# Ogre::Vector3 Class Reference

Standard 3-dimensional vector. More...

`#include <OgreVector3.h>`

List of all members.

## Public Member Functions

| Vector3 ()
| Vector3 (Real fX, Real fY, Real fZ)
| Vector3 (Real afCoordinate[3])
| Vector3 (int afCoordinate[3])
| Vector3 (const Real *const r)
| Vector3 (const Vector3 &rkVector)
Real | operator[] (size_t i) const
Real & | operator[] (size_t i)
Vector3 & | operator= (const Vector3 &rkVector)
| Assigns the value of the other vector.
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 * (Real fScalar) const
Vector3 | operator * (const Vector3 &rhs) const
Vector3 | operator/ (Real fScalar) const
Vector3 | operator/ (const Vector3 &rhs) const
Vector3 | operator- () const
Vector3 & | operator+= (const Vector3 &rkVector)
Vector3 & | operator-= (const Vector3 &rkVector)
Vector3 & | operator *= (Real fScalar)
Vector3 & | operator *= (const Vector3 &rkVector)
Vector3 & | operator/= (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 | dotProduct (const Vector3 &vec) const
| Calculates the 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.
Quaternion | getRotationTo (const Vector3 &dest) 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 | directionEquals (const Vector3 &rhs, const Radian &tolerance) const
| Returns whether this vector is within a directional tolerance of another vector.

## Static Public Attributes

const Vector3 | ZERO
const Vector3 | UNIT_X
const Vector3 | UNIT_Y
const Vector3 | UNIT_Z
const Vector3 | NEGATIVE_UNIT_X
const Vector3 | NEGATIVE_UNIT_Y
const Vector3 | NEGATIVE_UNIT_Z
const Vector3 | UNIT_SCALE

## Friends

Vector3 | operator * (Real fScalar, const Vector3 &rkVector)
_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 orthoganal 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 42 of file OgreVector3.h.

## Constructor & Destructor Documentation

Ogre::Vector3::Vector3 | ( |  | ) |

| Definition at line 53 of file OgreVector3.h.

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

| Definition at line 57 of file OgreVector3.h. References Ogre::Real.

Ogre::Vector3::Vector3 | ( | Real | afCoordinate[3] | ) |

| Definition at line 62 of file OgreVector3.h. References Ogre::Real.

Ogre::Vector3::Vector3 | ( | int | afCoordinate[3] | ) |

| Definition at line 69 of file OgreVector3.h. References Ogre::Real.

Ogre::Vector3::Vector3 | ( | const Real *const | r | ) |

| Definition at line 76 of file OgreVector3.h. References Ogre::Real.

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

| Definition at line 81 of file OgreVector3.h.

## Member Function Documentation

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.

  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 373 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

Definition at line 602 of file OgreVector3.h.

References Ogre::Real, and Ogre::Radian::valueRadians().

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 316 of file OgreVector3.h.

References Ogre::Real, x, y, and z.

Referenced by getRotationTo().

Quaternion Ogre::Vector3::getRotationTo | ( | const Vector3 & | dest | ) | const

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

Remarks:
  Don't call this if you think the dest vector can be close to the inverse of this vector, since then ANY axis of rotation is ok.

Definition at line 526 of file OgreVector3.h.

References crossProduct(), dotProduct(), normalise(), Ogre::Real, Ogre::Quaternion::w, x, Ogre::Quaternion::x, y, Ogre::Quaternion::y, z, and Ogre::Quaternion::z.

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

| Returns true if this vector is zero length. Definition at line 559 of file OgreVector3.h. References Ogre::Real.

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 282 of file OgreVector3.h.

References Ogre::Real.

Referenced by Ogre::Sphere::intersects().

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 436 of file OgreVector3.h.

References x, y, and z.

Referenced by 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 422 of file OgreVector3.h.

References x, y, and z.

Referenced by 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 387 of file OgreVector3.h. References x, y, and z.

Real Ogre::Vector3::normalise | ( | void |  | ) |

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 330 of file OgreVector3.h.

References Ogre::Real.

Referenced by getRotationTo(), and normalisedCopy().

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 568 of file OgreVector3.h. References normalise().

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

| Definition at line 157 of file OgreVector3.h. References x, y, and z.

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

| Definition at line 146 of file OgreVector3.h. References Ogre::Real, x, y, and z.

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

| Definition at line 243 of file OgreVector3.h. References x, y, and z.

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

| Definition at line 235 of file OgreVector3.h. References Ogre::Real.

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

| Definition at line 118 of file OgreVector3.h. References x, y, and z.

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

| Definition at line 124 of file OgreVector3.h. References x, y, and z.

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

| Definition at line 217 of file OgreVector3.h. References x, y, and z.

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

| Definition at line 194 of file OgreVector3.h. References x, y, and z.

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

| Definition at line 135 of file OgreVector3.h. References x, y, and z.

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

| Definition at line 226 of file OgreVector3.h. References x, y, and z.

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

| Definition at line 182 of file OgreVector3.h. References x, y, and z.

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

| Definition at line 168 of file OgreVector3.h. References Ogre::Real, x, y, and z.

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

| Definition at line 265 of file OgreVector3.h. References x, y, and z.

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

| Definition at line 252 of file OgreVector3.h. References Ogre::Real.

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 398 of file OgreVector3.h. References x, y, and z.

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

Assigns the value of the other vector.

Parameters:

  rkVector | The other vector

Definition at line 104 of file OgreVector3.h.

References x, y, and z.

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

| Definition at line 113 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 408 of file OgreVector3.h. References x, y, and z.

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

| Definition at line 93 of file OgreVector3.h. References Ogre::Real.

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

| Definition at line 86 of file OgreVector3.h. References Ogre::Real.

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 450 of file OgreVector3.h.

References Ogre::Real, and 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 589 of file OgreVector3.h.

References Ogre::Real, x, y, and z.

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 486 of file OgreVector3.h.

References Ogre::Quaternion::FromAngleAxis().

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 578 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 297 of file OgreVector3.h.

References Ogre::Real.

Referenced by perpendicular().

## Friends And Related Function Documentation

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

| Definition at line 205 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 625 of file OgreVector3.h.

## Member Data Documentation

const Vector3 Ogre::Vector3::NEGATIVE_UNIT_X `[static]`

| Definition at line 617 of file OgreVector3.h.

const Vector3 Ogre::Vector3::NEGATIVE_UNIT_Y `[static]`

| Definition at line 618 of file OgreVector3.h.

const Vector3 Ogre::Vector3::NEGATIVE_UNIT_Z `[static]`

| Definition at line 619 of file OgreVector3.h.

const Vector3 Ogre::Vector3::UNIT_SCALE `[static]`

| Definition at line 620 of file OgreVector3.h.

const Vector3 Ogre::Vector3::UNIT_X `[static]`

| Definition at line 614 of file OgreVector3.h.

const Vector3 Ogre::Vector3::UNIT_Y `[static]`

| Definition at line 615 of file OgreVector3.h.

const Vector3 Ogre::Vector3::UNIT_Z `[static]`

| Definition at line 616 of file OgreVector3.h.

Real Ogre::Vector3::val[3]

| Definition at line 49 of file OgreVector3.h.

Real Ogre::Vector3::x

Definition at line 47 of file OgreVector3.h.

Referenced by crossProduct(), dotProduct(), getRotationTo(), Ogre::Matrix4::getScale(), Ogre::Matrix4::getTrans(), Ogre::AxisAlignedBox::intersection(), Ogre::AxisAlignedBox::intersects(), makeCeil(), makeFloor(), Ogre::Matrix4::makeTrans(), midPoint(), operator *(), Ogre::Matrix4::operator *(), operator *=(), operator!=(), Ogre::EdgeListBuilder::vectorLess::operator()(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<(), Ogre::Vector4::operator=(), operator=(), operator==(), operator>(), positionEquals(), Ogre::Matrix4::setScale(), Ogre::Matrix4::setTrans(), Ogre::AxisAlignedBox::transform(), and Ogre::AxisAlignedBox::volume().

Real Ogre::Vector3::y

Definition at line 47 of file OgreVector3.h.

Referenced by crossProduct(), dotProduct(), getRotationTo(), Ogre::Matrix4::getScale(), Ogre::Matrix4::getTrans(), Ogre::AxisAlignedBox::intersection(), Ogre::AxisAlignedBox::intersects(), makeCeil(), makeFloor(), Ogre::Matrix4::makeTrans(), midPoint(), operator *(), Ogre::Matrix4::operator *(), operator *=(), operator!=(), Ogre::EdgeListBuilder::vectorLess::operator()(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<(), Ogre::Vector4::operator=(), operator=(), operator==(), operator>(), positionEquals(), Ogre::Matrix4::setScale(), Ogre::Matrix4::setTrans(), Ogre::AxisAlignedBox::transform(), and Ogre::AxisAlignedBox::volume().

Real Ogre::Vector3::z

Definition at line 47 of file OgreVector3.h.

Referenced by crossProduct(), dotProduct(), getRotationTo(), Ogre::Matrix4::getScale(), Ogre::Matrix4::getTrans(), Ogre::AxisAlignedBox::intersection(), Ogre::AxisAlignedBox::intersects(), makeCeil(), makeFloor(), Ogre::Matrix4::makeTrans(), midPoint(), operator *(), Ogre::Matrix4::operator *(), operator *=(), operator!=(), Ogre::EdgeListBuilder::vectorLess::operator()(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<(), Ogre::Vector4::operator=(), operator=(), operator==(), operator>(), positionEquals(), Ogre::Matrix4::setScale(), Ogre::Matrix4::setTrans(), Ogre::AxisAlignedBox::transform(), and Ogre::AxisAlignedBox::volume().

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

| Definition at line 613 of file OgreVector3.h.

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

- OgreVector3.h

Copyright © 2000-2005 by The OGRE Team
Last modified Sun Nov 20 12:41:16 2005