#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 1701 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().
01702 { 01703 vector<Vec3f> ret; 01704 01705 Vec3f b = Vec3f(0,0,1); 01706 ret.push_back(b); 01707 float theta_c_on_two = (float)platonic_params["theta_c_on_two"]; // already in radians 01708 float theta_c = 2*theta_c_on_two; 01709 01710 Vec3f c_on_two = Vec3f(0,-sin(theta_c_on_two),cos(theta_c_on_two)); 01711 Vec3f c = Vec3f(0,-sin(theta_c),cos(theta_c)); 01712 ret.push_back(c_on_two); 01713 01714 float cap_sig = platonic_params["az_max"]; 01715 Vec3f a = Vec3f(sin(theta_c)*sin(cap_sig),-sin(theta_c)*cos(cap_sig),cos(theta_c)); 01716 01717 Vec3f f = a+b+c; 01718 f.normalize(); 01719 01720 ret.push_back(f); 01721 01722 if ( inc_mirror ) { 01723 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)); 01724 ret.push_back(a_on_two); 01725 } 01726 01727 if ( get_az_alignment_offset() != 0 ) { 01728 Dict d("type","eman"); 01729 d["az"] = get_az_alignment_offset(); 01730 d["phi"] = 0.0f; 01731 d["alt"] = 0.0f; 01732 Transform t(d); 01733 for (vector<Vec3f>::iterator it = ret.begin(); it != ret.end(); ++it ) 01734 { 01735 *it = (*it)*t; 01736 } 01737 } 01738 // 01739 return ret; 01740 01741 }
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 1674 of file symmetry.cpp.
References get_asym_unit_points(), and v.
01674 { 01675 vector<Vec3f> v = get_asym_unit_points(inc_mirror); 01676 vector<vector<Vec3f> > ret; 01677 if (v.size() == 3) { 01678 vector<Vec3f> tmp; 01679 tmp.push_back(v[0]); 01680 tmp.push_back(v[2]); 01681 tmp.push_back(v[1]); 01682 ret.push_back(tmp); 01683 } 01684 else /* v.size() == 4*/ { 01685 vector<Vec3f> tmp; 01686 tmp.push_back(v[0]); 01687 tmp.push_back(v[2]); 01688 tmp.push_back(v[1]); 01689 ret.push_back(tmp); 01690 01691 vector<Vec3f> tmp2; 01692 tmp2.push_back(v[0]); 01693 tmp2.push_back(v[3]); 01694 tmp2.push_back(v[2]); 01695 ret.push_back(tmp2); 01696 } 01697 01698 return ret; 01699 }
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 1612 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().
01613 { 01614 Dict ret; 01615 ret["az_max"] = EMConsts::rad2deg * (float) platonic_params["az_max"]; 01616 // For icos and oct symmetries, excluding the mirror means halving az_maz 01617 if ( inc_mirror == false ) 01618 if ( get_name() == IcosahedralSym::NAME || get_name() == OctahedralSym::NAME ) 01619 ret["az_max"] = 0.5f*EMConsts::rad2deg * (float) platonic_params["az_max"]; 01620 //else 01621 //the alt_max variable should probably be altered if the symmetry is tet, but 01622 //this is taken care of in TetSym::is_in_asym_unit 01623 01624 ret["alt_max"] = (float)(EMConsts::rad2deg * (float) platonic_params["alt_max"]); 01625 return ret; 01626 }
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 1591 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().
01592 { 01593 //See the manuscript "The Transform Class in Sparx and EMAN2", Baldwin & Penczek 2007. J. Struct. Biol. 157 (250-261) 01594 //In particular see pages 257-259 01595 //cap_sig is capital sigma in the Baldwin paper 01596 float cap_sig = 2.0f*M_PI/ get_max_csym(); 01597 //In EMAN2 projection cap_sig is really az_max 01598 platonic_params["az_max"] = cap_sig; 01599 01600 // Alpha is the angle between (immediately) neighborhing 3 fold axes of symmetry 01601 // This follows the conventions in the Baldwin paper 01602 float alpha = acos(1.0f/(sqrtf(3.0f)*tan(cap_sig/2.0f))); 01603 // In EMAN2 projection alpha is really al_maz 01604 platonic_params["alt_max"] = alpha; 01605 01606 // This is half of "theta_c" as in the conventions of the Balwin paper. See also http://blake.bcm.edu/emanwiki/EMAN2/Symmetry. 01607 platonic_params["theta_c_on_two"] = 1.0f/2.0f*acos( cos(cap_sig)/(1.0f-cos(cap_sig))); 01608 01609 }
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 1629 of file symmetry.cpp.
References EMAN::EMConsts::deg2rad, get_delimiters(), platonic_alt_lower_bound(), and platonic_params.
01630 { 01631 Dict d = get_delimiters(inc_mirror); 01632 float alt_max = d["alt_max"]; 01633 float az_max = d["az_max"]; 01634 01635 if ( altitude >= 0 && altitude <= alt_max && azimuth <= az_max && azimuth >= 0) { 01636 01637 // Convert azimuth to radians 01638 float tmpaz = (float)(EMConsts::deg2rad * azimuth); 01639 01640 float cap_sig = platonic_params["az_max"]; 01641 float alt_max = platonic_params["alt_max"]; 01642 if ( tmpaz > ( cap_sig/2.0f ) )tmpaz = cap_sig - tmpaz; 01643 01644 float lower_alt_bound = platonic_alt_lower_bound(tmpaz, alt_max ); 01645 01646 // convert altitude to radians 01647 float tmpalt = (float)(EMConsts::deg2rad * altitude); 01648 if ( lower_alt_bound > tmpalt ) { 01649 if ( inc_mirror == false ) 01650 { 01651 if ( cap_sig/2.0f < tmpaz ) return false; 01652 else return true; 01653 } 01654 else return true; 01655 } 01656 return false; 01657 } 01658 return false; 01659 }
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 1661 of file symmetry.cpp.
References platonic_params.
Referenced by EMAN::TetrahedralSym::is_in_asym_unit(), and is_in_asym_unit().
01662 { 01663 float cap_sig = platonic_params["az_max"]; 01664 float theta_c_on_two = platonic_params["theta_c_on_two"]; 01665 01666 float baldwin_lower_alt_bound = sin(cap_sig/2.0f-azimuth)/tan(theta_c_on_two); 01667 baldwin_lower_alt_bound += sin(azimuth)/tan(alpha); 01668 baldwin_lower_alt_bound *= 1/sin(cap_sig/2.0f); 01669 baldwin_lower_alt_bound = atan(1/baldwin_lower_alt_bound); 01670 01671 return baldwin_lower_alt_bound; 01672 }
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().