An encapsulation of icosahedral symmetry Doctor Phil has this to say about icosahedral symmetry: "Each Platonic Solid has 2E symmetry elements. More...

#include <symmetry.h>

Inheritance diagram for EMAN::IcosahedralSym:

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Collaboration diagram for EMAN::IcosahedralSym:

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Public Member Functions
	IcosahedralSym ()
	Constructor calls PlatonicSym::init. More...

virtual	~IcosahedralSym ()

virtual string	get_name () const
	Return IcosahedralSym::NAME. More...

virtual string	get_desc () const
	Get a description. More...

virtual int	get_max_csym () const
	Gets the maximum symmetry of this object. More...

virtual Transform	get_sym (const int n) const
	This function provides access to the unique rotational symmetries of an icosahedron. More...

virtual int	get_nsym () const
	Gets the total number of unique rotational symmetry operations associated with this symmetry For icosahedral symmetry, this is 60. More...

virtual float	get_az_alignment_offset () const
	Get the azimuth alignment offset required to ensure that orientations align correctly with symmetric axes of the icosahedron. More...

Public Member Functions inherited from EMAN::PlatonicSym
	PlatonicSym ()

virtual	~PlatonicSym ()

virtual TypeDict	get_param_types () const
	Get a dictionary containing the permissable parameters of this class Platonic symmetries actually have no parameters. More...

virtual Dict	get_delimiters (const bool inc_mirror=false) const
	Returns the range of altitude and azimuth angles which encompass the asymmetric unit of the Platonic symmetry (and more). More...

virtual bool	is_in_asym_unit (const float &altitude, const float &azimuth, const bool inc_mirror) const
	A function to be used when generating orientations over portion of the unit sphere defined by parameters returned by get_delimiters. More...

virtual bool	is_platonic_sym () const
	Determines whether or not this Symmetry3D is the platonic type - returns true. More...

Public Member Functions inherited from EMAN::Symmetry3D
	Symmetry3D ()

virtual	~Symmetry3D ()

virtual bool	is_h_sym () const
	A function that is used to determine if this is a Helical symmetry object This function is only virtually overidden by the HSym symmetry, which returns true, not false. More...

virtual bool	is_c_sym () const
	A function that is used to determine if this is a c symmetry object This function is only virtually overidden by the CSym object, which returns true. More...

virtual bool	is_d_sym () const
	A function that is used to determine if this is a d symmetry object This function is only virtually overidden by the DSym object, which returns true. More...

virtual bool	is_tet_sym () const
	A function that is used to determine if this is the tetrahedral symmetry object This function is only virtually overidden by the TetSym object, which returns true. More...

vector< Transform >	gen_orientations (const string &generatorname="eman", const Dict &parms=Dict())
	Ask the Symmetry3D object to generate a set of orientations in its asymmetric unit using an OrientationGenerator constructed from the given parameters (using a Factory). More...

virtual Transform	reduce (const Transform &t3d, int n=0) const
	A function that will reduce an orientation, as characterized by Euler anges, into a specific asymmetric unit. More...

virtual int	in_which_asym_unit (const Transform &t3d) const
	A function that will determine in which asymmetric unit a given orientation resides The asymmetric unit 'number' will depend entirely on the order in which different symmetry operations are return by the Symmetry3D::get_sym function. More...

virtual int	point_in_which_asym_unit (const Vec3f &v) const
	A function that will determine in which asymmetric unit a given vector resides The asymmetric unit 'number' will depend entirely on the order in which different symmetry operations are return by the Symmetry3D::get_sym function The vector is a point. More...

virtual vector< Transform >	get_touching_au_transforms (bool inc_mirror=true) const
	Gets a vector of Transform objects that define the set of asymmetric units that touch the default asymmetric unit. More...

virtual vector< Transform >	get_syms () const

Public Member Functions inherited from EMAN::FactoryBase
	FactoryBase ()

virtual	~FactoryBase ()

Dict	get_params () const
	get a copy of the parameters of this class More...

void	set_params (const Dict &new_params)
	Set new parameters. More...

void	set_param (const string key, const EMObject val)

void	insert_params (const Dict &new_params)
	Insert parameters. More...

Dict	copy_relevant_params (const FactoryBase *const that) const

Static Public Member Functions
static Symmetry3D *	NEW ()
	Factory support function NEW. More...

Static Public Member Functions inherited from EMAN::Symmetry3D
static vector< Transform >	get_symmetries (const string &symmetry)

Static Public Attributes
static const string	NAME = "icos"
	The name of this class - used to access it from factories etc. Should be "icos". More...

Private Member Functions
	IcosahedralSym (const IcosahedralSym &)
	Disallow copy construction. More...

IcosahedralSym &	operator= (const IcosahedralSym &)
	Disallow assignment. More...

Additional Inherited Members
Public Types inherited from EMAN::Symmetry3D
typedef vector< vector< Vec3f > >::const_iterator	cit

typedef vector< vector< Vec3f > >::iterator	ncit

Protected Member Functions inherited from EMAN::PlatonicSym
void	init ()
	Init - Called to initialize platonic_params, should be called in the constructor of all Platonic solids that derive from this. More...

float	platonic_alt_lower_bound (const float &azimuth, const float &alpha) const
	Returns the lower bound of the asymmetric unit, as dependent on azimuth, and on alpha - alpha is alt_max for icos and oct, but may be alt_max/2.0 for tet depending on mirror symmetry etc. More...

virtual vector< Vec3f >	get_asym_unit_points (bool inc_mirror=false) const

virtual vector< vector< Vec3f > >	get_asym_unit_triangles (bool inc_mirror) const
	Get triangles that precisely occlude the projection area of the default asymmetric unit. More...

Protected Member Functions inherited from EMAN::Symmetry3D
void	cache_au_planes () const
	Establish the asymmetric unit planes cache. More...

void	delete_au_planes ()
	Clear the asymmetric unit planes cache. More...

Protected Attributes inherited from EMAN::PlatonicSym
Dict	platonic_params
	A dictionary that stores important angles, in radians. More...

Protected Attributes inherited from EMAN::Symmetry3D
float **	cached_au_planes
	The asymmetric unit planes are cached to provide a great speed up the point_in_which_asym_unit function, which is called by reduce and by in_which_asym_unit. More...

int	cache_size
	Have to remember the cache size. More...

int	num_triangles
	This is stores the number of triangles returned by get_asym_unit_triangles(true) More...

vector< vector< Vec3f > >	au_sym_triangles
	This cache is of size cache_size. More...

Protected Attributes inherited from EMAN::FactoryBase
Dict	params
	This is the dictionary the stores the parameters of the object. More...

Detailed Description

An encapsulation of icosahedral symmetry Doctor Phil has this to say about icosahedral symmetry: "Each Platonic Solid has 2E symmetry elements.

An icosahedron has m=5, n=3, F=20 E=30=nF/2, V=12=nF/m,since vertices shared by 5 triangles It is composed of 20 triangles. E=3*20/2 A dodecahedron has m=3, n=5 F=12 E=30 V=20 It is composed of 12 pentagons. E=5*12/2; V= 5*12/3, since vertices shared by 3 pentagons"

Author: David Woolford (based on previous work by Phil Baldwin and Steve Ludtke)

Date: Feb 2008

Definition at line 855 of file symmetry.h.

Constructor & Destructor Documentation

◆ IcosahedralSym() [1/2]

EMAN::IcosahedralSym::IcosahedralSym ( )

inline

Constructor calls PlatonicSym::init.

Definition at line 860 of file symmetry.h.

860{init(); }

EMAN::PlatonicSym::init

void init()

Init - Called to initialize platonic_params, should be called in the constructor of all Platonic soli...

Definition: symmetry.cpp:1673

References EMAN::PlatonicSym::init().

Referenced by NEW().

◆ ~IcosahedralSym()

virtual EMAN::IcosahedralSym::~IcosahedralSym ( )

inlinevirtual

Definition at line 861 of file symmetry.h.

861{ }

◆ IcosahedralSym() [2/2]

EMAN::IcosahedralSym::IcosahedralSym ( const IcosahedralSym & )

private

Disallow copy construction.

Member Function Documentation

◆ get_az_alignment_offset()

float IcosahedralSym::get_az_alignment_offset ( ) const

virtual

Get the azimuth alignment offset required to ensure that orientations align correctly with symmetric axes of the icosahedron.

This offset is directly related to the way the symmetric operations are generated by get_sym. All orientations generated as a result of using the delimiters supplied by this class should by offset by this azimuth to ensure proper alignment with tetrahedral objects in EMAN2

Reimplemented from EMAN::Symmetry3D.

Definition at line 1819 of file symmetry.cpp.

1819{ return 234.0; } // This offset positions a 3 fold axis on the positive x axis

Referenced by get_sym().

◆ get_desc()

virtual string EMAN::IcosahedralSym::get_desc ( ) const

inlinevirtual

Get a description.

Returns: a clear desciption of this class

Implements EMAN::FactoryBase.

Definition at line 879 of file symmetry.h.

879{ return "Icosahedral symmetry support"; }

◆ get_max_csym()

virtual int EMAN::IcosahedralSym::get_max_csym ( ) const

inlinevirtual

Gets the maximum symmetry of this object.

This is used by OrientationGenerators, and is probably not something a general user would utilize.

Returns: for icosahedral symmetry, this number is 5

Implements EMAN::Symmetry3D.

Definition at line 885 of file symmetry.h.

885{ return 5; }// 5 is the greatest symmetry

◆ get_name()

virtual string EMAN::IcosahedralSym::get_name ( ) const

inlinevirtual

Return IcosahedralSym::NAME.

Returns: the unique name of this class

Implements EMAN::FactoryBase.

Definition at line 874 of file symmetry.h.

874{ return NAME; };

EMAN::IcosahedralSym::NAME

static const string NAME

The name of this class - used to access it from factories etc. Should be "icos".

Definition: symmetry.h:910

References NAME.

◆ get_nsym()

virtual int EMAN::IcosahedralSym::get_nsym ( ) const

inlinevirtual

Gets the total number of unique rotational symmetry operations associated with this symmetry For icosahedral symmetry, this is 60.

Returns: 60

Implements EMAN::Symmetry3D.

Definition at line 899 of file symmetry.h.

899{ return 60; };

◆ get_sym()

Transform IcosahedralSym::get_sym ( const int n ) const

virtual

This function provides access to the unique rotational symmetries of an icosahedron.

We have placed the icosahedral symmetry group with a face along the z-axis. In all, there are 60 (accessed by get_nysm) unique rotational symmetric operations for the icosahedron.

Parameters

n	the symmetric operation number.

Returns: a transform containing the correct rotational symmetry operation.

Implements EMAN::Symmetry3D.

Definition at line 1821 of file symmetry.cpp.

{
        // These rotations courtesy of Phil Baldwin
        float   lvl0 = 0.0f; //  there is one pentagon on top; five-fold along z
        float   lvl1 = EMConsts::rad2deg*atan(2.0f);// 63.4349; // that is atan(2)  // there are 5 pentagons with centers at this height (angle)
        float   lvl2 = 180.0f - lvl1;//116.5651; //that is 180-lvl1  // there are 5 pentagons with centers at this height (angle)
        float   lvl3 = 180.0f;
 
        float ICOS[180] = { // This is with a pentagon normal to z
                0,lvl0,0,    0,lvl0,288,   0,lvl0,216,   0,lvl0,144,  0,lvl0,72,
                0,lvl1,36,   0,lvl1,324,   0,lvl1,252,   0,lvl1,180,  0,lvl1,108,
                72,lvl1,36,  72,lvl1,324,  72,lvl1,252,  72,lvl1,180,  72,lvl1,108,
                144,lvl1,36, 144,lvl1,324, 144,lvl1,252, 144,lvl1,180, 144,lvl1,108,
                216,lvl1,36, 216,lvl1,324, 216,lvl1,252, 216,lvl1,180, 216,lvl1,108,
                288,lvl1,36, 288,lvl1,324, 288,lvl1,252, 288,lvl1,180, 288,lvl1,108,
                36,lvl2,0,   36,lvl2,288,  36,lvl2,216,  36,lvl2,144,  36,lvl2,72,
                108,lvl2,0,  108,lvl2,288, 108,lvl2,216, 108,lvl2,144, 108,lvl2,72,
                180,lvl2,0,  180,lvl2,288, 180,lvl2,216, 180,lvl2,144, 180,lvl2,72,
                252,lvl2,0,  252,lvl2,288, 252,lvl2,216, 252,lvl2,144, 252,lvl2,72,
                324,lvl2,0,  324,lvl2,288, 324,lvl2,216, 324,lvl2,144, 324,lvl2,72,
                0,lvl3,0,    0,lvl3,288,   0,lvl3,216,   0,lvl3,144,   0,lvl3,72
        };
 
        int idx = n % 60;
        Dict d("type","eman");
//      Transform3D ret;
        if (get_az_alignment_offset() == 234.0) {
                d["az"]  = ICOS[idx * 3 ]+90;
                d["alt"] = ICOS[idx * 3 + 1];
                d["phi"] = ICOS[idx * 3 + 2]-90;
//              ret.set_rotation((float)ICOS[idx * 3 ]+90,(float)ICOS[idx * 3 + 1], (float)ICOS[idx * 3 + 2]-90);
        }
        else {
                d["az"]  = ICOS[idx * 3 ];
                d["alt"] = ICOS[idx * 3 + 1];
                d["phi"] = ICOS[idx * 3 + 2];
//              ret.set_rotation((float)ICOS[idx * 3 ],(float)ICOS[idx * 3 + 1], (float)ICOS[idx * 3 + 2]);
        }
 
//      ret.set_rotation((float)ICOS[idx * 3 ],(float)ICOS[idx * 3 + 1], (float)ICOS[idx * 3 + 2]);
//      if ( get_az_alignment_offset() != 0 ) {
//              Transform3D t(get_az_alignment_offset(),0,0);
//              ret = t*ret;
//      }
        return Transform(d);
 
}

References get_az_alignment_offset(), and EMAN::EMConsts::rad2deg.

◆ NEW()

static Symmetry3D * EMAN::IcosahedralSym::NEW ( )

inlinestatic

Factory support function NEW.

Returns: a newly instantiated class of this type

Definition at line 866 of file symmetry.h.

                {
                        return new IcosahedralSym();
                }

References IcosahedralSym().

◆ operator=()

IcosahedralSym & EMAN::IcosahedralSym::operator= ( const IcosahedralSym & )

private

Disallow assignment.

Member Data Documentation

◆ NAME

const string IcosahedralSym::NAME = "icos"

static

The name of this class - used to access it from factories etc. Should be "icos".

Definition at line 910 of file symmetry.h.

Referenced by EMAN::PlatonicSym::get_delimiters(), and get_name().

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

Public Member Functions

Static Public Member Functions

Static Public Attributes

Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ IcosahedralSym() [1/2]

◆ ~IcosahedralSym()

◆ IcosahedralSym() [2/2]

Member Function Documentation

◆ get_az_alignment_offset()

◆ get_desc()

◆ get_max_csym()

◆ get_name()

◆ get_nsym()

◆ get_sym()

◆ NEW()

◆ operator=()

Member Data Documentation

◆ NAME