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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 581 of file symmetry.h.


Constructor & Destructor Documentation

EMAN::PlatonicSym::PlatonicSym  )  [inline]
 

Definition at line 584 of file symmetry.h.

00584 {};

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

Definition at line 585 of file symmetry.h.

00585 {};

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 1741 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().

01742 {
01743         vector<Vec3f> ret;
01744 
01745         Vec3f b = Vec3f(0,0,1);
01746         ret.push_back(b);
01747         float theta_c_on_two = (float)platonic_params["theta_c_on_two"]; // already in radians
01748         float theta_c = 2*theta_c_on_two;
01749 
01750         Vec3f c_on_two = Vec3f(0,-sin(theta_c_on_two),cos(theta_c_on_two));
01751         Vec3f c = Vec3f(0,-sin(theta_c),cos(theta_c));
01752         ret.push_back(c_on_two);
01753 
01754         float cap_sig = platonic_params["az_max"];
01755         Vec3f a = Vec3f(sin(theta_c)*sin(cap_sig),-sin(theta_c)*cos(cap_sig),cos(theta_c));
01756 
01757         Vec3f f = a+b+c;
01758         f.normalize();
01759 
01760         ret.push_back(f);
01761 
01762         if ( inc_mirror ) {
01763                 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));
01764                 ret.push_back(a_on_two);
01765         }
01766 
01767         if ( get_az_alignment_offset() != 0 ) {
01768                 Dict d("type","eman");
01769                 d["az"] = get_az_alignment_offset();
01770                 d["phi"] = 0.0f;
01771                 d["alt"] = 0.0f;
01772                 Transform t(d);
01773                 for (vector<Vec3f>::iterator it = ret.begin(); it != ret.end(); ++it )
01774                 {
01775                         *it = (*it)*t;
01776                 }
01777         }
01778         //
01779         return ret;
01780 
01781 }

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 1714 of file symmetry.cpp.

References get_asym_unit_points(), and v.

01714                                                                                 {
01715         vector<Vec3f> v = get_asym_unit_points(inc_mirror);
01716         vector<vector<Vec3f> > ret;
01717         if (v.size() == 3) {
01718                 vector<Vec3f> tmp;
01719                 tmp.push_back(v[0]);
01720                 tmp.push_back(v[2]);
01721                 tmp.push_back(v[1]);
01722                 ret.push_back(tmp);
01723         }
01724         else /* v.size() == 4*/ {
01725                 vector<Vec3f> tmp;
01726                 tmp.push_back(v[0]);
01727                 tmp.push_back(v[2]);
01728                 tmp.push_back(v[1]);
01729                 ret.push_back(tmp);
01730 
01731                 vector<Vec3f> tmp2;
01732                 tmp2.push_back(v[0]);
01733                 tmp2.push_back(v[3]);
01734                 tmp2.push_back(v[2]);
01735                 ret.push_back(tmp2);
01736         }
01737 
01738         return ret;
01739 }

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 1652 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().

01653 {
01654         Dict ret;
01655         ret["az_max"] = EMConsts::rad2deg * (float) platonic_params["az_max"];
01656         // For icos and oct symmetries, excluding the mirror means halving az_maz
01657         if ( inc_mirror == false )
01658                 if ( get_name() ==  IcosahedralSym::NAME || get_name() == OctahedralSym::NAME )
01659                         ret["az_max"] = 0.5f*EMConsts::rad2deg * (float) platonic_params["az_max"];
01660                 //else
01661                 //the alt_max variable should probably be altered if the symmetry is tet, but
01662                 //this is taken care of in TetSym::is_in_asym_unit
01663 
01664         ret["alt_max"] = (float)(EMConsts::rad2deg * (float) platonic_params["alt_max"]);
01665         return ret;
01666 }

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 591 of file symmetry.h.

00592                 {
00593                         TypeDict d;
00594                         return d;
00595                 }

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 1631 of file symmetry.cpp.

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

01632 {
01633         //See the manuscript "The Transform Class in Sparx and EMAN2", Baldwin & Penczek 2007. J. Struct. Biol. 157 (250-261)
01634         //In particular see pages 257-259
01635         //cap_sig is capital sigma in the Baldwin paper
01636         float cap_sig =  2.0f*M_PI/ get_max_csym();
01637         //In EMAN2 projection cap_sig is really az_max
01638         platonic_params["az_max"] = cap_sig;
01639 
01640         // Alpha is the angle between (immediately) neighborhing 3 fold axes of symmetry
01641         // This follows the conventions in the Baldwin paper
01642         float alpha = acos(1.0f/(sqrtf(3.0f)*tan(cap_sig/2.0f)));
01643         // In EMAN2 projection alpha is really al_maz
01644         platonic_params["alt_max"] = alpha;
01645 
01646         // This is half of "theta_c" as in the conventions of the Balwin paper. See also http://blake.bcm.edu/emanwiki/EMAN2/Symmetry.
01647         platonic_params["theta_c_on_two"] = 1.0f/2.0f*acos( cos(cap_sig)/(1.0f-cos(cap_sig)));
01648 
01649 }

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 1669 of file symmetry.cpp.

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

01670 {
01671         Dict d = get_delimiters(inc_mirror);
01672         float alt_max = d["alt_max"];
01673         float az_max = d["az_max"];
01674 
01675         if ( altitude >= 0 &&  altitude <= alt_max && azimuth <= az_max && azimuth >= 0) {
01676 
01677                 // Convert azimuth to radians
01678                 float tmpaz = (float)(EMConsts::deg2rad * azimuth);
01679 
01680                 float cap_sig = platonic_params["az_max"];
01681                 float alt_max = platonic_params["alt_max"];
01682                 if ( tmpaz > ( cap_sig/2.0f ) )tmpaz = cap_sig - tmpaz;
01683 
01684                 float lower_alt_bound = platonic_alt_lower_bound(tmpaz, alt_max );
01685 
01686                 // convert altitude to radians
01687                 float tmpalt = (float)(EMConsts::deg2rad * altitude);
01688                 if ( lower_alt_bound > tmpalt ) {
01689                         if ( inc_mirror == false )
01690                         {
01691                                 if ( cap_sig/2.0f < tmpaz ) return false;
01692                                 else return true;
01693                         }
01694                         else return true;
01695                 }
01696                 return false;
01697         }
01698         return false;
01699 }

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 627 of file symmetry.h.

00627 { 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 1701 of file symmetry.cpp.

References platonic_params.

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

01702 {
01703         float cap_sig = platonic_params["az_max"];
01704         float theta_c_on_two = platonic_params["theta_c_on_two"];
01705 
01706         float baldwin_lower_alt_bound = sin(cap_sig/2.0f-azimuth)/tan(theta_c_on_two);
01707         baldwin_lower_alt_bound += sin(azimuth)/tan(alpha);
01708         baldwin_lower_alt_bound *= 1/sin(cap_sig/2.0f);
01709         baldwin_lower_alt_bound = atan(1/baldwin_lower_alt_bound);
01710 
01711         return baldwin_lower_alt_bound;
01712 }


Member Data Documentation

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(), 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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