Ogre::Vector3 Class Reference

Standard 3-dimensional vector. More...

#include <OgreVector3.h>

List of all members.

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)
Real operator[] (const size_t i) const
Realoperator[] (const size_t i)
Realptr ()
 Pointer accessor for direct copying.
const Realptr () const
 Pointer accessor for direct copying.
Vector3operator= (const Vector3 &rkVector)
 Assigns the value of the other vector.
Vector3operator= (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 Vector3operator+ () const
Vector3 operator- () const
Vector3operator+= (const Vector3 &rkVector)
Vector3operator+= (const Real fScalar)
Vector3operator-= (const Vector3 &rkVector)
Vector3operator-= (const Real fScalar)
Vector3operator*= (const Real fScalar)
Vector3operator*= (const Vector3 &rkVector)
Vector3operator/= (const Real fScalar)
Vector3operator/= (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)
 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.

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 46 of file OgreVector3.h.


Constructor & Destructor Documentation

Ogre::Vector3::Vector3 (  ) 

Definition at line 52 of file OgreVector3.h.

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

Definition at line 56 of file OgreVector3.h.

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

Definition at line 61 of file OgreVector3.h.

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

Definition at line 68 of file OgreVector3.h.

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

Definition at line 75 of file OgreVector3.h.

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

Definition at line 80 of file OgreVector3.h.


Member Function Documentation

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

Definition at line 88 of file OgreVector3.h.

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

Definition at line 95 of file OgreVector3.h.

Real* Ogre::Vector3::ptr (  ) 

Pointer accessor for direct copying.

Definition at line 102 of file OgreVector3.h.

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

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

Pointer accessor for direct copying.

Definition at line 107 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 116 of file OgreVector3.h.

References x, y, and z.

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

Definition at line 125 of file OgreVector3.h.

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

Definition at line 134 of file OgreVector3.h.

References x, y, and z.

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

Definition at line 139 of file OgreVector3.h.

References x, y, and z.

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

Definition at line 145 of file OgreVector3.h.

References x, y, and z.

Vector3 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 Real  fScalar  )  const

Definition at line 161 of file OgreVector3.h.

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

Definition at line 169 of file OgreVector3.h.

References x, y, and z.

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

Definition at line 177 of file OgreVector3.h.

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

Definition at line 189 of file OgreVector3.h.

References x, y, and z.

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

Definition at line 197 of file OgreVector3.h.

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

Definition at line 202 of file OgreVector3.h.

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

Definition at line 257 of file OgreVector3.h.

References x, y, and z.

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

Definition at line 266 of file OgreVector3.h.

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

Definition at line 274 of file OgreVector3.h.

References x, y, and z.

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

Definition at line 283 of file OgreVector3.h.

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

Definition at line 291 of file OgreVector3.h.

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

Definition at line 299 of file OgreVector3.h.

References x, y, and z.

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

Definition at line 308 of file OgreVector3.h.

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

Definition at line 321 of file OgreVector3.h.

References x, y, and z.

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 338 of file OgreVector3.h.

References Ogre::Math::Sqrt().

Referenced by angleBetween(), Ogre::VisibleObjectsBoundsInfo::merge(), and Ogre::VisibleObjectsBoundsInfo::mergeNonRenderedButInFrustum().

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 353 of file OgreVector3.h.

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

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 365 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 380 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 399 of file OgreVector3.h.

References x, y, and z.

Referenced by getRotationTo().

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 414 of file OgreVector3.h.

References Ogre::Math::Abs(), 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 428 of file OgreVector3.h.

References Ogre::Math::Sqrt().

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

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 472 of file OgreVector3.h.

References x, y, and z.

Referenced by getRotationTo().

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 483 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 greater that the ones of the vector it is compared against.

Definition at line 494 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 504 of file OgreVector3.h.

References x, y, and z.

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 518 of file OgreVector3.h.

References x, y, and z.

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

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 532 of file OgreVector3.h.

References x, y, and z.

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

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 546 of file OgreVector3.h.

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

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 583 of file OgreVector3.h.

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

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

Gets the angle between 2 vectors.

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

Definition at line 613 of file OgreVector3.h.

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

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 635 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::isZeroLength ( void   )  const

Returns true if this vector is zero length.

Definition at line 686 of file OgreVector3.h.

Referenced by getRotationTo().

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 695 of file OgreVector3.h.

References normalise().

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 705 of file OgreVector3.h.

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 716 of file OgreVector3.h.

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

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 730 of file OgreVector3.h.

References squaredLength().

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 743 of file OgreVector3.h.

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


Friends And Related Function Documentation

Vector3 operator* ( const Real  fScalar,
const Vector3 rkVector 
) [friend]

Definition at line 208 of file OgreVector3.h.

Vector3 operator/ ( const Real  fScalar,
const Vector3 rkVector 
) [friend]

Definition at line 216 of file OgreVector3.h.

Vector3 operator+ ( const Vector3 lhs,
const Real  rhs 
) [friend]

Definition at line 224 of file OgreVector3.h.

Vector3 operator+ ( const Real  lhs,
const Vector3 rhs 
) [friend]

Definition at line 232 of file OgreVector3.h.

Vector3 operator- ( const Vector3 lhs,
const Real  rhs 
) [friend]

Definition at line 240 of file OgreVector3.h.

Vector3 operator- ( const Real  lhs,
const Vector3 rhs 
) [friend]

Definition at line 248 of file OgreVector3.h.

_OgreExport friend std::ostream& operator<< ( std::ostream &  o,
const Vector3 v 
) [friend]

Function for writing to a stream.

Definition at line 766 of file OgreVector3.h.


Member Data Documentation

const Vector3 Ogre::Vector3::ZERO [static]

Definition at line 755 of file OgreVector3.h.

Referenced by getRotationTo(), and perpendicular().

Definition at line 756 of file OgreVector3.h.

Referenced by getRotationTo(), and perpendicular().

Definition at line 757 of file OgreVector3.h.

Definition at line 758 of file OgreVector3.h.

Definition at line 759 of file OgreVector3.h.

Definition at line 760 of file OgreVector3.h.

Definition at line 761 of file OgreVector3.h.


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

Copyright © 2008 Torus Knot Software Ltd
Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 2.5 License.
Last modified Sun Sep 27 22:08:22 2009