Symmetry definitions and properties. More...

Namespaces
	ConstexprProperties
	Compile-time calculation of shape classes' properties.

	Continuous
	Symmetry element, point group, and polyhedral shape continuous metrics.

	Data
	All symmetry data classes and some minor helper functions.

	Diophantine
	Functions to help treat a particular linear diophantine equation.

	Elements
	Namespace for classes and data of point group symmetry elements.

	Properties
	Runtime-computed properties of shapes.

Data Structures
struct	CoordinateSystem
	Coordinate system axis data class. More...

struct	InertialMoments
	Inertial moments data struct. More...

class	Partitioner
	Given S * E distinguishable objects, this class helps enumerate all partitions into S groups of size E. More...

Typedefs
using	Vertex = Temple::StrongIndex< vertex_index_tag, unsigned >
	Index of a shape vertex.

using	Permutation = std::vector< Vertex >
	Representation of a shape vertex permutation.

using	RotationsList = std::vector< Permutation >
	The type to store shape rotations.

using	AngleFunction = std::function< >
	Function returning angle between vertices. More...

using	Tetrahedron = std::array< boost::optional< Vertex >, 4 >
	This is a four-vertex tetrahedron definition. More...

using	TetrahedronList = std::vector< Tetrahedron >

using	Coordinates = Eigen::Matrix< double, 3, Eigen::Dynamic >
	Representation of idealized shape coordinates (does not include centroid)

using	InertialPositionsType = Eigen::Matrix< double, 3, Eigen::Dynamic >

Enumerations
enum	Top { Top::Line, Top::Asymmetric, Top::Prolate, Top::Oblate, Top::Spherical }
	What kind of top is the particle collection? More...

enum	PointGroup : unsigned { C1, Ci, Cs, C2, C3, C4, C5, C6, C7, C8, C2h, C3h, C4h, C5h, C6h, C7h, C8h, C2v, C3v, C4v, C5v, C6v, C7v, C8v, S4, S6, S8, D2, D3, D4, D5, D6, D7, D8, D2h, D3h, D4h, D5h, D6h, D7h, D8h, D2d, D3d, D4d, D5d, D6d, D7d, D8d, T, Td, Th, O, Oh, I, Ih, Cinfv, Dinfh }
	Point groups.

enum	Shape : unsigned { Shape::Line, Shape::Bent, Shape::EquilateralTriangle, Shape::VacantTetrahedron, Shape::T, Shape::Tetrahedron, Shape::Square, Shape::Seesaw, Shape::TrigonalPyramid, Shape::SquarePyramid, Shape::TrigonalBipyramid, Shape::Pentagon, Shape::Octahedron, Shape::TrigonalPrism, Shape::PentagonalPyramid, Shape::Hexagon, Shape::PentagonalBipyramid, Shape::CappedOctahedron, Shape::CappedTrigonalPrism, Shape::SquareAntiprism, Shape::Cube, Shape::TrigonalDodecahedron, Shape::HexagonalBipyramid, Shape::TricappedTrigonalPrism, Shape::CappedSquareAntiprism, Shape::HeptagonalBipyramid, Shape::BicappedSquareAntiprism, Shape::EdgeContractedIcosahedron, Shape::Icosahedron, Shape::Cuboctahedron }
	Enumeration of all contained symmetry names. More...

Functions
Eigen::Matrix3d	rotationMatrix (const CoordinateSystem &a, const CoordinateSystem &b)
	Gives the rotation matrix tranforming points between coordinate systems. More...

const std::string &	name (Shape shape)
	Fetch the string name of a shape. More...

Shape	nameFromString (const std::string &shapeNameString)
	Fetch the shape name from its string. More...

std::string	spaceFreeName (Shape shape)
	Fetch a space-free string of a shape for file naming. More...

unsigned	size (Shape shape)
	Fetch the number of vertices of a shape. More...

const RotationsList &	rotations (Shape shape)
	Fetches a shape's list of rotations. More...

const Permutation &	mirror (Shape shape)
	Fetches the mirror index mapping for a particular shape. More...

AngleFunction	angleFunction (Shape shape)
	Gets a shape's angle function. More...

Coordinates	coordinates (Shape shape)
	Fetch a shape's idealized coordiantes. More...

PointGroup	pointGroup (Shape shape)
	Get a shape's point group. More...

unsigned	nameIndex (Shape shape)
	Returns the index of a shape within allShapes. More...

const TetrahedronList &	tetrahedra (Shape shape)
	Fetches the list of tetrahedra defined in a shape. More...

bool	threeDimensional (Shape shape)
	Returns whether a shape is three dimensional. More...

InertialMoments	principalInertialMoments (const InertialPositionsType &positions)
	Determine the inertial moments of a set of positions. More...

Top	standardizeTop (Eigen::Ref< InertialPositionsType > normalizedPositions)
	Identifies the top of a set of positions and reorients the particle positions, aligning the main axis along z. More...

unsigned	reorientAsymmetricTop (Eigen::Ref< InertialPositionsType > normalizedPositions)
	Searches for Cn axes along the coordinate system axes, aligns the highest order Cn axis found along the z axis. More...

double	minimumAngle (Shape shape)
	Calculate the minimum angle in a symmetry. More...

double	maximumAngle (Shape shape)
	Calculate the maximum angle in a symmetry. More...

boost::optional< const Properties::ShapeTransitionGroup & >	getMapping (Shape a, Shape b, const boost::optional< Vertex > &removedIndexOption=boost::none)
	Cached access to mappings. Populates the cache from constexpr if generated. More...

bool	hasMultipleUnlinkedStereopermutations (Shape shape, unsigned nIdenticalLigands)
	Cached access to multiple unlinked values. More...

double	tau (const std::vector< double > &angles)
	Calculates the tau value for four and five angle symmetries. More...

Variables
constexpr unsigned	ORIGIN_PLACEHOLDER = std::numeric_limits<unsigned>::max()
	A placeholder value for constexpr tetrahedra specification of origin.

constexpr std::array< Shape, nShapes >	allShapes
	A list of all the enum class values. More...

const Temple::Array< std::pair < double, double >, nShapes >	shapeAngleBounds
	Precomputed min and max angle values in radians for all shapes.

constexpr unsigned	nShapes = 30
	Total number of shapes.

Detailed Description

Symmetry definitions and properties.

Typedef Documentation

using Scine::Molassembler::Shapes::AngleFunction = typedef std::function< >

Function returning angle between vertices.

All angle functions can be called with arbitrary (valid) parameters without failing. Valid here means that a != b and less than the size of the shape requested.

They return angles in radians.

using Scine::Molassembler::Shapes::Tetrahedron = typedef std::array<boost::optional<Vertex>, 4>

This is a four-vertex tetrahedron definition.

All shapes use None to signal to replace this position with the central atom as it is not part of the vertex indexing scheme.

using Scine::Molassembler::Shapes::TetrahedronList = typedef std::vector<Tetrahedron>

All shapes use boost::none to signal to replace this position with the central atom as it is not part of the vertex indexing scheme.

Enumeration Type Documentation

enum Scine::Molassembler::Shapes::Shape : unsigned

strong

Enumeration of all contained symmetry names.

List is in order of the number of symmetry positions

Enumerator
Line	See Data::Line.
Bent	See Data::Bent.
EquilateralTriangle	See Data::EquilateralTriangle.
VacantTetrahedron	See Data::VacantTetrahedron.
T	See Data::T.
Tetrahedron	See Data::Tetrahedron.
Square	See Data::Square.
Seesaw	See Data::Seesaw.
TrigonalPyramid	See Data::TrigonalPyramid.
SquarePyramid	See Data::SquarePyramid.
TrigonalBipyramid	See Data::TrigonalBipyramid.
Pentagon	See Data::Pentagon.
Octahedron	See Data::Octahedron.
TrigonalPrism	See Data::TrigonalPrism.
PentagonalPyramid	See Data::PentagonalPyramid.
Hexagon	See Data::Hexagon.
PentagonalBipyramid	See Data::PentagonalBipyramid.
CappedOctahedron	See Data::CappedOctahedron.
CappedTrigonalPrism	See Data::CappedTrigonalPrism.
SquareAntiprism	See Data::SquareAntiprism.
Cube	See Data::Cube.
TrigonalDodecahedron	See Data::TrigonalDodecahedron.
HexagonalBipyramid	See Data::HexagonalBipyramid.
TricappedTrigonalPrism	See Data::TricappedTrigonalPrism.
CappedSquareAntiprism	See Data::CappedSquareAntiPrism.
HeptagonalBipyramid	See Data::HeptagonalBipyramid.
BicappedSquareAntiprism	See Data::BicappedSquareAntiprism.
EdgeContractedIcosahedron	See Data::EdgeContractedIcosahedron.
Icosahedron	See Data::Icosahedron.
Cuboctahedron	See Data::Cuboctahedron.

enum Scine::Molassembler::Shapes::Top

strong

What kind of top is the particle collection?

Enumerator
Line	Line top: 0 ≅ IA << IB = IC.
Asymmetric	Asymmetric top: IA < IB < IC, degeneracy 0.
Prolate	Prolate top (think rugby football): IA < IB = IC.
Oblate	Oblate top (think disc): IA = IB < IC.
Spherical	Spherical top: IA = IB = IC.

Function Documentation

AngleFunction Scine::Molassembler::Shapes::angleFunction ( Shape shape )

Gets a shape's angle function.

Complexity \(\Theta(1)\)

Coordinates Scine::Molassembler::Shapes::coordinates ( Shape shape )

Fetch a shape's idealized coordiantes.

Complexity \(\Theta(1)\)

boost::optional<const Properties::ShapeTransitionGroup&> Scine::Molassembler::Shapes::getMapping	(	Shape	a,
		Shape	b,
		const boost::optional< Vertex > &	removedIndexOption = `boost::none`
	)

Cached access to mappings. Populates the cache from constexpr if generated.

Complexity \(\Theta(S!)\) where \(S\) is the size of the symmetry if the transition is not cached, \(\Theta(1)\) otherwise.

Parameters

a	Source shape
b	Target shape
removedIndexOption	The symmetry position removed from `source` if the transition is to be a symmetry position loss. Necessary if the size of the target is one less than that of the source. Defaults to None.

Returns: The symmetry transition if possible, None otherwise

bool Scine::Molassembler::Shapes::hasMultipleUnlinkedStereopermutations	(	Shape	shape,
		unsigned	nIdenticalLigands
	)

Cached access to multiple unlinked values.

Populates the cache with allHasMultipleUnlinkedStereopermutations if the constexpr number of unlinked stereopermutations was calculated at runtime. If not, calculates the value and stores it in the cache.

Complexity \(\Theta(S!)\) where \(S\) is the size of the symmetry if the symmetry and number of identical ligands is not cached, \(\Theta(1)\) otherwise

Parameters

symmetryName	symmetry for which to check the value
nIdenticalLigands	number of equivalent ligands

Returns: Whether there are multiple stereopermutations assuming no ligands are linked

double Scine::Molassembler::Shapes::maximumAngle ( Shape shape )

Calculate the maximum angle in a symmetry.

Calculates the maximum angle between symmetry positions in a symmetry class

Complexity \(\Theta(S^2)\)

double Scine::Molassembler::Shapes::minimumAngle ( Shape shape )

Calculate the minimum angle in a symmetry.

Calculates the minimum angle between symmetry positions in a symmetry class

Complexity \(\Theta(S^2)\)

See Also: ConstexprProperties::calculateSmallestAngle

const Permutation& Scine::Molassembler::Shapes::mirror ( Shape shape )

Fetches the mirror index mapping for a particular shape.

Complexity \(\Theta(1)\)

const std::string& Scine::Molassembler::Shapes::name ( Shape shape )

Fetch the string name of a shape.

Complexity \(\Theta(1)\)

Shape Scine::Molassembler::Shapes::nameFromString ( const std::string & shapeNameString )

Fetch the shape name from its string.

Complexity \(\Theta(S)\)

Exceptions

std::logic_error if no matching shape can be found

unsigned Scine::Molassembler::Shapes::nameIndex ( Shape shape )

Returns the index of a shape within allShapes.

Complexity \(\Theta(S)\)

PointGroup Scine::Molassembler::Shapes::pointGroup ( Shape shape )

Get a shape's point group.

Complexity \(\Theta(1)\)

InertialMoments Scine::Molassembler::Shapes::principalInertialMoments ( const InertialPositionsType & positions )

Determine the inertial moments of a set of positions.

Precondition: Assumes positions are in an inertial frame (COM is origin)

unsigned Scine::Molassembler::Shapes::reorientAsymmetricTop ( Eigen::Ref< InertialPositionsType > normalizedPositions )

Searches for Cn axes along the coordinate system axes, aligns the highest order Cn axis found along the z axis.

Parameters

normalizedPositions Particle positions

Note: Call standardizeTop() and use this if you get an asymmetric top.

Returns: The order of the highest Cn axis found. If no axis is found along the coordinate system axes, the result is 1, and particle positions are unaffected.

Eigen::Matrix3d Scine::Molassembler::Shapes::rotationMatrix	(	const CoordinateSystem &	a,
		const CoordinateSystem &	b
	)

Gives the rotation matrix tranforming points between coordinate systems.

You can transform points from a using the result of this function into coordinate system b.

Parameters

a	Source coordinate system
b	Target coordinate system

Returns: Rotation matrix transforming points from system a into b

const RotationsList& Scine::Molassembler::Shapes::rotations ( Shape shape )

Fetches a shape's list of rotations.

Complexity \(\Theta(1)\)

unsigned Scine::Molassembler::Shapes::size ( Shape shape )

Fetch the number of vertices of a shape.

Complexity \(\Theta(1)\)

std::string Scine::Molassembler::Shapes::spaceFreeName ( Shape shape )

Fetch a space-free string of a shape for file naming.

Complexity \(\Theta(1)\)

Top Scine::Molassembler::Shapes::standardizeTop ( Eigen::Ref< InertialPositionsType > normalizedPositions )

Identifies the top of a set of positions and reorients the particle positions, aligning the main axis along z.

Parameters

normalizedPositions Particle positions

Returns: The top of the molecule

double Scine::Molassembler::Shapes::tau ( const std::vector< double > & angles )

inline

Calculates the tau value for four and five angle symmetries.

Complexity \(\Theta(1)\)

Parameters

angles A sorted vector of the angles in your central symmetry. This must be of size four or five.

Returns: τ₄' or τ₅

const TetrahedronList& Scine::Molassembler::Shapes::tetrahedra ( Shape shape )

Fetches the list of tetrahedra defined in a shape.

Complexity \(\Theta(1)\)

bool Scine::Molassembler::Shapes::threeDimensional ( Shape shape )

Returns whether a shape is three dimensional.

Complexity \(\Theta(1)\)

Variable Documentation

constexpr std::array<Shape, nShapes> Scine::Molassembler::Shapes::allShapes

Initial value:

= Detail::makeAllShapes(
  std::make_index_sequence<nShapes>()
)

A list of all the enum class values.

Namespaces

Data Structures

Typedefs

Enumerations

Functions

Variables

Detailed Description

Typedef Documentation

Enumeration Type Documentation

Function Documentation

Variable Documentation