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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

Symmetry3DNEW ()
 Factory support function NEW.

Static Public Attributes

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 678 of file symmetry.h.


Constructor & Destructor Documentation

EMAN::TetrahedralSym::TetrahedralSym  )  [inline]
 

Constructor calls PlatonicSym::init.

Definition at line 683 of file symmetry.h.

00683 {init();}

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

Definition at line 684 of file symmetry.h.

00684 {}

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 1884 of file symmetry.cpp.

References b, EMAN::Dict::end(), get_az_alignment_offset(), EMAN::Vec3< Type >::normalize(), t, and EMAN::Vec3f.

01885 {
01886         vector<Vec3f> ret;
01887 
01888         Vec3f b = Vec3f(0,0,1);
01889         ret.push_back(b);
01890         float theta_c_on_two = (float)platonic_params["theta_c_on_two"]; // already in radians
01891         float theta_c = 2*theta_c_on_two;
01892 
01893         Vec3f c_on_two = Vec3f(0,-sin(theta_c_on_two),cos(theta_c_on_two));
01894         Vec3f c = Vec3f(0,-sin(theta_c),cos(theta_c));
01895         ret.push_back(c_on_two);
01896         float cap_sig = platonic_params["az_max"];
01897         if ( inc_mirror ) {
01898                 Vec3f a = Vec3f(sin(theta_c)*sin(cap_sig),-sin(theta_c)*cos(cap_sig),cos(theta_c));
01899 
01900                 Vec3f f = a+b+c;
01901                 f.normalize();
01902 
01903                 ret.push_back(f);
01904         }
01905 
01906         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));
01907         ret.push_back(a_on_two);
01908 
01909 
01910         if ( get_az_alignment_offset() != 0 ) {
01911                 Dict d("type","eman");
01912                 d["az"] = get_az_alignment_offset();
01913                 d["phi"] = 0.0f;
01914                 d["alt"] = 0.0f;
01915                 Transform t(d);
01916                 for (vector<Vec3f>::iterator it = ret.begin(); it != ret.end(); ++it )
01917                 {
01918                         *it = (*it)*t;
01919                 }
01920         }
01921 
01922         return ret;
01923 }

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 1821 of file symmetry.cpp.

Referenced by get_asym_unit_points().

01821 { 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 703 of file symmetry.h.

00703 { 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 709 of file symmetry.h.

00709 { 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 697 of file symmetry.h.

00697 { 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 739 of file symmetry.h.

00739 { 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 1856 of file symmetry.cpp.

01857 {
01858         // These rotations courtesy of Phil Baldwin
01859          // It has n=m=3; F=4, E=6=nF/2, V=4=nF/m
01860         static double lvl0=0;         // There is a face along z
01861         static double lvl1=109.4712;  //  that is acos(-1/3)  // There  are 3 faces at this angle
01862 
01863         static double TET[36] = {// This is with the face along z
01864                 0,lvl0,0,   0,lvl0,120,    0,lvl0,240,
01865   0,lvl1,60,   0,lvl1,180,    0,lvl1,300,
01866   120,lvl1,60, 120,lvl1,180,  120,lvl1,300,
01867   240,lvl1,60, 240,lvl1,180,  240,lvl1,300
01868         };
01869         //
01870         int idx = n % 12;
01871 //      Transform3D ret;
01872 //      ret.set_rotation((float)TET[idx * 3 ],(float)TET[idx * 3 + 1], (float)TET[idx * 3 + 2] );
01873 //      return ret;
01874 
01875         Dict d("type","eman");
01876         d["az"] = (float)TET[idx * 3 ];
01877         d["alt"] = (float)TET[idx * 3 + 1];
01878         d["phi"] = (float)TET[idx * 3 + 2];
01879         return Transform(d);
01880 
01881 }

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 1823 of file symmetry.cpp.

References EMAN::PlatonicSym::get_delimiters(), and EMAN::PlatonicSym::platonic_alt_lower_bound().

01824 {
01825         Dict d = get_delimiters(inc_mirror);
01826         float alt_max = d["alt_max"];
01827         float az_max = d["az_max"];
01828 
01829         if ( altitude >= 0 &&  altitude <= alt_max && azimuth <= az_max && azimuth >= 0) {
01830                 // convert azimuth to radians
01831                 float tmpaz = (float)(EMConsts::deg2rad * azimuth);
01832 
01833                 float cap_sig = platonic_params["az_max"];
01834                 float alt_max = platonic_params["alt_max"];
01835                 if ( tmpaz > ( cap_sig/2.0f ) )tmpaz = cap_sig - tmpaz;
01836 
01837                 float lower_alt_bound = platonic_alt_lower_bound(tmpaz, alt_max );
01838 
01839                 // convert altitude to radians
01840                 float tmpalt = (float)(EMConsts::deg2rad * altitude);
01841                 if ( lower_alt_bound > tmpalt ) {
01842                         if ( !inc_mirror ) {
01843                                 float upper_alt_bound = platonic_alt_lower_bound( tmpaz, alt_max/2.0f);
01844                                 // you could change the "<" to a ">" here to get the other mirror part of the asym unit
01845                                 if ( upper_alt_bound < tmpalt ) return false;
01846                                 else return true;
01847                         }
01848                         else return true;
01849                 }
01850                 return false;
01851         }
01852         else return false;
01853 }

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 761 of file symmetry.h.

00761 { return true; }

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

Factory support function NEW.

Returns:
a newly instantiated class of this type

Definition at line 689 of file symmetry.h.

00690                 {
00691                         return new TetrahedralSym();
00692                 }

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 43 of file symmetry.cpp.


The documentation for this class was generated from the following files:
Generated on Thu Dec 9 13:48:52 2010 for EMAN2 by  doxygen 1.3.9.1