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EMAN::TetrahedralSym Class Reference

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

#include <symmetry.h>

Inheritance diagram for EMAN::TetrahedralSym:

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Collaboration diagram for EMAN::TetrahedralSym:

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List of all members.

Public Member Functions

 TetrahedralSym ()
 Constructor calls PlatonicSym::init.
virtual ~TetrahedralSym ()
virtual string get_name () const
 Return TetrahedralSym::NAME.
virtual string get_desc () const
 Get a description.
virtual int get_max_csym () const
 Gets the maximum symmetry of this object.
virtual Transform get_sym (const int n) const
 This function provides access to the unique rotational symmetries of a tetrahedron.
virtual bool is_in_asym_unit (const float &altitude, const float &azimuth, const bool inc_mirror) const
 In tetrahedral symmetry special consideration must be taken when generating orientations in the asymmetric unit.
virtual int get_nsym () const
 Gets the total number of unique roational symmetry operations associated with this symmetry For tetrahedral symmetry symmetry, this is 12.
virtual float get_az_alignment_offset () const
 Get the azimuth alignment offset required to ensure that orientations align correctly with symmetric axes of the tetrahedron.
virtual vector< Vec3fget_asym_unit_points (bool inc_mirror=false) const
virtual bool is_tet_sym () const
 A function that is used to determine if this is the tetrahedral symmetry object.

Static Public Member Functions

static Symmetry3DNEW ()
 Factory support function NEW.

Static Public Attributes

static const string NAME = "tet"
 The name of this class - used to access it from factories etc. Should be "tet".

Private Member Functions

 TetrahedralSym (const TetrahedralSym &)
 Disallow copy construction.
TetrahedralSymoperator= (const TetrahedralSym &)
 Disallow assignment.

Detailed Description

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

The tetrahedron has n=m=3; F=4, E=6=nF/2, V=4=nF/m. It is composed of four triangles."

Author:
David Woolford (based on previous work by Phil Baldwin and Steve Ludtke)
Date:
Feb 2008

Definition at line 677 of file symmetry.h.


Constructor & Destructor Documentation

EMAN::TetrahedralSym::TetrahedralSym  )  [inline]
 

Constructor calls PlatonicSym::init.

Definition at line 682 of file symmetry.h.

References EMAN::PlatonicSym::init().

Referenced by NEW().

00682 {init();}

virtual EMAN::TetrahedralSym::~TetrahedralSym  )  [inline, virtual]
 

Definition at line 683 of file symmetry.h.

00683 {}

EMAN::TetrahedralSym::TetrahedralSym const TetrahedralSym  )  [private]
 

Disallow copy construction.


Member Function Documentation

vector< Vec3f > TetrahedralSym::get_asym_unit_points bool  inc_mirror = false  )  const [virtual]
 

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.

Reimplemented from EMAN::PlatonicSym.

Definition at line 1858 of file symmetry.cpp.

References b, get_az_alignment_offset(), EMAN::Vec3< Type >::normalize(), EMAN::PlatonicSym::platonic_params, and t.

01859 {
01860         vector<Vec3f> ret;
01861 
01862         Vec3f b = Vec3f(0,0,1);
01863         ret.push_back(b);
01864         float theta_c_on_two = (float)platonic_params["theta_c_on_two"]; // already in radians
01865         float theta_c = 2*theta_c_on_two;
01866 
01867         Vec3f c_on_two = Vec3f(0,-sin(theta_c_on_two),cos(theta_c_on_two));
01868         Vec3f c = Vec3f(0,-sin(theta_c),cos(theta_c));
01869         ret.push_back(c_on_two);
01870         float cap_sig = platonic_params["az_max"];
01871         if ( inc_mirror ) {
01872                 Vec3f a = Vec3f(sin(theta_c)*sin(cap_sig),-sin(theta_c)*cos(cap_sig),cos(theta_c));
01873 
01874                 Vec3f f = a+b+c;
01875                 f.normalize();
01876 
01877                 ret.push_back(f);
01878         }
01879 
01880         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));
01881         ret.push_back(a_on_two);
01882 
01883 
01884         if ( get_az_alignment_offset() != 0 ) {
01885                 Dict d("type","eman");
01886                 d["az"] = get_az_alignment_offset();
01887                 d["phi"] = 0.0f;
01888                 d["alt"] = 0.0f;
01889                 Transform t(d);
01890                 for (vector<Vec3f>::iterator it = ret.begin(); it != ret.end(); ++it )
01891                 {
01892                         *it = (*it)*t;
01893                 }
01894         }
01895 
01896         return ret;
01897 }

float TetrahedralSym::get_az_alignment_offset  )  const [virtual]
 

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

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 1795 of file symmetry.cpp.

Referenced by get_asym_unit_points().

01795 { return  0.0; }

virtual string EMAN::TetrahedralSym::get_desc  )  const [inline, virtual]
 

Get a description.

Returns:
a clear desciption of this class

Implements EMAN::FactoryBase.

Definition at line 702 of file symmetry.h.

00702 { return "Tetrahedral symmetry support"; }

virtual int EMAN::TetrahedralSym::get_max_csym  )  const [inline, virtual]
 

Gets the maximum symmetry of this object.

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

Returns:
for tetrahedral symmetry, this number is 3

Implements EMAN::Symmetry3D.

Definition at line 708 of file symmetry.h.

00708 { return 3; }

virtual string EMAN::TetrahedralSym::get_name  )  const [inline, virtual]
 

Return TetrahedralSym::NAME.

Returns:
the unique name of this class

Implements EMAN::FactoryBase.

Definition at line 696 of file symmetry.h.

References NAME.

00696 { return NAME; }

virtual int EMAN::TetrahedralSym::get_nsym  )  const [inline, virtual]
 

Gets the total number of unique roational symmetry operations associated with this symmetry For tetrahedral symmetry symmetry, this is 12.

Returns:
12

Implements EMAN::Symmetry3D.

Definition at line 738 of file symmetry.h.

00738 { return 12; };

Transform TetrahedralSym::get_sym const int  n  )  const [virtual]
 

This function provides access to the unique rotational symmetries of a tetrahedron.

In this implementation, the tetrahedral symmetry group has a face along the z-axis. In all, there are 12 (accessed by get_nysm) unique rotational symmetric operations for the tetrahedron. In the terminology defined Append A (titled Symmetry Elements) in the manuscript Baldwin and Penczek, 2007. The Transform Class in SPARX and EMAN2. JSB 157(250-261), Doctor Phil has this to say: "B^3=A^3=1; BABA=1; implies A^2=BAB, ABA=B^2 , AB^2A = B^2AB^2 and 12 words with at most a single A 1 B BB A BA AB BBA BAB ABB BBAB BABB BBABB at most one A is necessary"

Parameters:
n the symmetric operation number
Returns:
a transform3d containing the correct rotational symmetry operation.

Implements EMAN::Symmetry3D.

Definition at line 1830 of file symmetry.cpp.

01831 {
01832         // These rotations courtesy of Phil Baldwin
01833          // It has n=m=3; F=4, E=6=nF/2, V=4=nF/m
01834         static double lvl0=0;         // There is a face along z
01835         static double lvl1=109.4712;  //  that is acos(-1/3)  // There  are 3 faces at this angle
01836 
01837         static double TET[36] = {// This is with the face along z
01838                 0,lvl0,0,   0,lvl0,120,    0,lvl0,240,
01839   0,lvl1,60,   0,lvl1,180,    0,lvl1,300,
01840   120,lvl1,60, 120,lvl1,180,  120,lvl1,300,
01841   240,lvl1,60, 240,lvl1,180,  240,lvl1,300
01842         };
01843         //
01844         int idx = n % 12;
01845 //      Transform3D ret;
01846 //      ret.set_rotation((float)TET[idx * 3 ],(float)TET[idx * 3 + 1], (float)TET[idx * 3 + 2] );
01847 //      return ret;
01848 
01849         Dict d("type","eman");
01850         d["az"] = (float)TET[idx * 3 ];
01851         d["alt"] = (float)TET[idx * 3 + 1];
01852         d["phi"] = (float)TET[idx * 3 + 2];
01853         return Transform(d);
01854 
01855 }

bool TetrahedralSym::is_in_asym_unit const float &  altitude,
const float &  azimuth,
const bool  inc_mirror
const [virtual]
 

In tetrahedral symmetry special consideration must be taken when generating orientations in the asymmetric unit.

This function is a specialization of the functionality in PlatonicSym::is_in_asym_unit

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

Reimplemented from EMAN::PlatonicSym.

Definition at line 1797 of file symmetry.cpp.

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

01798 {
01799         Dict d = get_delimiters(inc_mirror);
01800         float alt_max = d["alt_max"];
01801         float az_max = d["az_max"];
01802 
01803         if ( altitude >= 0 &&  altitude <= alt_max && azimuth <= az_max && azimuth >= 0) {
01804                 // convert azimuth to radians
01805                 float tmpaz = (float)(EMConsts::deg2rad * azimuth);
01806 
01807                 float cap_sig = platonic_params["az_max"];
01808                 float alt_max = platonic_params["alt_max"];
01809                 if ( tmpaz > ( cap_sig/2.0f ) )tmpaz = cap_sig - tmpaz;
01810 
01811                 float lower_alt_bound = platonic_alt_lower_bound(tmpaz, alt_max );
01812 
01813                 // convert altitude to radians
01814                 float tmpalt = (float)(EMConsts::deg2rad * altitude);
01815                 if ( lower_alt_bound > tmpalt ) {
01816                         if ( !inc_mirror ) {
01817                                 float upper_alt_bound = platonic_alt_lower_bound( tmpaz, alt_max/2.0f);
01818                                 // you could change the "<" to a ">" here to get the other mirror part of the asym unit
01819                                 if ( upper_alt_bound < tmpalt ) return false;
01820                                 else return true;
01821                         }
01822                         else return true;
01823                 }
01824                 return false;
01825         }
01826         else return false;
01827 }

virtual bool EMAN::TetrahedralSym::is_tet_sym  )  const [inline, virtual]
 

A function that is used to determine if this is the tetrahedral symmetry object.

Returns:
true - indicating that this is not a tetrahedral symmetry object

Reimplemented from EMAN::Symmetry3D.

Definition at line 760 of file symmetry.h.

00760 { return true; }

static Symmetry3D* EMAN::TetrahedralSym::NEW  )  [inline, static]
 

Factory support function NEW.

Returns:
a newly instantiated class of this type

Definition at line 688 of file symmetry.h.

References TetrahedralSym().

00689                 {
00690                         return new TetrahedralSym();
00691                 }

TetrahedralSym& EMAN::TetrahedralSym::operator= const TetrahedralSym  )  [private]
 

Disallow assignment.


Member Data Documentation

const string TetrahedralSym::NAME = "tet" [static]
 

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

Definition at line 749 of file symmetry.h.

Referenced by get_name().


The documentation for this class was generated from the following files:
Generated on Tue May 25 17:38:25 2010 for EMAN2 by  doxygen 1.4.4