Standard 3-dimensional vector. More...

#include <ParaVector3.h>

Public Member Functions
	Vector3 (const float fX, const float fY, const float fZ)

	Vector3 (const float afCoordinate[3])

	Vector3 (const int afCoordinate[3])

	Vector3 (float *const r)

	Vector3 (const float scaler)

float	operator[] (const size_t i) const

float &	operator[] (const size_t i)

float *	ptr ()
	Pointer accessor for direct copying.

const float *	ptr () const
	Pointer accessor for direct copying.

Vector3 &	operator= (const Vector3 &rkVector)
	Assigns the value of the other vector. More...

	Vector3 (const DeviceVector3 &v)

Vector3 &	operator= (const DeviceVector3 &rkVector)

Vector3 &	operator= (const float fScaler)

bool	operator== (const Vector3 &rkVector) const

bool	operator!= (const Vector3 &rkVector) const

Vector3	operator+ (const Vector3 &rkVector) const

Vector3	operator- (const Vector3 &rkVector) const

Vector3	operator* (const float fScalar) const

Vector3	operator% (const Vector3 &rhs) const
	special cross product

Vector3	operator* (const Vector3 &rhs) const

Vector3	operator/ (const float fScalar) const

Vector3	operator/ (const Vector3 &rhs) const

const Vector3 &	operator+ () const

Vector3	operator- () const

Vector3 &	operator+= (const Vector3 &rkVector)

Vector3 &	operator+= (const float fScalar)

Vector3 &	operator-= (const Vector3 &rkVector)

Vector3 &	operator-= (const float fScalar)

Vector3 &	*operator=** (const float fScalar)

Vector3 &	*operator=** (const Vector3 &rkVector)

Vector3	operator* (const Matrix4 &mat) const
	row major multiply with an affine matrix. More...

Vector3 &	operator/= (const float fScalar)

Vector3 &	operator/= (const Vector3 &rkVector)

int	dominantAxis () const
	Returns the axis along which this vector is dominant.

float	length () const
	Returns the length (magnitude) of the vector. More...

float	squaredLength () const
	Returns the square of the length(magnitude) of the vector. More...

float	distance (const Vector3 &rhs) const
	Returns the distance to another vector. More...

float	squaredDistance (const Vector3 &rhs) const
	Returns the square of the distance to another vector. More...

float	dotProduct (const Vector3 &vec) const
	Calculates the dot (scalar) product of this vector with another. More...

float	absDotProduct (const Vector3 &vec) const
	Calculates the absolute dot (scalar) product of this vector with another. More...

float	normalise ()
	Normalises the vector. More...

Vector3	InvertYCopy () const

Vector3 &	InvertY ()

Vector3	crossProduct (const Vector3 &rkVector) const
	Calculates the cross-product of 2 vectors, i.e. More...

Vector3	midPoint (const Vector3 &vec) const
	Returns a vector at a point half way between this and the passed in vector.

Vector3	TransformNormal (const Matrix4 &m) const
	ignored translation(row 3). More...

Vector3	TransformCoord (const Matrix4 &m) const
	only use this function. More...

bool	operator< (const Vector3 &rhs) const
	Returns true if the vector's scalar components are all greater that the ones of the vector it is compared against.

bool	operator> (const Vector3 &rhs) const
	Returns true if the vector's scalar components are all smaller that the ones of the vector it is compared against.

void	makeFloor (const Vector3 &cmp)
	Sets this vector's components to the minimum of its own and the ones of the passed in vector. More...

void	makeCeil (const Vector3 &cmp)
	Sets this vector's components to the maximum of its own and the ones of the passed in vector. More...

Vector3	perpendicular (void) const
	Generates a vector perpendicular to this vector (eg an 'up' vector). More...

Vector3	randomDeviant (const Radian &angle, const Vector3 &up=Vector3::ZERO) const
	Generates a new random vector which deviates from this vector by a given angle in a random direction. More...

Radian	angleBetween (const Vector3 &dest)
	Gets the angle between 2 vectors. More...

Quaternion	getRotationTo (const Vector3 &dest, const Vector3 &fallbackAxis=Vector3::ZERO) const
	Gets the shortest arc quaternion to rotate this vector to the destination vector. More...

bool	isZeroLength (void) const
	Returns true if this vector is zero length. More...

Vector3	normalisedCopy (void) const
	As normalise, except that this vector is unaffected and the normalised vector is returned as a copy. More...

Vector3	reflect (const Vector3 &normal) const
	Calculates a reflection vector to the plane with the given normal . More...

bool	positionEquals (const Vector3 &rhs, float tolerance=1e-03) const
	Returns whether this vector is within a positional tolerance of another vector. More...

bool	positionCloses (const Vector3 &rhs, float tolerance=1e-03f) const
	Returns whether this vector is within a positional tolerance of another vector, also take scale of the vectors into account. More...

bool	directionEquals (const Vector3 &rhs, const Radian &tolerance) const
	Returns whether this vector is within a directional tolerance of another vector. More...

DeviceVector3_ptr	GetPointer ()

Public Attributes
float	x

float	y

float	z

Static Public Attributes
static const Vector3	ZERO

static const Vector3	UNIT_X

static const Vector3	UNIT_Y

static const Vector3	UNIT_Z

static const Vector3	NEGATIVE_UNIT_X

static const Vector3	NEGATIVE_UNIT_Y

static const Vector3	NEGATIVE_UNIT_Z

static const Vector3	UNIT_SCALE

Friends
Vector3	operator* (const float fScalar, const Vector3 &rkVector)

Vector3	operator/ (const float fScalar, const Vector3 &rkVector)

Vector3	operator+ (const Vector3 &lhs, const float rhs)

Vector3	operator+ (const float lhs, const Vector3 &rhs)

Vector3	operator- (const Vector3 &lhs, const float rhs)

Vector3	operator- (const float lhs, const Vector3 &rhs)

std::ostream &	operator<< (std::ostream &o, const Vector3 &v)
	Function for writing to a stream.

Detailed Description

Standard 3-dimensional vector.

Remarks: A direction in 3D space represented as distances along the 3 orthogonal axes (x, y, z). Note that positions, directions and scaling factors can be represented by a vector, depending on how you interpret the values.

Member Function Documentation

§ absDotProduct()

float ParaEngine::Vector3::absDotProduct ( const Vector3 & vec ) const

inline

Calculates the absolute dot (scalar) product of this vector with another.

Remarks: This function work similar dotProduct, except it use absolute value of each component of the vector to computing.

Parameters

vec	Vector with which to calculate the absolute dot product (together with this one).

Returns: A float representing the absolute dot product value.

§ angleBetween()

ParaEngine::Radian ParaEngine::Vector3::angleBetween ( const Vector3 & dest )

Gets the angle between 2 vectors.

Remarks: Vectors do not have to be unit-length but must represent directions.

§ crossProduct()

Vector3 ParaEngine::Vector3::crossProduct ( const Vector3 & rkVector ) const

inline

Calculates the cross-product of 2 vectors, i.e.

the vector that lies perpendicular to them both.

Remarks: The cross-product is normally used to calculate the normal vector of a plane, by calculating the cross-product of 2 non-equivalent vectors which lie on the plane (e.g. 2 edges of a triangle).

Parameters

vec	Vector which, together with this one, will be used to calculate the cross-product.

Returns

A vector which is the result of the cross-product. This vector will NOT be normalised, to maximise efficiency

call Vector3::normalise on the result if you wish this to be done. As for which side the resultant vector will be on, the returned vector will be on the side from which the arc from 'this' to rkVector is anticlockwise, e.g. UNIT_Y.crossProduct(UNIT_Z) = UNIT_X, whilst UNIT_Z.crossProduct(UNIT_Y) = -UNIT_X. This is because OGRE uses a right-handed coordinate system.

: For a clearer explanation, look a the left and the bottom edges of your monitor's screen. Assume that the first vector is the left edge and the second vector is the bottom edge, both of them starting from the lower-left corner of the screen. The resulting vector is going to be perpendicular to both of them and will go inside the screen, towards the cathode tube (assuming you're using a CRT monitor, of course).

§ directionEquals()

bool ParaEngine::Vector3::directionEquals	(	const Vector3 &	rhs,
		const Radian &	tolerance
	)		const

inline

Returns whether this vector is within a directional tolerance of another vector.

Parameters

rhs	The vector to compare with
tolerance	The maximum angle by which the vectors may vary and still be considered equal

Note: Both vectors should be normalised.

§ distance()

float ParaEngine::Vector3::distance ( const Vector3 & rhs ) const

inline

Returns the distance to another vector.

Warning: This operation requires a square root and is expensive in terms of CPU operations. If you don't need to know the exact distance (e.g. for just comparing distances) use squaredDistance() instead.

§ dotProduct()

float ParaEngine::Vector3::dotProduct ( const Vector3 & vec ) const

inline

Calculates the dot (scalar) product of this vector with another.

Remarks: The dot product can be used to calculate the angle between 2 vectors. If both are unit vectors, the dot product is the cosine of the angle; otherwise the dot product must be divided by the product of the lengths of both vectors to get the cosine of the angle. This result can further be used to calculate the distance of a point from a plane.

Parameters

vec	Vector with which to calculate the dot product (together with this one).

Returns: A float representing the dot product value.

§ getRotationTo()

ParaEngine::Quaternion ParaEngine::Vector3::getRotationTo	(	const Vector3 &	dest,
		const Vector3 &	fallbackAxis = `Vector3::ZERO`
	)		const

Gets the shortest arc quaternion to rotate this vector to the destination vector.

Remarks: If you call this with a dest vector that is close to the inverse of this vector, we will rotate 180 degrees around the 'fallbackAxis' (if specified, or a generated axis if not) since in this case ANY axis of rotation is valid.

§ isZeroLength()

bool ParaEngine::Vector3::isZeroLength ( void ) const

inline

Returns true if this vector is zero length.

§ length()

float ParaEngine::Vector3::length ( ) const

inline

Returns the length (magnitude) of the vector.

Warning: This operation requires a square root and is expensive in terms of CPU operations. If you don't need to know the exact length (e.g. for just comparing lengths) use squaredLength() instead.

§ makeCeil()

void ParaEngine::Vector3::makeCeil ( const Vector3 & cmp )

inline

Sets this vector's components to the maximum of its own and the ones of the passed in vector.

Remarks: 'Maximum' in this case means the combination of the highest value of x, y and z from both vectors. Highest is taken just numerically, not magnitude, so 1 > -3.

§ makeFloor()

void ParaEngine::Vector3::makeFloor ( const Vector3 & cmp )

inline

Sets this vector's components to the minimum of its own and the ones of the passed in vector.

Remarks: 'Minimum' in this case means the combination of the lowest value of x, y and z from both vectors. Lowest is taken just numerically, not magnitude, so -1 < 0.

§ normalise()

float ParaEngine::Vector3::normalise ( void )

inline

Normalises the vector.

Remarks: This method normalises the vector such that it's length / magnitude is 1. The result is called a unit vector.

Note: This function will not crash for zero-sized vectors, but there will be no changes made to their components.

Returns: The previous length of the vector.

§ normalisedCopy()

Vector3 ParaEngine::Vector3::normalisedCopy ( void ) const

inline

As normalise, except that this vector is unaffected and the normalised vector is returned as a copy.

§ operator*()

Vector3 ParaEngine::Vector3::operator* ( const Matrix4 & mat ) const

inline

row major multiply with an affine matrix.

§ operator=()

Vector3& ParaEngine::Vector3::operator= ( const Vector3 & rkVector )

inline

Assigns the value of the other vector.

Parameters

rkVector The other vector

§ perpendicular()

ParaEngine::Vector3 ParaEngine::Vector3::perpendicular ( void ) const

Generates a vector perpendicular to this vector (eg an 'up' vector).

Remarks: This method will return a vector which is perpendicular to this vector. There are an infinite number of possibilities but this method will guarantee to generate one of them. If you need more control you should use the Quaternion class.

§ positionCloses()

bool ParaEngine::Vector3::positionCloses	(	const Vector3 &	rhs,
		float	tolerance = `1e-03f`
	)		const

inline

Returns whether this vector is within a positional tolerance of another vector, also take scale of the vectors into account.

Parameters

rhs	The vector to compare with
tolerance	The amount (related to the scale of vectors) that distance of the vector may vary by and still be considered close

§ positionEquals()

bool ParaEngine::Vector3::positionEquals	(	const Vector3 &	rhs,
		float	tolerance = `1e-03`
	)		const

inline

Returns whether this vector is within a positional tolerance of another vector.

Parameters

rhs	The vector to compare with
tolerance	The amount that each element of the vector may vary by and still be considered equal

§ randomDeviant()

ParaEngine::Vector3 ParaEngine::Vector3::randomDeviant	(	const Radian &	angle,
		const Vector3 &	up = `Vector3::ZERO`
	)		const

Generates a new random vector which deviates from this vector by a given angle in a random direction.

Remarks: This method assumes that the random number generator has already been seeded appropriately.

Parameters

angle	The angle at which to deviate
up	Any vector perpendicular to this one (which could generated by cross-product of this vector and any other non-colinear vector). If you choose not to provide this the function will derive one on it's own, however if you provide one yourself the function will be faster (this allows you to reuse up vectors if you call this method more than once)

Returns: A random vector which deviates from this vector by angle. This vector will not be normalised, normalise it if you wish afterwards.

§ reflect()

Vector3 ParaEngine::Vector3::reflect ( const Vector3 & normal ) const

inline

Calculates a reflection vector to the plane with the given normal .

Remarks: NB assumes 'this' is pointing AWAY FROM the plane, invert if it is not.

§ squaredDistance()

float ParaEngine::Vector3::squaredDistance ( const Vector3 & rhs ) const

inline

Returns the square of the distance to another vector.

Remarks: This method is for efficiency - calculating the actual distance to another vector requires a square root, which is expensive in terms of the operations required. This method returns the square of the distance to another vector, i.e. the same as the distance but before the square root is taken. Use this if you want to find the longest / shortest distance without incurring the square root.

§ squaredLength()

float ParaEngine::Vector3::squaredLength ( ) const

inline

Returns the square of the length(magnitude) of the vector.

Remarks: This method is for efficiency - calculating the actual length of a vector requires a square root, which is expensive in terms of the operations required. This method returns the square of the length of the vector, i.e. the same as the length but before the square root is taken. Use this if you want to find the longest / shortest vector without incurring the square root.

§ TransformCoord()

Vector3 ParaEngine::Vector3::TransformCoord ( const Matrix4 & m ) const

only use this function.

when matrix contains non-linear projection. Result is (x/w, y/w, z/w)

§ TransformNormal()

ParaEngine::Vector3 ParaEngine::Vector3::TransformNormal ( const Matrix4 & m ) const

ignored translation(row 3).

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

Client/trunk/ParaEngineClient/math/ParaVector3.h
Client/trunk/ParaEngineClient/math/ParaVector3.cpp
Client/trunk/ParaEngineClient/math/ParaVector3.inl

Public Member Functions

Public Attributes

Static Public Attributes

Friends

Detailed Description

Member Function Documentation

§ absDotProduct()

§ angleBetween()

§ crossProduct()

§ directionEquals()

§ distance()

§ dotProduct()

§ getRotationTo()

§ isZeroLength()

§ length()

§ makeCeil()

§ makeFloor()

§ normalise()

§ normalisedCopy()

§ operator*()

§ operator=()

§ perpendicular()

§ positionCloses()

§ positionEquals()

§ randomDeviant()

§ reflect()

§ squaredDistance()

§ squaredLength()

§ TransformCoord()

§ TransformNormal()