EMAN2
Public Member Functions | Protected Member Functions | Protected Attributes | Private Member Functions
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.

{};
virtual EMAN::PlatonicSym::~PlatonicSym ( ) [inline, virtual]

Definition at line 585 of file symmetry.h.

{};
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_mirrorwhether 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 1743 of file symmetry.cpp.

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

Referenced by get_asym_unit_triangles().

{
        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;

}
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_mirrorwhether to include the mirror portion of the asymmetric unit

Implements EMAN::Symmetry3D.

Definition at line 1716 of file symmetry.cpp.

References get_asym_unit_points(), and v.

                                                                                {
        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;
}
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_mirrorwhether 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 1654 of file symmetry.cpp.

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

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

{
        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;
}
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.

                {
                        TypeDict d;
                        return d;
                }
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 1633 of file symmetry.cpp.

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

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

{
        //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)));

}
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:
altitudethe EMAN style altitude of the 3D orientation in degrees
azimuththe EMAN style azimuth of the 3D orientation in degrees
inc_mirrorwhether 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 1671 of file symmetry.cpp.

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

{
        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"];
                if ( tmpaz > ( cap_sig/2.0f ) )tmpaz = cap_sig - tmpaz;

                float lower_alt_bound = platonic_alt_lower_bound(tmpaz, alt_max );

                // convert altitude to radians
                float tmpalt = (float)(EMConsts::deg2rad * altitude);
                if ( lower_alt_bound > tmpalt ) {
                        if ( inc_mirror == false )
                        {
                                if ( cap_sig/2.0f < tmpaz ) return false;
                                else return true;
                        }
                        else return true;
                }
                return false;
        }
        return false;
}
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.

{ 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:
azimuthan EMAN style 3D azimuth angle, in radians
alphaan 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 1703 of file symmetry.cpp.

References platonic_params.

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

{
        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;
}

Member Data Documentation


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