	symmetry structure.
axis	desired symmetry axis order.
axis_flag	view modifier.

Returns: Matrix3 new rotation matrix.

◆ test_asymmetric_unit_view()

int test_asymmetric_unit_view	(	View	theview,
		Bsymmetry &	sym
	)

Returns an asymmetric unit index number.

Parameters

theview	view to test.
&sym	symmetry structure.

Returns: int view number.

◆ view_symmetry_reference()

View view_symmetry_reference ( Bsymmetry & sym )

Returns an asymmetric unit reference point.

Parameters

&sym	symmetry structure.

Returns: View reference view.

Variable Documentation

◆ verbose

int verbose

extern

Functions

Variables

Detailed Description

Function Documentation

◆ asymmetric_unit_views() [1/2]

◆ asymmetric_unit_views() [2/2]

◆ change_views_to_asymmetric_unit()

◆ find_asymmetric_unit_view()

◆ find_closest_symmetric_view()

◆ random_symmetric_view()

◆ reference_asymmetric_unit_views()

◆ side_views() [1/2]

◆ side_views() [2/2]

◆ sym_show_matrices()

◆ sym_show_operational_matrices()

◆ sym_show_pdb_matrices()

◆ symmetry_get_all_matrices()

◆ symmetry_get_all_views() [1/2]

◆ symmetry_get_all_views() [2/2]

◆ symmetry_get_axes()

◆ symmetry_helical_label()

◆ symmetry_rotate_to_axis()

◆ test_asymmetric_unit_view()

◆ view_symmetry_reference()

Variable Documentation

◆ verbose