#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 583 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 1675 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().
01676 { 01677 vector<Vec3f> ret; 01678 01679 Vec3f b = Vec3f(0,0,1); 01680 ret.push_back(b); 01681 float theta_c_on_two = (float)platonic_params["theta_c_on_two"]; // already in radians 01682 float theta_c = 2*theta_c_on_two; 01683 01684 Vec3f c_on_two = Vec3f(0,-sin(theta_c_on_two),cos(theta_c_on_two)); 01685 Vec3f c = Vec3f(0,-sin(theta_c),cos(theta_c)); 01686 ret.push_back(c_on_two); 01687 01688 float cap_sig = platonic_params["az_max"]; 01689 Vec3f a = Vec3f(sin(theta_c)*sin(cap_sig),-sin(theta_c)*cos(cap_sig),cos(theta_c)); 01690 01691 Vec3f f = a+b+c; 01692 f.normalize(); 01693 01694 ret.push_back(f); 01695 01696 if ( inc_mirror ) { 01697 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)); 01698 ret.push_back(a_on_two); 01699 } 01700 01701 if ( get_az_alignment_offset() != 0 ) { 01702 Dict d("type","eman"); 01703 d["az"] = get_az_alignment_offset(); 01704 d["phi"] = 0.0f; 01705 d["alt"] = 0.0f; 01706 Transform t(d); 01707 for (vector<Vec3f>::iterator it = ret.begin(); it != ret.end(); ++it ) 01708 { 01709 *it = (*it)*t; 01710 } 01711 } 01712 // 01713 return ret; 01714 01715 }
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 1648 of file symmetry.cpp.
References get_asym_unit_points(), and v.
01648 { 01649 vector<Vec3f> v = get_asym_unit_points(inc_mirror); 01650 vector<vector<Vec3f> > ret; 01651 if (v.size() == 3) { 01652 vector<Vec3f> tmp; 01653 tmp.push_back(v[0]); 01654 tmp.push_back(v[2]); 01655 tmp.push_back(v[1]); 01656 ret.push_back(tmp); 01657 } 01658 else /* v.size() == 4*/ { 01659 vector<Vec3f> tmp; 01660 tmp.push_back(v[0]); 01661 tmp.push_back(v[2]); 01662 tmp.push_back(v[1]); 01663 ret.push_back(tmp); 01664 01665 vector<Vec3f> tmp2; 01666 tmp2.push_back(v[0]); 01667 tmp2.push_back(v[3]); 01668 tmp2.push_back(v[2]); 01669 ret.push_back(tmp2); 01670 } 01671 01672 return ret; 01673 }
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 1586 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().
01587 { 01588 Dict ret; 01589 ret["az_max"] = EMConsts::rad2deg * (float) platonic_params["az_max"]; 01590 // For icos and oct symmetries, excluding the mirror means halving az_maz 01591 if ( inc_mirror == false ) 01592 if ( get_name() == IcosahedralSym::NAME || get_name() == OctahedralSym::NAME ) 01593 ret["az_max"] = 0.5f*EMConsts::rad2deg * (float) platonic_params["az_max"]; 01594 //else 01595 //the alt_max variable should probably be altered if the symmetry is tet, but 01596 //this is taken care of in TetSym::is_in_asym_unit 01597 01598 ret["alt_max"] = (float)(EMConsts::rad2deg * (float) platonic_params["alt_max"]); 01599 return ret; 01600 }
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 593 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 1565 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().
01566 { 01567 //See the manuscript "The Transform Class in Sparx and EMAN2", Baldwin & Penczek 2007. J. Struct. Biol. 157 (250-261) 01568 //In particular see pages 257-259 01569 //cap_sig is capital sigma in the Baldwin paper 01570 float cap_sig = 2.0f*M_PI/ get_max_csym(); 01571 //In EMAN2 projection cap_sig is really az_max 01572 platonic_params["az_max"] = cap_sig; 01573 01574 // Alpha is the angle between (immediately) neighborhing 3 fold axes of symmetry 01575 // This follows the conventions in the Baldwin paper 01576 float alpha = acos(1.0f/(sqrtf(3.0f)*tan(cap_sig/2.0f))); 01577 // In EMAN2 projection alpha is really al_maz 01578 platonic_params["alt_max"] = alpha; 01579 01580 // This is half of "theta_c" as in the conventions of the Balwin paper. See also http://blake.bcm.edu/emanwiki/EMAN2/Symmetry. 01581 platonic_params["theta_c_on_two"] = 1.0f/2.0f*acos( cos(cap_sig)/(1.0f-cos(cap_sig))); 01582 01583 }
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 1603 of file symmetry.cpp.
References EMAN::EMConsts::deg2rad, get_delimiters(), platonic_alt_lower_bound(), and platonic_params.
01604 { 01605 Dict d = get_delimiters(inc_mirror); 01606 float alt_max = d["alt_max"]; 01607 float az_max = d["az_max"]; 01608 01609 if ( altitude >= 0 && altitude <= alt_max && azimuth <= az_max && azimuth >= 0) { 01610 01611 // Convert azimuth to radians 01612 float tmpaz = (float)(EMConsts::deg2rad * azimuth); 01613 01614 float cap_sig = platonic_params["az_max"]; 01615 float alt_max = platonic_params["alt_max"]; 01616 if ( tmpaz > ( cap_sig/2.0f ) )tmpaz = cap_sig - tmpaz; 01617 01618 float lower_alt_bound = platonic_alt_lower_bound(tmpaz, alt_max ); 01619 01620 // convert altitude to radians 01621 float tmpalt = (float)(EMConsts::deg2rad * altitude); 01622 if ( lower_alt_bound > tmpalt ) { 01623 if ( inc_mirror == false ) 01624 { 01625 if ( cap_sig/2.0f < tmpaz ) return false; 01626 else return true; 01627 } 01628 else return true; 01629 } 01630 return false; 01631 } 01632 return false; 01633 }
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 629 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 1635 of file symmetry.cpp.
References platonic_params.
Referenced by EMAN::TetrahedralSym::is_in_asym_unit(), and is_in_asym_unit().
01636 { 01637 float cap_sig = platonic_params["az_max"]; 01638 float theta_c_on_two = platonic_params["theta_c_on_two"]; 01639 01640 float baldwin_lower_alt_bound = sin(cap_sig/2.0f-azimuth)/tan(theta_c_on_two); 01641 baldwin_lower_alt_bound += sin(azimuth)/tan(alpha); 01642 baldwin_lower_alt_bound *= 1/sin(cap_sig/2.0f); 01643 baldwin_lower_alt_bound = atan(1/baldwin_lower_alt_bound); 01644 01645 return baldwin_lower_alt_bound; 01646 }
Dict EMAN::PlatonicSym::platonic_params [protected] |
A dictionary that stores important angles, in radians.
Definition at line 633 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().