Ogre::Vector3 Class Reference
[Math]

Standard 3-dimensional vector. More...

#include <OgreVector3.h>

Public Member Functions
	Vector3 ()
	Vector3 (const Real fX, const Real fY, const Real fZ)
	Vector3 (const Real afCoordinate[3])
	Vector3 (const int afCoordinate[3])
	Vector3 (Real *const r)
	Vector3 (const Real scaler)
void	swap (Vector3 &other)
	Exchange the contents of this vector with another.
Real	operator[] (const size_t i) const
Real &	operator[] (const size_t i)
Real *	ptr ()
	Pointer accessor for direct copying.
const Real *	ptr () const
	Pointer accessor for direct copying.
Vector3 &	operator= (const Vector3 &rkVector)
	Assigns the value of the other vector.
Vector3 &	operator= (const Real 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 Real fScalar) const
Vector3	operator* (const Vector3 &rhs) const
Vector3	operator/ (const Real fScalar) const
Vector3	operator/ (const Vector3 &rhs) const
const Vector3 &	operator+ () const
Vector3	operator- () const
Vector3 &	operator+= (const Vector3 &rkVector)
Vector3 &	operator+= (const Real fScalar)
Vector3 &	operator-= (const Vector3 &rkVector)
Vector3 &	operator-= (const Real fScalar)
Vector3 &	operator*= (const Real fScalar)
Vector3 &	operator*= (const Vector3 &rkVector)
Vector3 &	operator/= (const Real fScalar)
Vector3 &	operator/= (const Vector3 &rkVector)
Real	length () const
	Returns the length (magnitude) of the vector.
Real	squaredLength () const
	Returns the square of the length(magnitude) of the vector.
Real	distance (const Vector3 &rhs) const
	Returns the distance to another vector.
Real	squaredDistance (const Vector3 &rhs) const
	Returns the square of the distance to another vector.
Real	dotProduct (const Vector3 &vec) const
	Calculates the dot (scalar) product of this vector with another.
Real	absDotProduct (const Vector3 &vec) const
	Calculates the absolute dot (scalar) product of this vector with another.
Real	normalise ()
	Normalises the vector.
Vector3	crossProduct (const Vector3 &rkVector) const
	Calculates the cross-product of 2 vectors, i.e.
Vector3	midPoint (const Vector3 &vec) const
	Returns a vector at a point half way between this and the passed in vector.
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.
void	makeCeil (const Vector3 &cmp)
	Sets this vector's components to the maximum of its own and the ones of the passed in vector.
Vector3	perpendicular (void) const
	Generates a vector perpendicular to this vector (eg an 'up' vector).
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.
Radian	angleBetween (const Vector3 &dest) const
	Gets the angle between 2 vectors.
Quaternion	getRotationTo (const Vector3 &dest, const Vector3 &fallbackAxis=Vector3::ZERO) const
	Gets the shortest arc quaternion to rotate this vector to the destination vector.
bool	isZeroLength (void) const
	Returns true if this vector is zero length.
Vector3	normalisedCopy (void) const
	As normalise, except that this vector is unaffected and the normalised vector is returned as a copy.
Vector3	reflect (const Vector3 &normal) const
	Calculates a reflection vector to the plane with the given normal .
bool	positionEquals (const Vector3 &rhs, Real tolerance=1e-03) const
	Returns whether this vector is within a positional tolerance of another vector.
bool	positionCloses (const Vector3 &rhs, Real tolerance=1e-03f) const
	Returns whether this vector is within a positional tolerance of another vector, also take scale of the vectors into account.
bool	directionEquals (const Vector3 &rhs, const Radian &tolerance) const
	Returns whether this vector is within a directional tolerance of another vector.
bool	isNaN () const
	Check whether this vector contains valid values.
Vector3	primaryAxis () const
	Extract the primary (dominant) axis from this direction vector.
Public Attributes
Real	x
Real	y
Real	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 Real fScalar, const Vector3 &rkVector)
Vector3	operator/ (const Real fScalar, const Vector3 &rkVector)
Vector3	operator+ (const Vector3 &lhs, const Real rhs)
Vector3	operator+ (const Real lhs, const Vector3 &rhs)
Vector3	operator- (const Vector3 &lhs, const Real rhs)
Vector3	operator- (const Real lhs, const Vector3 &rhs)
_OgreExport friend 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.

Definition at line 51 of file OgreVector3.h.

Constructor & Destructor Documentation

Ogre::Vector3::Vector3 ( )

Definition at line 57 of file OgreVector3.h.

Ogre::Vector3::Vector3	(	const Real	fX,
		const Real	fY,
		const Real	fZ
	)

Definition at line 61 of file OgreVector3.h.

Ogre::Vector3::Vector3 ( const Real afCoordinate[3] ) [explicit]

Definition at line 66 of file OgreVector3.h.

Ogre::Vector3::Vector3 ( const int afCoordinate[3] ) [explicit]

Definition at line 73 of file OgreVector3.h.

Ogre::Vector3::Vector3 ( Real *const r ) [explicit]

Definition at line 80 of file OgreVector3.h.

Ogre::Vector3::Vector3 ( const Real scaler ) [explicit]

Definition at line 85 of file OgreVector3.h.

Member Function Documentation

Real Ogre::Vector3::absDotProduct ( const Vector3 & vec ) const

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 Real representing the absolute dot product value.

Definition at line 428 of file OgreVector3.h.

References Ogre::Math::Abs(), x, y, and z.

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

Gets the angle between 2 vectors.

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

Definition at line 629 of file OgreVector3.h.

References Ogre::Math::ACos(), Ogre::Math::Clamp(), and length().

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

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).

Definition at line 488 of file OgreVector3.h.

References x, y, and z.

Referenced by getRotationTo().

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

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.

Definition at line 759 of file OgreVector3.h.

References Ogre::Math::Abs(), Ogre::Math::ACos(), and Ogre::Radian::valueRadians().

Real Ogre::Vector3::distance ( const Vector3 & rhs ) const

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.

Definition at line 379 of file OgreVector3.h.

Real Ogre::Vector3::dotProduct ( const Vector3 & vec ) const

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.

Definition at line 413 of file OgreVector3.h.

References x, y, and z.

Referenced by getRotationTo().

Quaternion Ogre::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.

Definition at line 651 of file OgreVector3.h.

References crossProduct(), dotProduct(), Ogre::Quaternion::FromAngleAxis(), Ogre::Quaternion::IDENTITY, isZeroLength(), Ogre::Quaternion::normalise(), normalise(), Ogre::Math::PI, Ogre::Math::Sqrt(), UNIT_X, UNIT_Y, Ogre::Quaternion::w, x, Ogre::Quaternion::x, y, Ogre::Quaternion::y, z, Ogre::Quaternion::z, and ZERO.

bool Ogre::Vector3::isNaN ( ) const

Check whether this vector contains valid values.

Definition at line 770 of file OgreVector3.h.

References Ogre::Math::isNaN().

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

Returns true if this vector is zero length.

Definition at line 702 of file OgreVector3.h.

Referenced by getRotationTo().

Real Ogre::Vector3::length ( ) const

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.

Definition at line 352 of file OgreVector3.h.

References Ogre::Math::Sqrt().

Referenced by angleBetween().

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

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.

Definition at line 548 of file OgreVector3.h.

References x, y, and z.

Referenced by Ogre::AxisAlignedBox::intersection(), and Ogre::AxisAlignedBox::merge().

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

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.

Definition at line 534 of file OgreVector3.h.

References x, y, and z.

Referenced by Ogre::AxisAlignedBox::intersection(), and Ogre::AxisAlignedBox::merge().

Vector3 Ogre::Vector3::midPoint ( const Vector3 & vec ) const

Returns a vector at a point half way between this and the passed in vector.

Definition at line 499 of file OgreVector3.h.

References x, y, and z.

Real Ogre::Vector3::normalise ( )

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.

Definition at line 442 of file OgreVector3.h.

References Ogre::Math::Sqrt().

Referenced by getRotationTo(), normalisedCopy(), Ogre::Matrix4::operator*(), and perpendicular().

Vector3 Ogre::Vector3::normalisedCopy ( void ) const

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

Definition at line 711 of file OgreVector3.h.

References normalise().

bool Ogre::Vector3::operator!= ( const Vector3 & rkVector ) const

Definition at line 153 of file OgreVector3.h.

References x, y, and z.

Vector3 Ogre::Vector3::operator* ( const Vector3 & rhs ) const

Definition at line 183 of file OgreVector3.h.

References x, y, and z.

Vector3 Ogre::Vector3::operator* ( const Real fScalar ) const

Definition at line 175 of file OgreVector3.h.

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

Definition at line 313 of file OgreVector3.h.

References x, y, and z.

Vector3& Ogre::Vector3::operator*= ( const Real fScalar )

Definition at line 305 of file OgreVector3.h.

const Vector3& Ogre::Vector3::operator+ ( ) const

Definition at line 211 of file OgreVector3.h.

Vector3 Ogre::Vector3::operator+ ( const Vector3 & rkVector ) const

Definition at line 159 of file OgreVector3.h.

References x, y, and z.

Vector3& Ogre::Vector3::operator+= ( const Real fScalar )

Definition at line 280 of file OgreVector3.h.

Vector3& Ogre::Vector3::operator+= ( const Vector3 & rkVector )

Definition at line 271 of file OgreVector3.h.

References x, y, and z.

Vector3 Ogre::Vector3::operator- ( ) const

Definition at line 216 of file OgreVector3.h.

Vector3 Ogre::Vector3::operator- ( const Vector3 & rkVector ) const

Definition at line 167 of file OgreVector3.h.

References x, y, and z.

Vector3& Ogre::Vector3::operator-= ( const Real fScalar )

Definition at line 297 of file OgreVector3.h.

Vector3& Ogre::Vector3::operator-= ( const Vector3 & rkVector )

Definition at line 288 of file OgreVector3.h.

References x, y, and z.

Vector3 Ogre::Vector3::operator/ ( const Vector3 & rhs ) const

Definition at line 203 of file OgreVector3.h.

References x, y, and z.

Vector3 Ogre::Vector3::operator/ ( const Real fScalar ) const

Definition at line 191 of file OgreVector3.h.

Vector3& Ogre::Vector3::operator/= ( const Vector3 & rkVector )

Definition at line 335 of file OgreVector3.h.

References x, y, and z.

Vector3& Ogre::Vector3::operator/= ( const Real fScalar )

Definition at line 322 of file OgreVector3.h.

bool Ogre::Vector3::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.

Definition at line 510 of file OgreVector3.h.

References x, y, and z.

Vector3& Ogre::Vector3::operator= ( const Real fScaler )

Definition at line 139 of file OgreVector3.h.

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

Assigns the value of the other vector.

Parameters:

rkVector

The other vector

Definition at line 130 of file OgreVector3.h.

References x, y, and z.

bool Ogre::Vector3::operator== ( const Vector3 & rkVector ) const

Definition at line 148 of file OgreVector3.h.

References x, y, and z.

bool Ogre::Vector3::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.

Definition at line 520 of file OgreVector3.h.

References x, y, and z.

Real& Ogre::Vector3::operator[] ( const size_t i )

Definition at line 109 of file OgreVector3.h.

Real Ogre::Vector3::operator[] ( const size_t i ) const

Definition at line 102 of file OgreVector3.h.

Vector3 Ogre::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.

Definition at line 562 of file OgreVector3.h.

References normalise(), squaredLength(), UNIT_X, and UNIT_Y.

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

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

Definition at line 746 of file OgreVector3.h.

References squaredLength().

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

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

Definition at line 732 of file OgreVector3.h.

References Ogre::Math::RealEqual(), x, y, and z.

Vector3 Ogre::Vector3::primaryAxis ( ) const

Extract the primary (dominant) axis from this direction vector.

Definition at line 776 of file OgreVector3.h.

References Ogre::Math::Abs(), NEGATIVE_UNIT_X, NEGATIVE_UNIT_Y, NEGATIVE_UNIT_Z, UNIT_X, UNIT_Y, and UNIT_Z.

const Real* Ogre::Vector3::ptr ( ) const

Pointer accessor for direct copying.

Definition at line 121 of file OgreVector3.h.

Real* Ogre::Vector3::ptr ( )

Pointer accessor for direct copying.

Definition at line 116 of file OgreVector3.h.

Referenced by Ogre::AnimableValue::setAsBaseValue().

Vector3 Ogre::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.

Definition at line 599 of file OgreVector3.h.

References Ogre::Quaternion::FromAngleAxis(), Ogre::Math::TWO_PI, Ogre::Math::UnitRandom(), and ZERO.

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

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.

Definition at line 721 of file OgreVector3.h.

Real Ogre::Vector3::squaredDistance ( const Vector3 & rhs ) const

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.

Definition at line 394 of file OgreVector3.h.

Real Ogre::Vector3::squaredLength ( ) const

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.

Definition at line 367 of file OgreVector3.h.

Referenced by Ogre::Sphere::intersects(), Ogre::Sphere::merge(), perpendicular(), and positionCloses().

void Ogre::Vector3::swap ( Vector3 & other )

Exchange the contents of this vector with another.

Definition at line 95 of file OgreVector3.h.

References std::swap(), x, y, and z.