Representation of ellipsoidal aggregate. More...

#include <aggregate.hpp>

Inheritance diagram for aggregpacking::Ellipsoid:

Public Member Functions
	Ellipsoid ()
	Default constructor.

	Ellipsoid (const Vector3 &p)
	Constructor from position. More...

	Ellipsoid (double a, double b, double c)
	Constructor from semiaxes. More...

	Ellipsoid (const Vector3 &p, double a, double b, double c)
	Constructor from position and semiaxes. More...

	Ellipsoid (const Sphere &s)
	Constructor from Sphere. More...

double	getA ()
	Getter for 1st semiaxis.

double	getB ()
	Getter for 2nd semiaxis.

double	getC ()
	Getter for 3rd semiaxis.

void	setA (double a)
	Setter for 1st semiaxis. More...

void	setB (double b)
	Setter for 2nd semiaxis. More...

void	setC (double c)
	Setter for 3rd semiaxis. More...

double	getRandomAxesRatio ()
	Getter for randomAxesRatio.

void	setRandomAxesRatio (double v)
	Setter for randomAxesRatio.

double	computeRelativeDistanceFrom (const Vector3 &p) const
	Computes relative distance between gvien point and given Ellipsoid. Relative distance means in direction pos–p, the value is 1 on surface of the Ellipsoid, in the center is 0, inside Ellipsoid (0,1) and outside Ellipsoid >1. More...

virtual bool	containsPoint (const Vector3 &p) const
	Ckecks, whether given point is contained by receiver. More...

virtual bool	containsSphere (const Sphere &s) const
	Ckecks, whether given sphere is contained by receiver. More...

virtual double	computeDistanceFrom (const Aggregate &aggreg) const
	Computes distance of receiver from given Aggregate. More...

virtual double	computeVolume () const
	Computes volume of receiver.

virtual void	fromSize (double s)
	Adjust receiver dimensions accodring to given size. Sets b=0.5s, a=b(1+0.5random), c=b(1-0.5*random) More...

void	computeProjectionOnCoordAxis (double &s0, double &w, int axis) const
	Computes parameters of its projction onto coordinate axis (such that the projection is s0+-w) More...

virtual double	computeMaxCoord (int axis) const
	Computes maximum coordinate along given axis. More...

virtual double	computeMinCoord (int axis) const
	Computes minimum coordinate along given axis. More...

virtual double	getSize () const
	Returns size of receiver (what sieve opening it would normally pass), i.e. the middle value from a,b,c.

virtual double	getMaxSize () const
	Returns maximum size of receiver.

Matrix3	computeMatrixB () const
	Computes matrix $\mathbf{B} = \mathbf{R\Sigma}$ .

Matrix3	computeMatrixBT () const
	Computes matrix $\mathbf{B}^\mathsf{T} = \mathbf{\Sigma R}^\mathsf{T}$ .

Matrix3	computeMatrixBInversed () const
	Computes matrix $\mathbf{B}^{-1} = \mathbf{\Sigma}^{-1}\mathbf{R}^\mathsf{T}$ .

Matrix3	computeMatrixBTInversed () const
	Computes matrix $\mathbf{B}^{-\mathsf{T}} = \mathbf{R\Sigma}^{-1}$ .

Matrix3	computeMatrixSigma () const
	Computes matrix $\mathbf{\Sigma}$ , a diagonal matrix with $[\Sigma]_{(ii)}=1/a_i$ , where is th smiaxis length.

Matrix3	computeMatrixSigmaInversed () const
	Computes matrix $\mathbf{\Sigma}^{-1}$ , a diagonal matrix with $[\Sigma]_{(ii)}=a_i$ , where is th smiaxis length.

Matrix3	computeMatrixSigmaSquare () const
	Computes matrix $\mathbf{\Sigma\Sigma}$ .

Matrix3	computeMatrixA () const
	Computes matrix $\mathbf{A}=\mathbf{BB}^\mathsf{T}=\mathbf{R\Sigma}^2\mathbf{R}^\mathsf{T}$ .

Vector3	computeNearestPointFrom (const Vector3 &p) const
	Computes nearest point of receiver to given point. Returns given point if it lies inside the receiver, returns point on its surface otherwise. More...

Vector3	computeFarthestPointFrom (const Vector3 &p) const
	Computes farthest point of receiver to given point. Returns point on its surface. The computation is based on Monte-Carlo random sampling. More...

double	computeEstimatedDistanceFrom (const Ellipsoid &e) const
	Computes estimated distance between receiver and given Ellipsoid. Mainly used as a quick check if two Ellipsoids overlap (return < 0) or not (return > 0) More...

virtual const string &	getClassName ()
	Returns string representation of Ellipsoid class name.

bool	operator== (const Aggregate &other) const
	Equality operator. More...

bool	operator!= (const Aggregate &other) const
	Inequality operator. More...

bool	isInsideCube (double s) const
	Determines if receiver is entirely inside cube. The cube is in positive octant and has one corner in origin. More...

int	getNumber ()
	Getter for number.

void	setNumber (int n)
	Setter for number. More...

const Vector3 &	getPos () const
	Getter for position (by reference)

Vector3	getPos ()
	Getter for position (by value)

void	setPos (const Vector3 &p)
	Setter for position. More...

void	setPos (double x, double y, double z)
	Setter for position (from individual components) More...

const Quaternion &	getOri () const
	Getter for orientation (by reference)

Quaternion	getOri ()
	Getter for orientation (by value)

void	setOri (const Quaternion &q)
	Setter for orientation. More...

Static Public Member Functions
static double	computeRelativeDistanceFrom (const Vector3 &p, const Matrix3 &bT, const Vector3 &pos)
	Computes relative distance between gvien point and given Ellipsoid. Relative distance means in direction pos–p, the value is 1 on surface of the Ellipsoid, in the center is 0, inside Ellipsoid (0,1) and outside Ellipsoid >1. More...

static bool	containsPoint (const Vector3 &p, const Matrix3 &bT, const Vector3 &pos)
	Auxiliary structure to test if point lies inside given Ellipsoid. More...

static Vector3	computeNearestPointFrom (const Vector3 &p, const Matrix3 &bT, const Vector3 &pos)
	Computes nearest point of Ellipsoid to given point. Returns given point if it lies inside the Ellipsoid, returns point on its surface otherwise. More...

static Vector3	computeFarthestPointFrom (const Vector3 &p, const Matrix3 &bT, const Vector3 &pos)
	Computes farthest point of Ellipsoid to given point. Returns point on its surface. The computation is based on Monte-Carlo random sampling. More...

static Aggregate *	Load (istream &is)
	Create and return a new aggregate from given istream. More...

Static Public Attributes
static const string	className = "Ellipsoid"
	String representation of Ellipsoid class name.

Protected Attributes
int	number
	Number.

Vector3	pos
	Position.

Quaternion	ori
	Orientation.

Private Attributes
double	a
	1st semiaxis lengths

double	b
	2nd semiaxis lengths

double	c
	3rd semiaxis lengths

Static Private Attributes
static double	randomAxesRatio = 0.5
	Random axes ratio. Given semiaxis b, a=b(1+randomAxesRatioR), c=b(1-randomAxesRatioR), R is a random number in range (0,1) More...

Friends
ostream &	operator<< (ostream &os, const Ellipsoid &o)
	Ellipsoid to ostream shift operator.

istream &	operator>> (istream &is, Ellipsoid &o)
	Ellipsoid from istream shift operator.

Detailed Description

Representation of ellipsoidal aggregate.

Ellipsoidal particles are defined as a set of 3D space points $\mathbf{x}$ :

$\{ \mathbf{x}\ |\ (\mathbf{x}-\mathbf{c})^\mathsf{T}\mathbf{BB}^\mathsf{T}(\mathbf{x}-\mathbf{c}) \le 1 \}$

$\mathbf{c}$ is the ellipsoid center. $\mathbf{B} = \mathbf{\Sigma}\mathbf{R}^\mathsf{T}$ is a matrix defining the ellipsoid. From other possible definitions (see below) it is used most often. $\mathbf{\Sigma}$ is a diagonal matrix with $[\Sigma]_{(ii)}=1/a_i$ ( $a_i$ is a length of $i$ th semiaxis) and $\mathbf{R}$ is an orthogonal rotational matrix (matrix representation of rotation quaternion) with columns equal to rotated coordinate axes.

Alternative definition with $\mathbf{A}=\mathbf{BB}^\mathsf{T}=\mathbf{R\Sigma}^2\mathbf{R}^\mathsf{T}$ is also possible or substituting $\mathbf{y}=\mathbf{B}^\mathsf{T}(\mathbf{x}-\mathbf{c})$ one can define:

$\{ \mathbf{x}\ |\ ||\mathbf{B}^\mathsf{T}(\mathbf{x}-\mathbf{c})|| \le 1 \}$

$\{ \mathbf{x}\ |\ (\mathbf{x}-\mathbf{c})^\mathsf{T}\mathbf{A}^\mathsf{T}(\mathbf{x}-\mathbf{c}) \le 1 \}$

$\{ \mathbf{x}\ |\ (\mathbf{x}-\mathbf{c})^\mathsf{T}\mathbf{R\Sigma}^2\mathbf{R}^\mathsf{T}(\mathbf{x}-\mathbf{c}) \le 1 \}$

$\{ \mathbf{x}\ |\ \mathbf{x}=\mathbf{c}+\mathbf{B}^{-\mathsf{T}}\mathbf{y}, ||\mathbf{y})|| \le 1 \}$

Constructor & Destructor Documentation

aggregpacking::Ellipsoid::Ellipsoid ( const Vector3 & p )

inline

Constructor from position.

Parameters

p position

aggregpacking::Ellipsoid::Ellipsoid	(	double	a,
		double	b,
		double	c
	)

inline

Constructor from semiaxes.

Parameters

a	1st semiaxis length
b	2nd semiaxis length
c	3rd semiaxis length

aggregpacking::Ellipsoid::Ellipsoid	(	const Vector3 &	p,
		double	a,
		double	b,
		double	c
	)

inline

Constructor from position and semiaxes.

Parameters

p	position
a	1st semiaxis length
b	2nd semiaxis length
c	3rd semiaxis length

aggregpacking::Ellipsoid::Ellipsoid ( const Sphere & s )

Constructor from Sphere.

Parameters

s	given Sphere object

Member Function Documentation

double aggregpacking::Ellipsoid::computeDistanceFrom ( const Aggregate & aggreg ) const

virtual

Computes distance of receiver from given Aggregate.

Positive when the aggregates are separate, negative whan they overlap

Parameters

aggreg Aggregate object to compute distance from

Returns: distance between receiver and given Aggregate

Implements aggregpacking::Aggregate.

double aggregpacking::Ellipsoid::computeEstimatedDistanceFrom ( const Ellipsoid & e ) const

Computes estimated distance between receiver and given Ellipsoid. Mainly used as a quick check if two Ellipsoids overlap (return < 0) or not (return > 0)

Parameters

e	given Ellipsoid

Vector3 aggregpacking::Ellipsoid::computeFarthestPointFrom	(	const Vector3 &	p,
		const Matrix3 &	bT,
		const Vector3 &	pos
	)

static

Computes farthest point of Ellipsoid to given point. Returns point on its surface. The computation is based on Monte-Carlo random sampling.

Parameters

p	given point
bT	$\mathbf{R}^\mathsf{T}$ matrix of given Ellipsoid
pos	position of given Ellipsoid

Vector3 aggregpacking::Ellipsoid::computeFarthestPointFrom ( const Vector3 & p ) const

Computes farthest point of receiver to given point. Returns point on its surface. The computation is based on Monte-Carlo random sampling.

Parameters

p	given point

double aggregpacking::Ellipsoid::computeMaxCoord ( int axis ) const

virtual

Computes maximum coordinate along given axis.

Parameters

axis	0=x, 1=y, 2=z

Implements aggregpacking::Aggregate.

double aggregpacking::Ellipsoid::computeMinCoord ( int axis ) const

virtual

Computes minimum coordinate along given axis.

Parameters

axis	0=x, 1=y, 2=z

Implements aggregpacking::Aggregate.

Vector3 aggregpacking::Ellipsoid::computeNearestPointFrom	(	const Vector3 &	p,
		const Matrix3 &	bT,
		const Vector3 &	pos
	)

static

Computes nearest point of Ellipsoid to given point. Returns given point if it lies inside the Ellipsoid, returns point on its surface otherwise.

Parameters

p	given point
bT	$\mathbf{R}^\mathsf{T}$ matrix of given Ellipsoid
pos	position of given Ellipsoid

Vector3 aggregpacking::Ellipsoid::computeNearestPointFrom ( const Vector3 & p ) const

Computes nearest point of receiver to given point. Returns given point if it lies inside the receiver, returns point on its surface otherwise.

Parameters

p	given point

void aggregpacking::Ellipsoid::computeProjectionOnCoordAxis	(	double &	s0,
		double &	w,
		int	axis
	)		const

Computes parameters of its projction onto coordinate axis (such that the projection is s0+-w)

Parameters

s0	projection of receiver's center
w	extreme projection length
axis	x=0, y=1, z=2

double aggregpacking::Ellipsoid::computeRelativeDistanceFrom	(	const Vector3 &	p,
		const Matrix3 &	bT,
		const Vector3 &	pos
	)

static

Computes relative distance between gvien point and given Ellipsoid. Relative distance means in direction pos–p, the value is 1 on surface of the Ellipsoid, in the center is 0, inside Ellipsoid (0,1) and outside Ellipsoid >1.

Parameters

p	given point
bT	$\mathbf{R}^\mathsf{T}$ matrix of given Ellipsoid
pos	position of given Ellipsoid

double aggregpacking::Ellipsoid::computeRelativeDistanceFrom ( const Vector3 & p ) const

Computes relative distance between gvien point and given Ellipsoid. Relative distance means in direction pos–p, the value is 1 on surface of the Ellipsoid, in the center is 0, inside Ellipsoid (0,1) and outside Ellipsoid >1.

Parameters

p	given point

bool aggregpacking::Ellipsoid::containsPoint	(	const Vector3 &	p,
		const Matrix3 &	bT,
		const Vector3 &	pos
	)

static

Auxiliary structure to test if point lies inside given Ellipsoid.

Parameters

p	given point
bT	$\mathbf{R}^\mathsf{T}$ matrix of given Ellipsoid
pos	position of given Ellipsoid

bool aggregpacking::Ellipsoid::containsPoint ( const Vector3 & p ) const

virtual

Ckecks, whether given point is contained by receiver.

Parameters

p	point coordinates

Returns: true if receiver contains given point, false otherwise

Implements aggregpacking::Aggregate.

bool aggregpacking::Ellipsoid::containsSphere ( const Sphere & s ) const

virtual

Ckecks, whether given sphere is contained by receiver.

Parameters

s	given sphere object

Returns: true if receiver contains entirely given sphere, false otherwise

Implements aggregpacking::Aggregate.

void aggregpacking::Ellipsoid::fromSize ( double s )

virtual

Adjust receiver dimensions accodring to given size. Sets b=0.5*s, a=b*(1+0.5*random), c=b*(1-0.5*random)

Parameters

s	given size

Implements aggregpacking::Aggregate.

bool aggregpacking::Aggregate::isInsideCube ( double s ) const

inherited

Determines if receiver is entirely inside cube. The cube is in positive octant and has one corner in origin.

Parameters

s cube size

Returns: true if receiver is entirely contained by a cube with given size, false otherwise

Aggregate * aggregpacking::Aggregate::Load ( istream & is )

staticinherited

Create and return a new aggregate from given istream.

Parameters

is	input stream

bool aggregpacking::Aggregate::operator!= ( const Aggregate & other ) const

inlineinherited

Inequality operator.

Intended for Python

Parameters

other instance to compare with

bool aggregpacking::Aggregate::operator== ( const Aggregate & other ) const

inlineinherited

Equality operator.

Intended for Python

Parameters

other instance to compare with

void aggregpacking::Ellipsoid::setA ( double a )

inline

Setter for 1st semiaxis.

a new semiaxis length

void aggregpacking::Ellipsoid::setB ( double b )

inline

Setter for 2nd semiaxis.

b new semiaxis length

void aggregpacking::Ellipsoid::setC ( double c )

inline

Setter for 3rd semiaxis.

c new semiaxis length

void aggregpacking::Aggregate::setNumber ( int n )

inlineinherited

Setter for number.

Parameters

n	new number

void aggregpacking::Aggregate::setOri ( const Quaternion & q )

inlineinherited

Setter for orientation.

Parameters

q	new orientation

void aggregpacking::Aggregate::setPos ( const Vector3 & p )

inlineinherited

Setter for position.

Parameters

p	new position

void aggregpacking::Aggregate::setPos	(	double	x,
		double	y,
		double	z
	)

inlineinherited

Setter for position (from individual components)

Parameters

x	x coordinate
y	y coordinate
z	z coordinate

Member Data Documentation

double aggregpacking::Ellipsoid::randomAxesRatio = 0.5

staticprivate

Random axes ratio. Given semiaxis b, a=b*(1+randomAxesRatio*R), c=b*(1-randomAxesRatio*R), R is a random number in range (0,1)

default value is 0.5

The documentation for this class was generated from the following files:

aggregate.hpp
aggregate.cpp

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Private Attributes

Static Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation