A base (or parent) class for the Platonic symmetries. More...

#include <symmetry.h>

Inheritance diagram for EMAN::PlatonicSym:

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Collaboration diagram for EMAN::PlatonicSym:

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Public Member Functions
	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 Transform	get_sym (const int n) const =0
	Every Symmetry3D object must provide access to the full set of its symmetry operators via this function. More...

virtual int	get_nsym () const =0
	The total number of unique symmetry operations that will be return by this object when a calling program access Symmetry3D::get_sym. More...

virtual float	get_az_alignment_offset () const
	This functionality is only relevant to platonic symmetries. More...

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...

virtual int	get_max_csym () const =0
	The Symmetry3D object must return the maximum degree of symmetry it exhibits about any one axis. 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 ()

virtual string	get_name () const =0
	Get the unique name of this class (especially for factory based instantiation access) More...

virtual string	get_desc () const =0
	Get a clear, concise description of this class. More...

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

Protected Member Functions
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
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...

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

PlatonicSym &	operator= (const PlatonicSym &)
	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

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

Detailed Description

A base (or parent) class for the Platonic symmetries.

It cannot be instantieted on its own. Doctor Phil says: "see www.math.utah.edu/~alfeld/math/polyhedra/polyhedra.html for pictures of platonic solids" Also, see http://blake.bcm.edu/emanwiki/EMAN2/Symmetry for a good pictorial description of what's going on here This class has a fundamental role to play in terms of the Platonic symmetries that derive from it. It is based heavily on the manuscript Baldwin and Penczek, 2007. The Transform Class in SPARX and EMAN2. JSB 157(250-261), where the important angles of the asymmetric units in Platonic solids are described. The MOST IMPORTANT THING TO NOTE is anything that derives from this class must call init() in its constructor. However, because it is unlikey that any class will inherit from this one seeing as the set of Platonic symmetries is finite.

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

Date: Feb 2008

Definition at line 581 of file symmetry.h.

Constructor & Destructor Documentation

◆ PlatonicSym() [1/2]

EMAN::PlatonicSym::PlatonicSym ( )

inline

Definition at line 584 of file symmetry.h.

584{};

◆ ~PlatonicSym()

virtual EMAN::PlatonicSym::~PlatonicSym ( )

inlinevirtual

Definition at line 585 of file symmetry.h.

585{};

◆ PlatonicSym() [2/2]

EMAN::PlatonicSym::PlatonicSym ( const PlatonicSym & )

private

Disallow copy construction.

Member Function Documentation

◆ get_asym_unit_points()

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

protectedvirtual

Parameters

inc_mirror whether or not to include the mirror portion of the asymmetric unit

Returns: a cyclic set of points which can be connected using great arcs on the unit sphere to demarcate the asymmetric unit. The last should may be connected to the first.

Implements EMAN::Symmetry3D.

Reimplemented in EMAN::TetrahedralSym.

Definition at line 1777 of file symmetry.cpp.

{
        vector<Vec3f> ret;
 
        Vec3f b = Vec3f(0,0,1);
        ret.push_back(b);
        float theta_c_on_two = (float)platonic_params["theta_c_on_two"]; // already in radians
        float theta_c = 2*theta_c_on_two;
 
        Vec3f c_on_two = Vec3f(0,-sin(theta_c_on_two),cos(theta_c_on_two));
        Vec3f c = Vec3f(0,-sin(theta_c),cos(theta_c));
        ret.push_back(c_on_two);
 
        float cap_sig = platonic_params["az_max"];
        Vec3f a = Vec3f(sin(theta_c)*sin(cap_sig),-sin(theta_c)*cos(cap_sig),cos(theta_c));
 
        Vec3f f = a+b+c;
        f.normalize();
 
        ret.push_back(f);
 
        if ( inc_mirror ) {
                Vec3f a_on_two = Vec3f(sin(theta_c_on_two)*sin(cap_sig),-sin(theta_c_on_two)*cos(cap_sig),cos(theta_c_on_two));
                ret.push_back(a_on_two);
        }
 
        if ( get_az_alignment_offset() != 0 ) {
                Dict d("type","eman");
                d["az"] = get_az_alignment_offset();
                d["phi"] = 0.0f;
                d["alt"] = 0.0f;
                Transform t(d);
                for (vector<Vec3f>::iterator it = ret.begin(); it != ret.end(); ++it )
                {
                        *it = (*it)*t;
                }
        }
        //
        return ret;
 
}

References EMAN::Symmetry3D::get_az_alignment_offset(), EMAN::Vec3< Type >::normalize(), and platonic_params.

Referenced by get_asym_unit_triangles().

◆ get_asym_unit_triangles()

vector< vector< Vec3f > > PlatonicSym::get_asym_unit_triangles ( bool inc_mirror ) const

protectedvirtual

Get triangles that precisely occlude the projection area of the default asymmetric unit.

This is used for collision detection in Symmetry3D::reduce

Parameters

inc_mirror whether to include the mirror portion of the asymmetric unit

Implements EMAN::Symmetry3D.

Definition at line 1750 of file symmetry.cpp.

                                                                                {
        vector<Vec3f> v = get_asym_unit_points(inc_mirror);
        vector<vector<Vec3f> > ret;
        if (v.size() == 3) {
                vector<Vec3f> tmp;
                tmp.push_back(v[0]);
                tmp.push_back(v[2]);
                tmp.push_back(v[1]);
                ret.push_back(tmp);
        }
        else /* v.size() == 4*/ {
                vector<Vec3f> tmp;
                tmp.push_back(v[0]);
                tmp.push_back(v[2]);
                tmp.push_back(v[1]);
                ret.push_back(tmp);
 
                vector<Vec3f> tmp2;
                tmp2.push_back(v[0]);
                tmp2.push_back(v[3]);
                tmp2.push_back(v[2]);
                ret.push_back(tmp2);
        }
 
        return ret;
}

References get_asym_unit_points().

◆ get_delimiters()

Dict PlatonicSym::get_delimiters ( const bool inc_mirror = false ) const

virtual

Returns the range of altitude and azimuth angles which encompass the asymmetric unit of the Platonic symmetry (and more).

As a general rule you may generate your orientations evenly over the range altitude range as accessed by "alt_max" key in the return dictionary, and over the azimuth range as accessed by the "az_max", but your must call the function is_in_asym_unit as you do it, to accomodate for orientations in the range that are actually beyond the asymmetric unit. See http://blake.bcm.edu/emanwiki/EMAN2/Symmetry for pictures and descriptions. If the inc_mirror is true, the return "az_max" key is twice as large as if not, but only if the platonic symmetry is Icos or Oct. If the symmetry is Tet, the mirror considerations are taken into account in is_in_asym_unit. This is a bit of a design flaw, but it works.

Parameters

inc_mirror whether or not to consider the mirror portion of the asymmetric unit (only changes the return values if the symmetry is Icos or Oct)

Returns: a dictionary containing the "az_max" and "alt_max" keys which define angles, in degrees

Implements EMAN::Symmetry3D.

Definition at line 1694 of file symmetry.cpp.

{
        Dict ret;
        ret["az_max"] = EMConsts::rad2deg * (float) platonic_params["az_max"];
        // For icos and oct symmetries, excluding the mirror means halving az_maz
        if ( inc_mirror == false )
                if ( get_name() ==  IcosahedralSym::NAME || get_name() == OctahedralSym::NAME )
                        ret["az_max"] = 0.5f*EMConsts::rad2deg * (float) platonic_params["az_max"];
                //else
                //the alt_max variable should probably be altered if the symmetry is tet, but
                //this is taken care of in TetSym::is_in_asym_unit
 
        ret["alt_max"] = (float)(EMConsts::rad2deg * (float) platonic_params["alt_max"]);
        return ret;
}

References EMAN::FactoryBase::get_name(), EMAN::OctahedralSym::NAME, EMAN::IcosahedralSym::NAME, platonic_params, and EMAN::EMConsts::rad2deg.

Referenced by is_in_asym_unit(), and EMAN::TetrahedralSym::is_in_asym_unit().

◆ get_param_types()

virtual TypeDict EMAN::PlatonicSym::get_param_types ( ) const

inlinevirtual

Get a dictionary containing the permissable parameters of this class Platonic symmetries actually have no parameters.

Returns: a dictionary containing the permissable parameters of this class ( which is none)

Implements EMAN::FactoryBase.

Definition at line 591 of file symmetry.h.

                {
                        TypeDict d;
                        return d;
                }

◆ init()

void PlatonicSym::init ( )

protected

Init - Called to initialize platonic_params, should be called in the constructor of all Platonic solids that derive from this.

This function generates the important angles of the platonic symmetries which is dependent only on the function get_max_csym ( which must be defined in all classes that inherit from this class)

Definition at line 1673 of file symmetry.cpp.

{
        //See the manuscript "The Transform Class in Sparx and EMAN2", Baldwin & Penczek 2007. J. Struct. Biol. 157 (250-261)
        //In particular see pages 257-259
        //cap_sig is capital sigma in the Baldwin paper
        float cap_sig =  2.0f*M_PI/ get_max_csym();
        //In EMAN2 projection cap_sig is really az_max
        platonic_params["az_max"] = cap_sig;
 
        // Alpha is the angle between (immediately) neighborhing 3 fold axes of symmetry
        // This follows the conventions in the Baldwin paper
        float alpha = acos(1.0f/(sqrtf(3.0f)*tan(cap_sig/2.0f)));
        // In EMAN2 projection alpha is really al_maz
        platonic_params["alt_max"] = alpha;
 
        // This is half of "theta_c" as in the conventions of the Balwin paper. See also http://blake.bcm.edu/emanwiki/EMAN2/Symmetry.
        platonic_params["theta_c_on_two"] = 1.0f/2.0f*acos( cos(cap_sig)/(1.0f-cos(cap_sig)));
 
}

References EMAN::Symmetry3D::get_max_csym(), and platonic_params.

Referenced by EMAN::IcosahedralSym::IcosahedralSym(), EMAN::OctahedralSym::OctahedralSym(), EMAN::TetrahedralSym::TetrahedralSym(), and EMAN::Icosahedral2Sym::~Icosahedral2Sym().

◆ is_in_asym_unit()

bool PlatonicSym::is_in_asym_unit	(	const float &	altitude,
		const float &	azimuth,
		const bool	inc_mirror
	)		const

virtual

A function to be used when generating orientations over portion of the unit sphere defined by parameters returned by get_delimiters.

altitude and azimuth alone are not enough to correctly demarcate the asymmetric unit. See the get_delimiters comments.

Parameters

altitude	the EMAN style altitude of the 3D orientation in degrees
azimuth	the EMAN style azimuth of the 3D orientation in degrees
inc_mirror	whether or not to include orientations if they are in the mirror portion of the asymmetric unit

Returns: true or false, depending on whether or not the orientation is within the asymmetric unit

Implements EMAN::Symmetry3D.

Reimplemented in EMAN::TetrahedralSym.

Definition at line 1711 of file symmetry.cpp.

{
        Dict d = get_delimiters(inc_mirror);
        float alt_max = d["alt_max"];
        float az_max = d["az_max"];
 
        if ( altitude >= 0 &&  altitude <= alt_max && azimuth < az_max && azimuth >= 0) {
 
                // Convert azimuth to radians
                float tmpaz = (float)(EMConsts::deg2rad * azimuth);
 
                float cap_sig = platonic_params["az_max"];
                float alt_max = platonic_params["alt_max"];
                tmpaz = Util::get_min( tmpaz, cap_sig-tmpaz);
 
                // convert altitude to radians
                float tmpalt = (float)(EMConsts::deg2rad * altitude);
                if ( platonic_alt_lower_bound(tmpaz, alt_max ) > tmpalt ) return true;
                        /*if ( inc_mirror == false ) {
                                if ( tmpaz > cap_sig/2.0f) return false;  //  this if is always false so I removed it PAP
                                else return true;
                        }       else return true;*/
                else return false;
        }       else return false;
}

References EMAN::EMConsts::deg2rad, get_delimiters(), EMAN::Util::get_min(), platonic_alt_lower_bound(), and platonic_params.

◆ is_platonic_sym()

virtual bool EMAN::PlatonicSym::is_platonic_sym ( ) const

inlinevirtual

Determines whether or not this Symmetry3D is the platonic type - returns true.

Returns: true - indicating that this is a platonic symmetry object

Reimplemented from EMAN::Symmetry3D.

Definition at line 627 of file symmetry.h.

627{ return true; }

◆ operator=()

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

private

Disallow assignment.

◆ platonic_alt_lower_bound()

float PlatonicSym::platonic_alt_lower_bound	(	const float &	azimuth,
		const float &	alpha
	)		const

protected

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.

Parameters

azimuth	an EMAN style 3D azimuth angle, in radians
alpha	an EMAN style altitude angle that helps to define arcs on the unit sphere. See Baldwin and Penczek, 2007. The Transform Class in SPARX and EMAN2. JSB 157(250-261) where the angle alpha is described

Returns: the altitude corresponding to the lower bound for the given azimuth, in radians

Definition at line 1737 of file symmetry.cpp.

{
        float cap_sig = platonic_params["az_max"];
        float theta_c_on_two = platonic_params["theta_c_on_two"];
 
        float baldwin_lower_alt_bound = sin(cap_sig/2.0f-azimuth)/tan(theta_c_on_two);
        baldwin_lower_alt_bound += sin(azimuth)/tan(alpha);
        baldwin_lower_alt_bound *= 1/sin(cap_sig/2.0f);
        baldwin_lower_alt_bound = atan(1/baldwin_lower_alt_bound);
 
        return baldwin_lower_alt_bound;
}

References platonic_params.

Referenced by is_in_asym_unit(), and EMAN::TetrahedralSym::is_in_asym_unit().

Member Data Documentation

◆ platonic_params

Dict EMAN::PlatonicSym::platonic_params

protected

A dictionary that stores important angles, in radians.

Definition at line 631 of file symmetry.h.

Referenced by get_asym_unit_points(), EMAN::TetrahedralSym::get_asym_unit_points(), get_delimiters(), init(), is_in_asym_unit(), EMAN::TetrahedralSym::is_in_asym_unit(), and platonic_alt_lower_bound().

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

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ PlatonicSym() [1/2]

◆ ~PlatonicSym()

◆ PlatonicSym() [2/2]

Member Function Documentation

◆ get_asym_unit_points()

◆ get_asym_unit_triangles()

◆ get_delimiters()

◆ get_param_types()

◆ init()

◆ is_in_asym_unit()

◆ is_platonic_sym()

◆ operator=()

◆ platonic_alt_lower_bound()

Member Data Documentation

◆ platonic_params