#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 581 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 1735 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().
01736 { 01737 vector<Vec3f> ret; 01738 01739 Vec3f b = Vec3f(0,0,1); 01740 ret.push_back(b); 01741 float theta_c_on_two = (float)platonic_params["theta_c_on_two"]; // already in radians 01742 float theta_c = 2*theta_c_on_two; 01743 01744 Vec3f c_on_two = Vec3f(0,-sin(theta_c_on_two),cos(theta_c_on_two)); 01745 Vec3f c = Vec3f(0,-sin(theta_c),cos(theta_c)); 01746 ret.push_back(c_on_two); 01747 01748 float cap_sig = platonic_params["az_max"]; 01749 Vec3f a = Vec3f(sin(theta_c)*sin(cap_sig),-sin(theta_c)*cos(cap_sig),cos(theta_c)); 01750 01751 Vec3f f = a+b+c; 01752 f.normalize(); 01753 01754 ret.push_back(f); 01755 01756 if ( inc_mirror ) { 01757 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)); 01758 ret.push_back(a_on_two); 01759 } 01760 01761 if ( get_az_alignment_offset() != 0 ) { 01762 Dict d("type","eman"); 01763 d["az"] = get_az_alignment_offset(); 01764 d["phi"] = 0.0f; 01765 d["alt"] = 0.0f; 01766 Transform t(d); 01767 for (vector<Vec3f>::iterator it = ret.begin(); it != ret.end(); ++it ) 01768 { 01769 *it = (*it)*t; 01770 } 01771 } 01772 // 01773 return ret; 01774 01775 }
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 1708 of file symmetry.cpp.
References get_asym_unit_points(), and v.
01708 { 01709 vector<Vec3f> v = get_asym_unit_points(inc_mirror); 01710 vector<vector<Vec3f> > ret; 01711 if (v.size() == 3) { 01712 vector<Vec3f> tmp; 01713 tmp.push_back(v[0]); 01714 tmp.push_back(v[2]); 01715 tmp.push_back(v[1]); 01716 ret.push_back(tmp); 01717 } 01718 else /* v.size() == 4*/ { 01719 vector<Vec3f> tmp; 01720 tmp.push_back(v[0]); 01721 tmp.push_back(v[2]); 01722 tmp.push_back(v[1]); 01723 ret.push_back(tmp); 01724 01725 vector<Vec3f> tmp2; 01726 tmp2.push_back(v[0]); 01727 tmp2.push_back(v[3]); 01728 tmp2.push_back(v[2]); 01729 ret.push_back(tmp2); 01730 } 01731 01732 return ret; 01733 }
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 1646 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().
01647 { 01648 Dict ret; 01649 ret["az_max"] = EMConsts::rad2deg * (float) platonic_params["az_max"]; 01650 // For icos and oct symmetries, excluding the mirror means halving az_maz 01651 if ( inc_mirror == false ) 01652 if ( get_name() == IcosahedralSym::NAME || get_name() == OctahedralSym::NAME ) 01653 ret["az_max"] = 0.5f*EMConsts::rad2deg * (float) platonic_params["az_max"]; 01654 //else 01655 //the alt_max variable should probably be altered if the symmetry is tet, but 01656 //this is taken care of in TetSym::is_in_asym_unit 01657 01658 ret["alt_max"] = (float)(EMConsts::rad2deg * (float) platonic_params["alt_max"]); 01659 return ret; 01660 }
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 591 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 1625 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().
01626 { 01627 //See the manuscript "The Transform Class in Sparx and EMAN2", Baldwin & Penczek 2007. J. Struct. Biol. 157 (250-261) 01628 //In particular see pages 257-259 01629 //cap_sig is capital sigma in the Baldwin paper 01630 float cap_sig = 2.0f*M_PI/ get_max_csym(); 01631 //In EMAN2 projection cap_sig is really az_max 01632 platonic_params["az_max"] = cap_sig; 01633 01634 // Alpha is the angle between (immediately) neighborhing 3 fold axes of symmetry 01635 // This follows the conventions in the Baldwin paper 01636 float alpha = acos(1.0f/(sqrtf(3.0f)*tan(cap_sig/2.0f))); 01637 // In EMAN2 projection alpha is really al_maz 01638 platonic_params["alt_max"] = alpha; 01639 01640 // This is half of "theta_c" as in the conventions of the Balwin paper. See also http://blake.bcm.edu/emanwiki/EMAN2/Symmetry. 01641 platonic_params["theta_c_on_two"] = 1.0f/2.0f*acos( cos(cap_sig)/(1.0f-cos(cap_sig))); 01642 01643 }
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 1663 of file symmetry.cpp.
References EMAN::EMConsts::deg2rad, get_delimiters(), platonic_alt_lower_bound(), and platonic_params.
01664 { 01665 Dict d = get_delimiters(inc_mirror); 01666 float alt_max = d["alt_max"]; 01667 float az_max = d["az_max"]; 01668 01669 if ( altitude >= 0 && altitude <= alt_max && azimuth <= az_max && azimuth >= 0) { 01670 01671 // Convert azimuth to radians 01672 float tmpaz = (float)(EMConsts::deg2rad * azimuth); 01673 01674 float cap_sig = platonic_params["az_max"]; 01675 float alt_max = platonic_params["alt_max"]; 01676 if ( tmpaz > ( cap_sig/2.0f ) )tmpaz = cap_sig - tmpaz; 01677 01678 float lower_alt_bound = platonic_alt_lower_bound(tmpaz, alt_max ); 01679 01680 // convert altitude to radians 01681 float tmpalt = (float)(EMConsts::deg2rad * altitude); 01682 if ( lower_alt_bound > tmpalt ) { 01683 if ( inc_mirror == false ) 01684 { 01685 if ( cap_sig/2.0f < tmpaz ) return false; 01686 else return true; 01687 } 01688 else return true; 01689 } 01690 return false; 01691 } 01692 return false; 01693 }
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 627 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 1695 of file symmetry.cpp.
References platonic_params.
Referenced by EMAN::TetrahedralSym::is_in_asym_unit(), and is_in_asym_unit().
01696 { 01697 float cap_sig = platonic_params["az_max"]; 01698 float theta_c_on_two = platonic_params["theta_c_on_two"]; 01699 01700 float baldwin_lower_alt_bound = sin(cap_sig/2.0f-azimuth)/tan(theta_c_on_two); 01701 baldwin_lower_alt_bound += sin(azimuth)/tan(alpha); 01702 baldwin_lower_alt_bound *= 1/sin(cap_sig/2.0f); 01703 baldwin_lower_alt_bound = atan(1/baldwin_lower_alt_bound); 01704 01705 return baldwin_lower_alt_bound; 01706 }
Dict EMAN::PlatonicSym::platonic_params [protected] |
A dictionary that stores important angles, in radians.
Definition at line 631 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().