This template class represents three-dimensional physical interval vectors. More...

Public Types
enum	OverlapType { IncludeNone , IncludeAll , Subdivide }
	The overlap type. More...

typedef SBQuantityProduct2< Quantity, Quantity >::Type	QuantitySquared
	The type of the squared quantity.

typedef SBQuantityProduct3< Quantity, Quantity, Quantity >::Type	QuantityCubed
	The type of the cubed quantity.

Useful functions
static const SBDTypePhysicalIAVector3< Quantity >	zero
	The zero physical interval vector.

static const SBDTypePhysicalIAVector3< Quantity >	empty
	The empty physical interval vector, with all components set to (+infinite, -infinite)

static const SBDTypePhysicalIAVector3< Quantity >	infinite
	The infinite physical interval vector, with all components set to (+infinite, -infinite)

SBDTypePhysicalInterval< Quantity >	i [3]
	The components of the physical interval vector.

void	setZero ()
	Sets all components to [0,0].

SBDTypePhysicalVector3< Quantity >	center () const
	Returns the center [ 0.5(i[0].i[0]+i[0].i[1]) 0.5(i[1].i[0]+i[1].i[1]) 0.5*(i[2].i[0]+i[2].i[1]) ] of the physical interval vector.

SBDTypePhysicalVector3< Quantity >	diameter () const
	Returns the diameter [ (i[0].i[1]-i[0].i[0]) (i[1].i[1]-i[1].i[0]) (i[2].i[1]-i[2].i[0]) ] of the physical interval vector.

QuantityCubed	volume () const
	Returns the volume (i[0].i[1]-i[0].i[0])(i[1].i[1]-i[1].i[0])(i[2].i[1]-i[2].i[0]) of the physical interval vector.

QuantitySquared	area () const
	Returns the area 2.0((i[0].i[1]-i[0].i[0])(i[0].i[1]-i[0].i[0])+(i[1].i[1]-i[1].i[0])(i[1].i[1]-i[1].i[0])+(i[2].i[1]-i[2].i[0])(i[2].i[1]-i[2].i[0])) of the physical interval vector.

Quantity	lengthsSum () const
	Returns the sum i[0].diameter()+i[1].diameter()+i[2].diameter() of the components diameters of the physical interval vector.

SBDTypePhysicalVector3< Quantity >	lowerBound () const
	Returns the lower bound [ i[0].i[0] i[1].i[0] i[2].i[0] ] of the physical interval vector.

SBDTypePhysicalVector3< Quantity >	upperBound () const
	Returns the upper bound [ i[0].i[1] i[1].i[1] i[2].i[1] ] of the physical interval vector.

void	collapseToUpperBound ()
	Sets the upper bounds of the intervals equal to the lower bounds.

void	collapseToLowerBound ()
	Sets the lower bounds of the intervals equal to the upper bounds.

bool	overlaps (const SBDTypePhysicalIAVector3< Quantity > &u) const
	Returns true when this physical interval vector overlaps physical interval vector `u`.

bool	overlaps (const SBDTypePhysicalIAVector3< Quantity > &u, const Quantity &cutoffDistance) const
	Returns true when the Manhattan distance between this physical interval vector and physical interval vector `u` is smaller than `cutoffDistance`.

bool	overlaps (const SBDTypePhysicalIAVector3< Quantity > &u, const SBDTypeSymmetryTransform &t) const
	Returns true when this physical interval vector overlaps physical interval vector `u` transformed by `t`.

OverlapType	overlapsAdvanced (SBDTypePhysicalIAVector3< Quantity > &u, const Quantity &cutoff, const QuantitySquared &cutoff2) const
	Returns the OverlapType between this physical interval vector and physical interval vector `u`.

OverlapType	overlapsAdvanced (SBDTypePhysicalIAVector3 &u, const Quantity &cutoff, const QuantitySquared &cutoff2, const SBDTypeSymmetryTransform &t) const
	Returns the OverlapType between this physical interval vector and physical interval vector `u` transformed by `t`.

bool	contains (const SBDTypePhysicalVector3< Quantity > &u) const
	Returns true when this physical interval vector contains the physical vector `u`.

bool	contains (const SBDTypePhysicalIAVector3 &u) const
	Returns true when this physical interval vector contains in physical interval vector `u`.

bool	isContainedIn (const SBDTypePhysicalIAVector3 &u) const
	Returns true when this physical interval vector is contained in physical interval vector `u`.

QuantitySquared	distance2ToPoint (const SBDTypePhysicalVector3< Quantity > &u) const
	Returns the squared Euclidean distance between this physical interval vector and physical vector `u`.

void	split (SBDTypePhysicalIAVector3< Quantity > &u1, SBDTypePhysicalIAVector3< Quantity > &u2) const
	Splits this physical interval vector along the longest axis into physical interval vectors `u1` and`u2`.

void	expand (Quantity r)
	Expands all components of this physical interval vector by offset `r`.

void	shrink (Quantity r)
	Shrinks all components of this physical interval vector by offset `r`.

void	reset (const SBDTypePhysicalVector3< Quantity > &v)
	Sets this physical interval vector to [ [`u.v`[0], `u.v`[0]] [`u.v`[1], `u.v`[1]] [`u.v`[2], `u.v`[2]] ].

void	bound (const SBDTypePhysicalVector3< Quantity > &u)
	Enlarges this physical interval vector to contain the physical vector `u`.

void	bound (const SBDTypePhysicalIAVector3< Quantity > &u)
	Enlarges this physical interval vector to contain the physical interval vector `u`.

void	fit (const SBDTypePhysicalIAVector3< Quantity > &a, const SBDTypePhysicalIAVector3< Quantity > &b)
	Sets the components of this physical interval vector to exactly bound both physical interval vectors `a` and `b`.

void	print () const
	Prints this physical interval vector.

Constructors
	SBDTypePhysicalIAVector3 ()
	Constructs a physical interval vector with all components set to [0,0].

	SBDTypePhysicalIAVector3 (const Quantity &x)
	Constructs a physical interval vector with all components set to [`x`, `x`].

	SBDTypePhysicalIAVector3 (const Quantity &x, const Quantity &y, const Quantity &z)
	Constructs the physical interval vector [ [`x`, `x`] [`y`, `y`] [`z`, `z`] ].

	SBDTypePhysicalIAVector3 (Quantity v[3][2])
	Constructs the physical interval vector [ [`v`[0][0], `v`[0][1]] [`v`[1][0], `v`[1][1]] [`v`[2][0], `v`[2][1]] ].

	SBDTypePhysicalIAVector3 (Quantity xl, Quantity xu, Quantity yl, Quantity yu, Quantity zl, Quantity zu)
	Constructs the physical interval vector [ [`xl`, `xu`] [`yl`, `yu`] [`zl`, `zu`] ].

	SBDTypePhysicalIAVector3 (SBDTypePhysicalInterval< Quantity > v[3])
	Constructs the physical interval vector [ `v`[0] `v`[1] `v`[2] ].

	SBDTypePhysicalIAVector3 (const SBDTypePhysicalInterval< Quantity > &x, const SBDTypePhysicalInterval< Quantity > &y, const SBDTypePhysicalInterval< Quantity > &z)
	Constructs the physical interval vector [ `x` `y` `z` ].

	SBDTypePhysicalIAVector3 (SBDTypePhysicalVector3< Quantity > const &u)
	Constructs the physical interval vector [ [`u.v`[0], `u.v`[0]] [`u.v`[1], `u.v`[1]] [`u.v`[2], `u.v`[2]] ].

	SBDTypePhysicalIAVector3 (const SBDTypePhysicalIAVector3< Quantity > &u)
	Copy constructor.

	SBDTypePhysicalIAVector3 (double x)
	Constructs a dimensionless physical interval vector with all components set to [`x`, `x`].

	SBDTypePhysicalIAVector3 (double x, double y, double z)
	Constructs the dimensionless physical interval vector [ [`x`, `x`] [`y`, `y`] [`z`, `z`] ].

	SBDTypePhysicalIAVector3 (double val[3][2])
	Constructs the dimensionless physical interval vector [ [`v`[0][0], `v`[0][1]] [`v`[1][0], `v`[1][1]] [`v`[2][0], `v`[2][1]] ].

	SBDTypePhysicalIAVector3 (double xl, double xu, double yl, double yu, double zl, double zu)
	Constructs the physical interval vector [ [`xl`, `xu`] [`yl`, `yu`] [`zl`, `zu`] ].

Serialization
void	serialize (SBCSerializer *serializer, const SBVersionNumber &sdkVersionNumber=SB_SDK_VERSION_NUMBER) const
	Serializes the physical interval vector using the provided `serializer`.

void	unserialize (SBCSerializer *serializer, const SBVersionNumber &sdkVersionNumber=SB_SDK_VERSION_NUMBER)
	Unserializes the physical interval vector using the provided `serializer`.

Accessors
SBDTypePhysicalIAVector3< SBQuantity::dimensionless >	getValue () const
	Returns a dimensionless physical interval vector whose bounds are equal to those of this physical interval vector.

void	setValue (const SBDTypePhysicalIAVector3< SBQuantity::dimensionless > &u)
	Sets the bounds of this physical interval vector equal to those of the dimensionless physical interval vector `u`.

Operators
template<typename QuantityB >
SBDTypePhysicalInterval< SBQuantityType< typename SBDQuantityUnitMultiplication< typename Quantity::UnitType, typename QuantityB::UnitType >::UnitType > >	operator\| (const SBDTypePhysicalIAVector3< QuantityB > &u) const
	Returns the dot product of this physical interval vector with physical interval vector `u`.

template<typename QuantityB >
SBDTypePhysicalIAVector3< SBQuantityType< typename SBDQuantityUnitMultiplication< typename Quantity::UnitType, typename QuantityB::UnitType >::UnitType > >	operator^ (const SBDTypePhysicalIAVector3< QuantityB > &u) const
	Returns the cross product of this physical interval vector with physical interval vector `u`.

SBDTypePhysicalIAVector3< Quantity >	operator+ (const SBDTypePhysicalIAVector3< Quantity > &u) const
	Returns the sum of this physical interval vector with physical interval vector `u`.

SBDTypePhysicalIAVector3< Quantity >	operator- (const SBDTypePhysicalIAVector3< Quantity > &u) const
	Returns the difference of this physical interval vector with physical interval vector `u`.

SBDTypePhysicalIAVector3< Quantity >	operator* (double d) const
	Returns the product of this physical interval vector with double `d`.

template<typename QuantityB >
SBDTypePhysicalIAVector3< SBQuantityType< typename SBDQuantityUnitMultiplication< typename Quantity::UnitType, typename QuantityB::UnitType >::UnitType > >	operator* (QuantityB d) const
	Returns the product of this physical interval vector with physical quantity `d`.

template<typename QuantityB >
SBDTypePhysicalIAVector3< SBQuantityType< typename SBDQuantityUnitMultiplication< typename Quantity::UnitType, typename QuantityB::UnitType >::UnitType > >	operator* (SBDTypePhysicalInterval< QuantityB > d) const
	Returns the product of this physical interval vector with physical interval `d`.

template<typename QuantityB >
SBDTypePhysicalIAVector3< SBQuantityType< typename SBDQuantityUnitMultiplication< typename Quantity::UnitType, typename QuantityB::UnitType >::UnitType > >	operator* (const SBDTypePhysicalIAVector3< QuantityB > &u) const
	Returns the component-wise product of this physical interval vector with physical interval vector `u`.

template<typename QuantityB >
SBDTypePhysicalIAVector3< Quantity > &	operator*= (QuantityB d) const
	Multiplies this physical interval vector with physical quantity `d`.

template<typename QuantityB >
SBDTypePhysicalIAVector3< Quantity > &	operator*= (SBDTypePhysicalInterval< QuantityB > d) const
	Multiplies this physical interval vector with physical interval `d`.

template<typename QuantityB >
SBDTypePhysicalIAVector3< Quantity > &	operator*= (SBDTypePhysicalIAVector3< QuantityB > d) const
	Multiplies this physical interval vector with physical interval vector `d`.

SBDTypePhysicalIAVector3< Quantity >	operator/ (double d) const
	Returns the division of this physical interval vector by double `d`.

template<typename QuantityB >
SBDTypePhysicalIAVector3< SBQuantityType< typename SBDQuantityUnitDivision< typename Quantity::UnitType, typename QuantityB::UnitType >::UnitType > >	operator/ (QuantityB d) const
	Returns the division of this physical interval vector by physical quantity `d`.

template<typename QuantityB >
SBDTypePhysicalIAVector3< SBQuantityType< typename SBDQuantityUnitDivision< typename Quantity::UnitType, typename QuantityB::UnitType >::UnitType > >	operator/ (SBDTypePhysicalInterval< QuantityB > d) const
	Returns the division of this physical interval vector by physical interval `d`.

template<typename QuantityB >
SBDTypePhysicalIAVector3< SBQuantityType< typename SBDQuantityUnitDivision< typename Quantity::UnitType, typename QuantityB::UnitType >::UnitType > >	operator/ (const SBDTypePhysicalIAVector3< QuantityB > &u) const
	Returns the component-wise division of this physical interval vector by physical interval vector `u`.

template<typename QuantityB >
SBDTypePhysicalIAVector3< Quantity > &	operator/= (QuantityB d) const
	Divides this physical interval vector by physical quantity `d`.

template<typename QuantityB >
SBDTypePhysicalIAVector3< Quantity > &	operator/= (SBDTypePhysicalInterval< QuantityB > d) const
	Divides this physical interval vector by physical interval `d`.

template<typename QuantityB >
SBDTypePhysicalIAVector3< Quantity > &	operator/= (SBDTypePhysicalIAVector3< QuantityB > d) const
	Divides this physical interval vector by physical interval vector `d`.

SBDTypePhysicalIAVector3< Quantity > &	operator= (const SBDTypePhysicalIAVector3< Quantity > &u)
	Copy assignment.

SBDTypePhysicalIAVector3< Quantity >	operator- () const
	Returns the opposite of this physical interval vector.

SBDTypePhysicalIAVector3< Quantity > &	operator+= (const SBDTypePhysicalIAVector3< Quantity > &u)
	Adds physical interval vector `u` to this physical interval vector.

SBDTypePhysicalIAVector3< Quantity > &	operator-= (const SBDTypePhysicalIAVector3< Quantity > &u)
	Subtracts physical interval vector `u` from this physical interval vector.

template<typename QuantityB >
	operator SBDTypePhysicalIAVector3< QuantityB > () const
	Converts this physical interval vector to a physical interval vector with units `QuantityB`.

template<typename QuantityB >
bool	operator== (const SBDTypePhysicalIAVector3< QuantityB > &u) const
	Returns true if this physical interval vector is equal to physical interval vector `u` (component-wise)

template<typename QuantityB >
bool	operator!= (const SBDTypePhysicalIAVector3< QuantityB > &u) const
	Returns true if this physical interval vector is different from physical interval vector `u` (component-wise)

SBDTypePhysicalInterval< Quantity > &	operator[] (int index)
	Returns a reference to component `index`.

const SBDTypePhysicalInterval< Quantity > &	operator[] (int index) const
	Returns a reference to component `index` (const version)

Detailed Description

template<typename Quantity>
class SBDTypePhysicalIAVector3< Quantity >

Template Parameters

Quantity The quantity type of the components

The SBDTypePhysicalIAVector3 template class represents physical three-dimensional interval vectors, i.e. three-dimensional vectors whose components are intervals of physical quantities. Interval vectors may be used to describe bounds on physical vectors (e.g. bounds on positions, on velocities, etc.), and perform interval arithmetics (IA) on these vectors.

Physical interval vectors use SAMSON's unit system. In a physical (interval) vector, all interval components have the same unit, so that the SBDTypePhysicalIAVector3 template class is parameterized by only one type: Quantity.

Most of the time, developers of SAMSON Extensions do not have to use this template, but may directly use some predefined types, e.g. SBIAVector3 (dimensionless interval vector), SBIAPosition3 (interval vector with units of length), SBIAForce3 (interval vector with units of force), etc.

For example, SBIAPosition3 may be seen as the coordinates of a three-dimensional, axis-aligned box that bounds atomic coordinates, so that this class may be used to perform proximity queries (neighbor search), in particular thanks to functions such as SBIAPosition3::overlaps.

Interval arithmetics may be particularly useful to compute bounds on physical quantities:

// bound on the first position
 
SBIAPosition3 x1(
    SBQuantity::angstrom(1.7), SBQuantity::angstrom(1.8),
    SBQuantity::angstrom(0.8), SBQuantity::angstrom(0.9),
    SBQuantity::angstrom(7.5), SBQuantity::angstrom(7.6)
    );
 
// bound on the second position
 
SBIAPosition3 x2(
    SBQuantity::angstrom(0.2), SBQuantity::angstrom(0.3),
    SBQuantity::angstrom(0.4), SBQuantity::angstrom(0.5),
    SBQuantity::angstrom(7.7), SBQuantity::angstrom(7.8)
    );
 
// bound on the squared distance
SBSquareLengthInterval l2 = ((x2 - x1) | (x2 - x1));

Short name: SBPhysicalIAVector3

See also: SAMSON's unit system; SBDTypePhysicalInterval

Member Enumeration Documentation

◆ OverlapType

template<typename Quantity >

enum SBDTypePhysicalIAVector3::OverlapType

Enumerator
IncludeNone	Include all pairs.
IncludeAll	None is included.
Subdivide	Subdivide.

Member Function Documentation

◆ operator*()

template<typename Quantity >

template<typename QuantityB >

SBDTypePhysicalIAVector3< SBQuantityType< typename SBDQuantityUnitMultiplication< typename Quantity::UnitType, typename QuantityB::UnitType >::UnitType > > SBDTypePhysicalIAVector3< Quantity >::operator* ( const SBDTypePhysicalIAVector3< QuantityB > & u ) const

inline

This operator returns the component-wise product of this physical interval vector with physical interval vector u, i.e. a physical interval vector in which each component is the product of the corresponding components in this physical interval vector and physical interval vector u.

◆ operator*=() [1/3]

template<typename Quantity >

template<typename QuantityB >

SBDTypePhysicalIAVector3< Quantity > & SBDTypePhysicalIAVector3< Quantity >::operator*= ( QuantityB d ) const

inline

Parameters

d	A dimensionless physical quantity or a numeric type (i.e. int, float, double, etc)

◆ operator*=() [2/3]

template<typename Quantity >

template<typename QuantityB >

SBDTypePhysicalIAVector3< Quantity > & SBDTypePhysicalIAVector3< Quantity >::operator*= ( SBDTypePhysicalIAVector3< QuantityB > d ) const

inline

Parameters

d	A dimensionless physical interval vector

◆ operator*=() [3/3]

template<typename Quantity >

template<typename QuantityB >

SBDTypePhysicalIAVector3< Quantity > & SBDTypePhysicalIAVector3< Quantity >::operator*= ( SBDTypePhysicalInterval< QuantityB > d ) const

inline

Parameters

d	A dimensionless physical interval

◆ operator/()

template<typename Quantity >

template<typename QuantityB >

SBDTypePhysicalIAVector3< SBQuantityType< typename SBDQuantityUnitDivision< typename Quantity::UnitType, typename QuantityB::UnitType >::UnitType > > SBDTypePhysicalIAVector3< Quantity >::operator/ ( const SBDTypePhysicalIAVector3< QuantityB > & u ) const

inline

This operator returns the component-wise division of this physical interval vector by physical interval vector u, i.e. a physical interval vector in which each component is the division of the corresponding components in this physical interval vector and physical interval vector u.

◆ operator/=() [1/3]

template<typename Quantity >

template<typename QuantityB >

SBDTypePhysicalIAVector3< Quantity > & SBDTypePhysicalIAVector3< Quantity >::operator/= ( QuantityB d ) const

inline

Parameters

d	A dimensionless physical quantity or a numeric type (i.e. int, float, double, etc)

◆ operator/=() [2/3]

template<typename Quantity >

template<typename QuantityB >

SBDTypePhysicalIAVector3< Quantity > & SBDTypePhysicalIAVector3< Quantity >::operator/= ( SBDTypePhysicalIAVector3< QuantityB > d ) const

inline

Parameters

d	A dimensionless physical interval vector

◆ operator/=() [3/3]

template<typename Quantity >

template<typename QuantityB >

SBDTypePhysicalIAVector3< Quantity > & SBDTypePhysicalIAVector3< Quantity >::operator/= ( SBDTypePhysicalInterval< QuantityB > d ) const

inline

Parameters

d	A dimensionless physical interval

Public Types

Useful functions

Constructors

Serialization

Accessors

Operators

Detailed Description

Member Enumeration Documentation

◆ OverlapType

Member Function Documentation

◆ operator*()

◆ operator*=() [1/3]

◆ operator*=() [2/3]

◆ operator*=() [3/3]

◆ operator/()

◆ operator/=() [1/3]

◆ operator/=() [2/3]

◆ operator/=() [3/3]