SPAvector Class Reference
[Geometric Atoms]

Represents a displacement vector in 3D Cartesian space. More...

#include <vector.hxx>

Inheritance diagram for SPAvector:

[legend]

List of all members.

Public Member Functions
double &	component (int i)
	Extracts the ith component of a vector and allows it to be modified.
double	component (int i) const
	Returns a copy of the ith component of a vector.
void	debug (FILE *fp=debug_file_ptr) const
	Outputs debug information to the screen or to the specified file.
void	debug_str (char *str) const
	Concatenates the debug information to the passed string.
logical	is_zero (const double tol=SPAresabs) const
	Returns TRUE if the length of the SPAvector is less than the given tolerance.
double	len () const
	Returns the length of the vector.
double	len_sq () const
	Returns the length squared, ( x*x + y*y + z*z ).
SPAvector	make_ortho ()
	Returns a SPAvector orthogonal to this SPAvector.
double	max_norm (int &i) const
	This method returns the maximum of the fabs of each component, and tells which component was the maximum.
double	numerically_stable_len () const
	Not appropriate for general use.
SPAvector const &	operator*= (SPAtransf const &t)
	Transforms this vector by an affine transformation.
SPAvector const &	operator*= (SPAmatrix const &m)
	Transforms this vector by a 3 X 3 matrix.
SPAvector const &	operator*= (double d)
	Multiplication of a vector by a scalar.
SPAvector const &	operator+= (SPAvector const &v)
	Adds two vectors.
SPAvector const &	operator-= (SPAvector const &v)
	Binary minus operation.
SPAvector const &	operator/= (double d)
	Division of a vector by a scalar.
SPAunit_vector	orthogonal () const
	Returns a unit vector that is orthogonal to the given vector.
void	set_component (int i, double new_c)
	Sets the value of ith component of a vector.
void	set_x (double new_x)
	Sets the x-coordinate of a vector.
void	set_y (double new_y)
	Sets the y-coordinate of a vector.
void	set_z (double new_z)
	Sets the z-coordinate of a vector.
	SPAvector (SPAvector const &v)
	C++ copy constructor requests memory for this object and populates it with the data from the object supplied as an argument.
	SPAvector (double v[3])
	C++ initialize constructor requests memory for this object and populates it with the data supplied as arguments.
	SPAvector (double x, double y, double z)
	C++ initialize constructor requests memory for this object and populates it with the data supplied as arguments.
	SPAvector ()
	C++ allocation constructor requests memory for this object but does not populate it.
double &	x ()
	Extracts the x-component of a vector for an update and allows it to be modified.
double	x () const
	Returns the x-component of a vector.
double &	y ()
	Extracts the y-component of a vector for an update and allows it to be modified.
double	y () const
	Returns the y-component of a vector.
double &	z ()
	Extracts the z-component of a vector for an update and allows it to be modified.
double	z () const
	Extracts the z-component of a vector.
Friends
logical	antiparallel (SPAunit_vector const &v1, SPAunit_vector const &v2, const double res)
	Determines if two vectors are anti-parallel (within some resolution).
logical	antiparallel (SPAunit_vector const &v1, SPAvector const &v2, const double res)
	Determines if two vectors are anti-parallel (within some resolution).
logical	antiparallel (SPAvector const &v1, SPAvector const &v2, const double res)
	Determines if two vectors are anti-parallel (within some resolution).
logical	biparallel (SPAunit_vector const &v1, SPAunit_vector const &v2, const double res)
	Determines if two vectors are bi-parallel (within some resolution).
logical	biparallel (SPAunit_vector const &v1, SPAvector const &v2, const double res)
	Determines if two vectors are bi-parallel (within some resolution).
logical	biparallel (SPAvector const &v1, SPAvector const &v2, const double res)
	Determines if two vectors are bi-parallel (within some resolution).
SPAunit_vector	normalise (SPAvector const &v)
	Converts a vector into a unit vector.
double	operator% (SPAunit_vector const &uv, SPAposition const &p)
	Returns the dot-product of a unit vector and a position.
double	operator% (SPAposition const &p, SPAunit_vector const &uv)
	Returns the dot-product of a position and a unit vector.
double	operator% (SPAvector const &v, SPAposition const &p)
	Returns the scalar product of vector with a position.
double	operator% (SPAposition const &p, SPAvector const &v)
	Returns the scalar product of a position with a vector.
double	operator% (SPAvector const &v1, SPAvector const &v2)
	Returns the scalar product (that is, the dot product) of two vectors.
SPAvector	operator* (SPAvector const &v, SPAtransf const *t)
	Transforms a vector by an affine transformation.
SPAvector	operator* (SPAvector const &v, SPAtransf const &t)
	Transforms a vector by an affine transformation.
SPAvector	operator* (SPAvector const &v, SPAmatrix const &m)
	Transforms a vector by a 3 X 3 matrix.
SPAvector	operator* (SPAmatrix const &m, SPAvector const &v)
	Transforms a vector by a 3 X 3 matrix.
SPAvector	operator* (SPAvector const &v, double d)
	Multiplies a vector by a scalar value.
SPAvector	operator* (double d, SPAvector const &v)
	Multiplies a vector by a scalar value.
SPAvector	operator* (SPAvector const &v1, SPAvector const &v2)
	Cross product of two vectors - Also applies to unit vectors.
SPAvector	operator+ (SPAvector const &v1, SPAvector const &v2)
	Addition of two vectors.
SPAvector	operator- (SPAvector const &v1, SPAvector const &v2)
	Binary minus operation.
SPAvector	operator- (SPAvector const &nv)
	Unary minus operator.
SPAvector	operator/ (SPAvector const &v, double d)
	Division of a vector by a scalar.
logical	parallel (SPAunit_vector const &v1, SPAunit_vector const &v2, const double res)
	Determines if two vectors are parallel (within some resolution).
logical	parallel (SPAunit_vector const &v1, SPAvector const &v2, const double res)
	Determines if two vectors are parallel (within some resolution).
logical	parallel (SPAvector const &v1, SPAvector const &v2, const double res)
	Determines if two vectors are parallel (within some resolution).
logical	perpendicular (SPAunit_vector const &v1, SPAunit_vector const &v2, const double res)
	Determines if two vectors are perpendicular (within some resolution).
logical	perpendicular (SPAunit_vector const &v1, SPAvector const &v2, const double res)
	Determines if two vectors are perpendicular (within some resolution).
logical	perpendicular (SPAvector const &v1, SPAvector const &v2, const double res)
	Determines if two vectors are perpendicular (within some resolution).
logical	same_vector (SPAvector const &v1, SPAvector const &v2, const double res)
	Determines whether or not two vectors are the same.

---

Detailed Description

Represents a displacement vector in 3D Cartesian space.

See also:

SPAtransf

---

Constructor & Destructor Documentation

SPAvector::SPAvector

(

)

[inline]

C++ allocation constructor requests memory for this object but does not populate it.

SPAvector::SPAvector	(	double	x,
		double	y,
		double	z
	)			[inline]

C++ initialize constructor requests memory for this object and populates it with the data supplied as arguments.

Role: Creates a SPAvector from three doubles representing the x, y, and z coordinate values.

Parameters:

	x	x-coordinate.
	y	y-coordinate.
	z	z-coordinate.

SPAvector::SPAvector

(

double

v[3]

)

[inline]

C++ initialize constructor requests memory for this object and populates it with the data supplied as arguments.

Parameters:

v

array of 3 doubles.

SPAvector::SPAvector

(

SPAvector const &

v

)

[inline]

C++ copy constructor requests memory for this object and populates it with the data from the object supplied as an argument.

Parameters:

v

vector.

---

Member Function Documentation

double& SPAvector::component

(

int

i

)

[inline]

Extracts the ith component of a vector and allows it to be modified.

Parameters:

i

ith component.

double SPAvector::component

(

int

i

)

const [inline]

Returns a copy of the ith component of a vector.

Parameters:

i

ith component.

void SPAvector::debug

(

FILE *

fp = debug_file_ptr

)

const

Outputs debug information to the screen or to the specified file.

Parameters:

fp

file pointer.

void SPAvector::debug_str

(

char *

str

)

const

Concatenates the debug information to the passed string.

Parameters:

str

string.

logical SPAvector::is_zero

(

const double

tol = SPAresabs

)

const

Returns TRUE if the length of the SPAvector is less than the given tolerance.

Parameters:

tol

zero tolerance.

double SPAvector::len

(

)

const [inline]

Returns the length of the vector.

double SPAvector::len_sq

(

)

const [inline]

Returns the length squared, ( x*x + y*y + z*z ).

Faster to compute than calling the len method.

SPAvector SPAvector::make_ortho

(

)

Returns a SPAvector orthogonal to this SPAvector.

double SPAvector::max_norm

(

int &

i

)

const

This method returns the maximum of the fabs of each component, and tells which component was the maximum.

Role: In case of a "tie" the index, i, will default to the larger index. For example, given the vector (1, 1, 1), i = 2.

Parameters:

i

index of max component.

double SPAvector::numerically_stable_len

(

)

const

Not appropriate for general use.

Role: This method is more expensive than len, but (theoretically) gives the same value and is stable for very small (those for which v%v would be lost in numerical noise) or very large norms (those for which v%v would give overflow).

SPAvector const& SPAvector::operator*=

(

SPAtransf const &

t

)

Transforms this vector by an affine transformation.

Parameters:

t

transform.

Reimplemented in SPAunit_vector.

SPAvector const& SPAvector::operator*=

(

SPAmatrix const &

m

)

[inline]

Transforms this vector by a 3 X 3 matrix.

Parameters:

m

matrix

SPAvector const& SPAvector::operator*=

(

double

d

)

[inline]

Multiplication of a vector by a scalar.

Parameters:

d

scalar value.

SPAvector const& SPAvector::operator+=

(

SPAvector const &

v

)

[inline]

Adds two vectors.

Parameters:

v

vector.

SPAvector const& SPAvector::operator-=

(

SPAvector const &

v

)

[inline]

Binary minus operation.

Parameters:

v

vector.

SPAvector const& SPAvector::operator/=

(

double

d

)

Division of a vector by a scalar.

Parameters:

d

scalar value.

SPAunit_vector SPAvector::orthogonal

(

)

const

Returns a unit vector that is orthogonal to the given vector.

If the given vector is less than SPAresmch in length, this method returns the unit vector (0,0,1).

void SPAvector::set_component	(	int	i,
		double	new_c
	)			[inline]

Sets the value of ith component of a vector.

Parameters:

	i	ith component.
	new_c	new value.

void SPAvector::set_x

(

double

new_x

)

[inline]

Sets the x-coordinate of a vector.

Parameters:

new_x

x-coordinate.

void SPAvector::set_y

(

double

new_y

)

[inline]

Sets the y-coordinate of a vector.

Parameters:

new_y

y-coordinate.

void SPAvector::set_z

(

double

new_z

)

[inline]

Sets the z-coordinate of a vector.

Parameters:

new_z

z-coordinate.

double& SPAvector::x

(

)

[inline]

Extracts the x-component of a vector for an update and allows it to be modified.

double SPAvector::x

(

)

const [inline]

Returns the x-component of a vector.

double& SPAvector::y

(

)

[inline]

Extracts the y-component of a vector for an update and allows it to be modified.

double SPAvector::y

(

)

const [inline]

Returns the y-component of a vector.

double& SPAvector::z

(

)

[inline]

Extracts the z-component of a vector for an update and allows it to be modified.

double SPAvector::z

(

)

const [inline]

Extracts the z-component of a vector.

---

Friends And Related Function Documentation

logical antiparallel	(	SPAunit_vector const &	v1,
		SPAunit_vector const &	v2,
		const double	res
	)			[friend]

Determines if two vectors are anti-parallel (within some resolution).

"Anti-parallel" indicates that the vectors are parallel, but in opposite directions. The default tolerance is SPAresnor.

Effect: Read-only

Parameters:

	v1	first vector.
	v2	second vector.
	res	resolution.

logical antiparallel	(	SPAunit_vector const &	v1,
		SPAvector const &	v2,
		const double	res
	)			[friend]

Determines if two vectors are anti-parallel (within some resolution).

"Anti-parallel" indicates that the vectors are parallel, but in opposite directions. The default tolerance is SPAresnor.

Effect: Read-only

Parameters:

	v1	first vector.
	v2	second vector.
	res	resolution.

logical antiparallel	(	SPAvector const &	v1,
		SPAvector const &	v2,
		const double	res
	)			[friend]

Determines if two vectors are anti-parallel (within some resolution).

"Anti-parallel" indicates that the vectors are parallel, but in opposite directions. The default tolerance is SPAresnor.

Effect: Read-only

Parameters:

	v1	first vector.
	v2	second vector.
	res	resolution.

logical biparallel	(	SPAunit_vector const &	v1,
		SPAunit_vector const &	v2,
		const double	res
	)			[friend]

Determines if two vectors are bi-parallel (within some resolution).

"Bi-parallel" indicates that the vectors are parallel and may be in either the same or opposite directions. The default tolerance is SPAresnor.

Effect: Read-only

Parameters:

	v1	first vector.
	v2	second vector.
	res	resolution.

logical biparallel	(	SPAunit_vector const &	v1,
		SPAvector const &	v2,
		const double	res
	)			[friend]

Determines if two vectors are bi-parallel (within some resolution).

"Bi-parallel" indicates that the vectors are parallel and may be in either the same or opposite directions. The default tolerance is SPAresnor.

Effect: Read-only

Parameters:

	v1	first vector.
	v2	second vector.
	res	resolution.

logical biparallel	(	SPAvector const &	v1,
		SPAvector const &	v2,
		const double	res
	)			[friend]

Determines if two vectors are bi-parallel (within some resolution).

"Bi-parallel" indicates that the vectors are parallel and may be in either the same or opposite directions. The default tolerance is SPAresnor.

Effect: Read-only

Parameters:

	v1	first vector.
	v2	second vector.
	res	resolution.

SPAunit_vector normalise

(

SPAvector const &

v

)

[friend]

Converts a vector into a unit vector.

Effect: Read-only

Parameters:

v

vector.

Reimplemented in SPAunit_vector.

double operator%	(	SPAunit_vector const &	uv,
		SPAposition const &	p
	)			[friend]

Returns the dot-product of a unit vector and a position.

Parameters:

	uv	unit vector.
	p	position.

Reimplemented in SPAunit_vector.

double operator%	(	SPAposition const &	p,
		SPAunit_vector const &	uv
	)			[friend]

Returns the dot-product of a position and a unit vector.

Parameters:

	p	position.
	uv	unit vector.

Reimplemented in SPAunit_vector.

double operator%	(	SPAvector const &	v,
		SPAposition const &	p
	)			[friend]

Returns the scalar product of vector with a position.

Parameters:

	v	vector.
	p	position.

double operator%	(	SPAposition const &	p,
		SPAvector const &	v
	)			[friend]

Returns the scalar product of a position with a vector.

Parameters:

	p	position.
	v	vector.

double operator%	(	SPAvector const &	v1,
		SPAvector const &	v2
	)			[friend]

Returns the scalar product (that is, the dot product) of two vectors.

Parameters:

	v1	first vector.
	v2	second vector.

SPAvector operator*	(	SPAvector const &	v,
		SPAtransf const *	t
	)			[friend]

Transforms a vector by an affine transformation.

Parameters:

	v	vector.
	t	transformation.

SPAvector operator*	(	SPAvector const &	v,
		SPAtransf const &	t
	)			[friend]

Transforms a vector by an affine transformation.

Parameters:

	v	vector.
	t	transformation.

SPAvector operator*	(	SPAvector const &	v,
		SPAmatrix const &	m
	)			[friend]

Transforms a vector by a 3 X 3 matrix.

Parameters:

	v	vector.
	m	matrix.

SPAvector operator*	(	SPAmatrix const &	m,
		SPAvector const &	v
	)			[friend]

Transforms a vector by a 3 X 3 matrix.

Parameters:

	m	matrix.
	v	vector.

SPAvector operator*	(	SPAvector const &	v,
		double	d
	)			[friend]

Multiplies a vector by a scalar value.

Parameters:

	v	vector.
	d	scalar value.

SPAvector operator*	(	double	d,
		SPAvector const &	v
	)			[friend]

Multiplies a vector by a scalar value.

Parameters:

	d	scalar value.
	v	vector.

SPAvector operator*	(	SPAvector const &	v1,
		SPAvector const &	v2
	)			[friend]

Cross product of two vectors - Also applies to unit vectors.

Parameters:

	v1	first vector.
	v2	second vector.

SPAvector operator+	(	SPAvector const &	v1,
		SPAvector const &	v2
	)			[friend]

Addition of two vectors.

Parameters:

	v1	first vector.
	v2	second vector.

SPAvector operator-	(	SPAvector const &	v1,
		SPAvector const &	v2
	)			[friend]

Binary minus operation.

Parameters:

	v1	first vector.
	v2	second vector.

SPAvector operator-

(

SPAvector const &

nv

)

[friend]

Unary minus operator.

Role: Returns the negation of the given vector.

Parameters:

nv

given vector.

SPAvector operator/	(	SPAvector const &	v,
		double	d
	)			[friend]

Division of a vector by a scalar.

Parameters:

	v	vector.
	d	scalar value.

logical parallel	(	SPAunit_vector const &	v1,
		SPAunit_vector const &	v2,
		const double	res
	)			[friend]

Determines if two vectors are parallel (within some resolution).

The default tolerance is SPAresnor.

Effect: Read-only

Parameters:

	v1	first vector.
	v2	second vector.
	res	resolution.

logical parallel	(	SPAunit_vector const &	v1,
		SPAvector const &	v2,
		const double	res
	)			[friend]

Determines if two vectors are parallel (within some resolution).

The default tolerance is SPAresnor.

Effect: Read-only

Parameters:

	v1	first vector.
	v2	second vector.
	res	resolution.

logical parallel	(	SPAvector const &	v1,
		SPAvector const &	v2,
		const double	res
	)			[friend]

Determines if two vectors are parallel (within some resolution).

The default tolerance is SPAresnor.

Effect: Read-only

Parameters:

	v1	first vector.
	v2	second vector.
	res	resolution.

logical perpendicular	(	SPAunit_vector const &	v1,
		SPAunit_vector const &	v2,
		const double	res
	)			[friend]

Determines if two vectors are perpendicular (within some resolution).

The default tolerance is SPAresnor.

Effect: Read-only

Parameters:

	v1	first vector.
	v2	second vector.
	res	resolution.

logical perpendicular	(	SPAunit_vector const &	v1,
		SPAvector const &	v2,
		const double	res
	)			[friend]

Determines if two vectors are perpendicular (within some resolution).

The default tolerance is SPAresnor.

Effect: Read-only

Parameters:

	v1	first vector.
	v2	second vector.
	res	resolution.

logical perpendicular	(	SPAvector const &	v1,
		SPAvector const &	v2,
		const double	res
	)			[friend]

Determines if two vectors are perpendicular (within some resolution).

The default tolerance is SPAresnor.

Effect: Read-only

Parameters:

	v1	first vector.
	v2	second vector.
	res	resolution.

logical same_vector	(	SPAvector const &	v1,
		SPAvector const &	v2,
		const double	res
	)			[friend]

Determines whether or not two vectors are the same.

The default tolerance is SPAresabs.

Effect: System routine

Parameters:

	v1	first vector.
	v2	second vector.
	res	resolution for comparison.