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EMAN::PlatonicSym Class Reference

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

#include <symmetry.h>

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List of all members.

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

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.
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.
virtual vector< Vec3fget_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.

Protected Attributes

Dict platonic_params
 A dictionary that stores important angles, in radians.

Private Member Functions

 PlatonicSym (const PlatonicSym &)
 Disallow copy construction.
PlatonicSymoperator= (const PlatonicSym &)
 Disallow assignment.

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 584 of file symmetry.h.


Constructor & Destructor Documentation

EMAN::PlatonicSym::PlatonicSym  )  [inline]
 

Definition at line 587 of file symmetry.h.

00587 {};

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

Definition at line 588 of file symmetry.h.

00588 {};

EMAN::PlatonicSym::PlatonicSym const PlatonicSym  )  [private]
 

Disallow copy construction.


Member Function Documentation

vector< Vec3f > PlatonicSym::get_asym_unit_points bool  inc_mirror = false  )  const [protected, 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.

Implements EMAN::Symmetry3D.

Reimplemented in EMAN::TetrahedralSym.

Definition at line 1704 of file symmetry.cpp.

References b, EMAN::Dict::end(), EMAN::Symmetry3D::get_az_alignment_offset(), EMAN::Vec3< Type >::normalize(), platonic_params, t, and EMAN::Vec3f.

Referenced by get_asym_unit_triangles().

01705 {
01706         vector<Vec3f> ret;
01707 
01708         Vec3f b = Vec3f(0,0,1);
01709         ret.push_back(b);
01710         float theta_c_on_two = (float)platonic_params["theta_c_on_two"]; // already in radians
01711         float theta_c = 2*theta_c_on_two;
01712 
01713         Vec3f c_on_two = Vec3f(0,-sin(theta_c_on_two),cos(theta_c_on_two));
01714         Vec3f c = Vec3f(0,-sin(theta_c),cos(theta_c));
01715         ret.push_back(c_on_two);
01716 
01717         float cap_sig = platonic_params["az_max"];
01718         Vec3f a = Vec3f(sin(theta_c)*sin(cap_sig),-sin(theta_c)*cos(cap_sig),cos(theta_c));
01719 
01720         Vec3f f = a+b+c;
01721         f.normalize();
01722 
01723         ret.push_back(f);
01724 
01725         if ( inc_mirror ) {
01726                 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));
01727                 ret.push_back(a_on_two);
01728         }
01729 
01730         if ( get_az_alignment_offset() != 0 ) {
01731                 Dict d("type","eman");
01732                 d["az"] = get_az_alignment_offset();
01733                 d["phi"] = 0.0f;
01734                 d["alt"] = 0.0f;
01735                 Transform t(d);
01736                 for (vector<Vec3f>::iterator it = ret.begin(); it != ret.end(); ++it )
01737                 {
01738                         *it = (*it)*t;
01739                 }
01740         }
01741         //
01742         return ret;
01743 
01744 }

vector< vector< Vec3f > > PlatonicSym::get_asym_unit_triangles bool  inc_mirror  )  const [protected, virtual]
 

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 1677 of file symmetry.cpp.

References get_asym_unit_points(), and v.

01677                                                                                 {
01678         vector<Vec3f> v = get_asym_unit_points(inc_mirror);
01679         vector<vector<Vec3f> > ret;
01680         if (v.size() == 3) {
01681                 vector<Vec3f> tmp;
01682                 tmp.push_back(v[0]);
01683                 tmp.push_back(v[2]);
01684                 tmp.push_back(v[1]);
01685                 ret.push_back(tmp);
01686         }
01687         else /* v.size() == 4*/ {
01688                 vector<Vec3f> tmp;
01689                 tmp.push_back(v[0]);
01690                 tmp.push_back(v[2]);
01691                 tmp.push_back(v[1]);
01692                 ret.push_back(tmp);
01693 
01694                 vector<Vec3f> tmp2;
01695                 tmp2.push_back(v[0]);
01696                 tmp2.push_back(v[3]);
01697                 tmp2.push_back(v[2]);
01698                 ret.push_back(tmp2);
01699         }
01700 
01701         return ret;
01702 }

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 1615 of file symmetry.cpp.

References EMAN::FactoryBase::get_name(), and platonic_params.

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

01616 {
01617         Dict ret;
01618         ret["az_max"] = EMConsts::rad2deg * (float) platonic_params["az_max"];
01619         // For icos and oct symmetries, excluding the mirror means halving az_maz
01620         if ( inc_mirror == false )
01621                 if ( get_name() ==  IcosahedralSym::NAME || get_name() == OctahedralSym::NAME )
01622                         ret["az_max"] = 0.5f*EMConsts::rad2deg * (float) platonic_params["az_max"];
01623                 //else
01624                 //the alt_max variable should probably be altered if the symmetry is tet, but
01625                 //this is taken care of in TetSym::is_in_asym_unit
01626 
01627         ret["alt_max"] = (float)(EMConsts::rad2deg * (float) platonic_params["alt_max"]);
01628         return ret;
01629 }

virtual TypeDict EMAN::PlatonicSym::get_param_types  )  const [inline, virtual]
 

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 594 of file symmetry.h.

00595                 {
00596                         TypeDict d;
00597                         return d;
00598                 }

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 1594 of file symmetry.cpp.

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

01595 {
01596         //See the manuscript "The Transform Class in Sparx and EMAN2", Baldwin & Penczek 2007. J. Struct. Biol. 157 (250-261)
01597         //In particular see pages 257-259
01598         //cap_sig is capital sigma in the Baldwin paper
01599         float cap_sig =  2.0f*M_PI/ get_max_csym();
01600         //In EMAN2 projection cap_sig is really az_max
01601         platonic_params["az_max"] = cap_sig;
01602 
01603         // Alpha is the angle between (immediately) neighborhing 3 fold axes of symmetry
01604         // This follows the conventions in the Baldwin paper
01605         float alpha = acos(1.0f/(sqrtf(3.0f)*tan(cap_sig/2.0f)));
01606         // In EMAN2 projection alpha is really al_maz
01607         platonic_params["alt_max"] = alpha;
01608 
01609         // This is half of "theta_c" as in the conventions of the Balwin paper. See also http://blake.bcm.edu/emanwiki/EMAN2/Symmetry.
01610         platonic_params["theta_c_on_two"] = 1.0f/2.0f*acos( cos(cap_sig)/(1.0f-cos(cap_sig)));
01611 
01612 }

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 1632 of file symmetry.cpp.

References get_delimiters(), platonic_alt_lower_bound(), and platonic_params.

01633 {
01634         Dict d = get_delimiters(inc_mirror);
01635         float alt_max = d["alt_max"];
01636         float az_max = d["az_max"];
01637 
01638         if ( altitude >= 0 &&  altitude <= alt_max && azimuth <= az_max && azimuth >= 0) {
01639 
01640                 // Convert azimuth to radians
01641                 float tmpaz = (float)(EMConsts::deg2rad * azimuth);
01642 
01643                 float cap_sig = platonic_params["az_max"];
01644                 float alt_max = platonic_params["alt_max"];
01645                 if ( tmpaz > ( cap_sig/2.0f ) )tmpaz = cap_sig - tmpaz;
01646 
01647                 float lower_alt_bound = platonic_alt_lower_bound(tmpaz, alt_max );
01648 
01649                 // convert altitude to radians
01650                 float tmpalt = (float)(EMConsts::deg2rad * altitude);
01651                 if ( lower_alt_bound > tmpalt ) {
01652                         if ( inc_mirror == false )
01653                         {
01654                                 if ( cap_sig/2.0f < tmpaz ) return false;
01655                                 else return true;
01656                         }
01657                         else return true;
01658                 }
01659                 return false;
01660         }
01661         return false;
01662 }

virtual bool EMAN::PlatonicSym::is_platonic_sym  )  const [inline, virtual]
 

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 630 of file symmetry.h.

00630 { return true; }

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

Disallow assignment.

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 1664 of file symmetry.cpp.

References platonic_params.

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

01665 {
01666         float cap_sig = platonic_params["az_max"];
01667         float theta_c_on_two = platonic_params["theta_c_on_two"];
01668 
01669         float baldwin_lower_alt_bound = sin(cap_sig/2.0f-azimuth)/tan(theta_c_on_two);
01670         baldwin_lower_alt_bound += sin(azimuth)/tan(alpha);
01671         baldwin_lower_alt_bound *= 1/sin(cap_sig/2.0f);
01672         baldwin_lower_alt_bound = atan(1/baldwin_lower_alt_bound);
01673 
01674         return baldwin_lower_alt_bound;
01675 }


Member Data Documentation

Dict EMAN::PlatonicSym::platonic_params [protected]
 

A dictionary that stores important angles, in radians.

Definition at line 634 of file symmetry.h.

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


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