#include <symmetry.h>
Inheritance diagram for EMAN::PlatonicSym:
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< Vec3f > | get_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. | |
PlatonicSym & | operator= (const PlatonicSym &) |
Disallow assignment. |
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.
Definition at line 584 of file symmetry.h.
EMAN::PlatonicSym::PlatonicSym | ( | ) | [inline] |
virtual EMAN::PlatonicSym::~PlatonicSym | ( | ) | [inline, virtual] |
EMAN::PlatonicSym::PlatonicSym | ( | const PlatonicSym & | ) | [private] |
Disallow copy construction.
vector< Vec3f > PlatonicSym::get_asym_unit_points | ( | bool | inc_mirror = false |
) | const [protected, virtual] |
inc_mirror | whether or not to include the mirror portion of the asymmetric unit |
Implements EMAN::Symmetry3D.
Reimplemented in EMAN::TetrahedralSym.
Definition at line 1704 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().
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
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.
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) |
Implements EMAN::Symmetry3D.
Definition at line 1615 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().
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.
Implements EMAN::FactoryBase.
Definition at line 594 of file symmetry.h.
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.
Referenced by EMAN::IcosahedralSym::IcosahedralSym(), EMAN::OctahedralSym::OctahedralSym(), and EMAN::TetrahedralSym::TetrahedralSym().
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.
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 |
Implements EMAN::Symmetry3D.
Reimplemented in EMAN::TetrahedralSym.
Definition at line 1632 of file symmetry.cpp.
References EMAN::EMConsts::deg2rad, 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.
Reimplemented from EMAN::Symmetry3D.
Definition at line 630 of file symmetry.h.
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.
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 |
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 }
Dict EMAN::PlatonicSym::platonic_params [protected] |
A dictionary that stores important angles, in radians.
Definition at line 634 of file symmetry.h.
Referenced by EMAN::TetrahedralSym::get_asym_unit_points(), get_asym_unit_points(), get_delimiters(), init(), EMAN::TetrahedralSym::is_in_asym_unit(), is_in_asym_unit(), and platonic_alt_lower_bound().