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Ogre::Math Class Reference

Class to provide access to common mathematical functions. More...

#include <OgreMath.h>

List of all members.

Public Types

enum  AngleUnit { AU_DEGREE, AU_RADIAN }
 The angular units used by the API. More...


Public Member Functions

 Math (unsigned int trigTableSize=4096)
 Default constructor.

 ~Math ()
 Default destructor.


Static Public Member Functions

int IAbs (int iValue)
int ICeil (float fValue)
int IFloor (float fValue)
int ISign (int iValue)
Real Abs (Real fValue)
Degree Abs (const Degree &dValue)
Radian Abs (const Radian &rValue)
Radian ACos (Real fValue)
Radian ASin (Real fValue)
Radian ATan (Real fValue)
Radian ATan2 (Real fY, Real fX)
Real Ceil (Real fValue)
Real Cos (const Radian &fValue, bool useTables=false)
 Cosine function.

Real Cos (Real fValue, bool useTables=false)
 Cosine function.

Real Exp (Real fValue)
Real Floor (Real fValue)
Real Log (Real fValue)
Real Pow (Real fBase, Real fExponent)
Real Sign (Real fValue)
Radian Sign (const Radian &rValue)
Degree Sign (const Degree &dValue)
Real Sin (const Radian &fValue, bool useTables=false)
 Sine function.

Real Sin (Real fValue, bool useTables=false)
 Sine function.

Real Sqr (Real fValue)
Real Sqrt (Real fValue)
Radian Sqrt (const Radian &fValue)
Degree Sqrt (const Degree &fValue)
Real InvSqrt (Real fValue)
 Inverse square root i.e.

Real UnitRandom ()
Real RangeRandom (Real fLow, Real fHigh)
Real SymmetricRandom ()
Real Tan (const Radian &fValue, bool useTables=false)
 Tangent function.

Real Tan (Real fValue, bool useTables=false)
 Tangent function.

Real DegreesToRadians (Real degrees)
Real RadiansToDegrees (Real radians)
void setAngleUnit (AngleUnit unit)
 These functions used to set the assumed angle units (radians or degrees) expected when using the Angle type.

AngleUnit getAngleUnit (void)
 Get the unit being used for angles.

Real AngleUnitsToRadians (Real units)
 Convert from the current AngleUnit to radians.

Real RadiansToAngleUnits (Real radians)
 Convert from radians to the current AngleUnit .

Real AngleUnitsToDegrees (Real units)
 Convert from the current AngleUnit to degrees.

Real DegreesToAngleUnits (Real degrees)
 Convert from degrees to the current AngleUnit.

bool pointInTri2D (Real px, Real pz, Real ax, Real az, Real bx, Real bz, Real cx, Real cz)
 Checks wether a given point is inside a triangle, in a 2-dimensional (Cartesian) space.

std::pair< bool, Real > intersects (const Ray &ray, const Plane &plane)
 Ray / plane intersection, returns boolean result and distance.

std::pair< bool, Real > intersects (const Ray &ray, const Sphere &sphere, bool discardInside=true)
 Ray / sphere intersection, returns boolean result and distance.

std::pair< bool, Real > intersects (const Ray &ray, const AxisAlignedBox &sphere)
 Ray / box intersection, returns boolean result and distance.

bool intersects (const Sphere &sphere, const AxisAlignedBox &box)
 Sphere / box intersection test.

bool intersects (const Plane &plane, const AxisAlignedBox &box)
 Plane / box intersection test.

std::pair< bool, Real > intersects (const Ray &ray, const std::vector< Plane > &planeList, bool normalIsOutside)
 Ray / convex plane list intersection test.

std::pair< bool, Real > intersects (const Ray &ray, const std::list< Plane > &planeList, bool normalIsOutside)
 Ray / convex plane list intersection test.

bool intersects (const Sphere &sphere, const Plane &plane)
 Sphere / plane intersection test.

bool RealEqual (Real a, Real b, Real tolerance=std::numeric_limits< Real >::epsilon())
 Compare 2 reals, using tolerance for inaccuracies.

Vector3 calculateTangentSpaceVector (const Vector3 &position1, const Vector3 &position2, const Vector3 &position3, Real u1, Real v1, Real u2, Real v2, Real u3, Real v3)
 Calculates the tangent space vector for a given set of positions / texture coords.

Matrix4 buildReflectionMatrix (const Plane &p)
 Build a reflection matrix for the passed in plane.

Vector4 calculateFaceNormal (const Vector3 &v1, const Vector3 &v2, const Vector3 &v3)
 Calculate a face normal, including the w component which is the offset from the origin.

Vector3 calculateBasicFaceNormal (const Vector3 &v1, const Vector3 &v2, const Vector3 &v3)
 Calculate a face normal, no w-information.

Vector4 calculateFaceNormalWithoutNormalize (const Vector3 &v1, const Vector3 &v2, const Vector3 &v3)
 Calculate a face normal without normalize, including the w component which is the offset from the origin.

Vector3 calculateBasicFaceNormalWithoutNormalize (const Vector3 &v1, const Vector3 &v2, const Vector3 &v3)
 Calculate a face normal without normalize, no w-information.


Static Public Attributes

const Real POS_INFINITY
const Real NEG_INFINITY
const Real PI
const Real TWO_PI
const Real HALF_PI
const Real fDeg2Rad
const Real fRad2Deg

Protected Member Functions

void buildTrigTables ()
 Private function to build trig tables.


Static Protected Member Functions

Real SinTable (Real fValue)
Real TanTable (Real fValue)

Static Protected Attributes

AngleUnit msAngleUnit
int mTrigTableSize
 Size of the trig tables as determined by constructor.

Real mTrigTableFactor
 Radian -> index factor value ( mTrigTableSize / 2 * PI ).

Real * mSinTable
Real * mTanTable

Detailed Description

Class to provide access to common mathematical functions.

Remarks:
Most of the maths functions are aliased versions of the C runtime library functions. They are aliased here to provide future optimisation opportunities, either from faster RTLs or custom math approximations.
Note:

This is based on MgcMath.h from Wild Magic.

Definition at line 165 of file OgreMath.h.

Member Enumeration Documentation

enum Ogre::Math::AngleUnit
 

The angular units used by the API.

This functionality is now deprecated in favor of discreet angular unit types ( see Degree and Radian above ). The only place this functionality is actually still used is when parsing files. Search for usage of the Angle class for those instances

Enumeration values:
AU_DEGREE 
AU_RADIAN 

Definition at line 173 of file OgreMath.h.

Constructor & Destructor Documentation

Ogre::Math::Math (  unsigned int  trigTableSize = 4096  ) 
 

Default constructor.

Parameters:
trigTableSize Optional parameter to set the size of the tables used to implement Sin, Cos, Tan

Ogre::Math::~Math (   ) 
 

Default destructor.

Member Function Documentation

Radian Ogre::Math::Abs (  const Radian &  rValue  )  [static]
 

Definition at line 216 of file OgreMath.h.

References Ogre::Radian::valueRadians().

Degree Ogre::Math::Abs (  const Degree &  dValue  )  [static]
 

Definition at line 215 of file OgreMath.h.

References Ogre::Degree::valueDegrees().

Real Ogre::Math::Abs (  Real  fValue  )  [static]
 

Definition at line 214 of file OgreMath.h.

References Ogre::Real.

Radian Ogre::Math::ACos (  Real  fValue  )  [static]
 

Real Ogre::Math::AngleUnitsToDegrees (  Real  units  )  [static]
 

Convert from the current AngleUnit to degrees.

Real Ogre::Math::AngleUnitsToRadians (  Real  units  )  [static]
 

Convert from the current AngleUnit to radians.

Radian Ogre::Math::ASin (  Real  fValue  )  [static]
 

Radian Ogre::Math::ATan (  Real  fValue  )  [static]
 

Definition at line 219 of file OgreMath.h.

References Ogre::Real.

Radian Ogre::Math::ATan2 (  Real  fY,
Real  fX
)  [static]
 

Definition at line 220 of file OgreMath.h.

References Ogre::Real.

Matrix4 Ogre::Math::buildReflectionMatrix (  const Plane &  p  )  [static]
 

Build a reflection matrix for the passed in plane.

void Ogre::Math::buildTrigTables (   )  [protected]
 

Private function to build trig tables.

Vector3 Ogre::Math::calculateBasicFaceNormal (  const Vector3 &  v1,
const Vector3 &  v2,
const Vector3 &  v3
)  [static]
 

Calculate a face normal, no w-information.

Vector3 Ogre::Math::calculateBasicFaceNormalWithoutNormalize (  const Vector3 &  v1,
const Vector3 &  v2,
const Vector3 &  v3
)  [static]
 

Calculate a face normal without normalize, no w-information.

Vector4 Ogre::Math::calculateFaceNormal (  const Vector3 &  v1,
const Vector3 &  v2,
const Vector3 &  v3
)  [static]
 

Calculate a face normal, including the w component which is the offset from the origin.

Vector4 Ogre::Math::calculateFaceNormalWithoutNormalize (  const Vector3 &  v1,
const Vector3 &  v2,
const Vector3 &  v3
)  [static]
 

Calculate a face normal without normalize, including the w component which is the offset from the origin.

Vector3 Ogre::Math::calculateTangentSpaceVector (  const Vector3 &  position1,
const Vector3 &  position2,
const Vector3 &  position3,
Real  u1,
Real  v1,
Real  u2,
Real  v2,
Real  u3,
Real  v3
)  [static]
 

Calculates the tangent space vector for a given set of positions / texture coords.

Real Ogre::Math::Ceil (  Real  fValue  )  [static]
 

Definition at line 221 of file OgreMath.h.

References Ogre::Real.

Real Ogre::Math::Cos (  Real  fValue,
bool  useTables = false
)  [static]
 

Cosine function.

Parameters:
fValue Angle in radians
useTables If true, uses lookup tables rather than calculation - faster but less accurate.

Definition at line 240 of file OgreMath.h.

References Ogre::Real.

Real Ogre::Math::Cos (  const Radian &  fValue,
bool  useTables = false
)  [static]
 

Cosine function.

Parameters:
fValue Angle in radians
useTables If true, uses lookup tables rather than calculation - faster but less accurate.

Definition at line 230 of file OgreMath.h.

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

Real Ogre::Math::DegreesToAngleUnits (  Real  degrees  )  [static]
 

Convert from degrees to the current AngleUnit.

Real Ogre::Math::DegreesToRadians (  Real  degrees  )  [static]
 

Definition at line 323 of file OgreMath.h.

References Ogre::Real.

Real Ogre::Math::Exp (  Real  fValue  )  [static]
 

Definition at line 244 of file OgreMath.h.

References Ogre::Real.

Real Ogre::Math::Floor (  Real  fValue  )  [static]
 

Definition at line 246 of file OgreMath.h.

References Ogre::Real.

AngleUnit Ogre::Math::getAngleUnit (  void   )  [static]
 

Get the unit being used for angles.

int Ogre::Math::IAbs (  int  iValue  )  [static]
 

Definition at line 209 of file OgreMath.h.

int Ogre::Math::ICeil (  float  fValue  )  [static]
 

Definition at line 210 of file OgreMath.h.

int Ogre::Math::IFloor (  float  fValue  )  [static]
 

Definition at line 211 of file OgreMath.h.

bool Ogre::Math::intersects (  const Sphere &  sphere,
const Plane &  plane
)  [static]
 

Sphere / plane intersection test.

Remarks:
NB just do a plane.getDistance(sphere.getCenter()) for more detail!

std::pair<bool, Real> Ogre::Math::intersects (  const Ray &  ray,
const std::list< Plane > &  planeList,
bool  normalIsOutside
)  [static]
 

Ray / convex plane list intersection test.

Parameters:
ray The ray to test with
plaeList List of planes which form a convex volume
normalIsOutside Does the normal point outside the volume

std::pair<bool, Real> Ogre::Math::intersects (  const Ray &  ray,
const std::vector< Plane > &  planeList,
bool  normalIsOutside
)  [static]
 

Ray / convex plane list intersection test.

Parameters:
ray The ray to test with
plaeList List of planes which form a convex volume
normalIsOutside Does the normal point outside the volume

bool Ogre::Math::intersects (  const Plane &  plane,
const AxisAlignedBox &  box
)  [static]
 

Plane / box intersection test.

bool Ogre::Math::intersects (  const Sphere &  sphere,
const AxisAlignedBox &  box
)  [static]
 

Sphere / box intersection test.

std::pair<bool, Real> Ogre::Math::intersects (  const Ray &  ray,
const AxisAlignedBox &  sphere
)  [static]
 

Ray / box intersection, returns boolean result and distance.

std::pair<bool, Real> Ogre::Math::intersects (  const Ray &  ray,
const Sphere &  sphere,
bool  discardInside = true
)  [static]
 

Ray / sphere intersection, returns boolean result and distance.

std::pair<bool, Real> Ogre::Math::intersects (  const Ray &  ray,
const Plane &  plane
)  [static]
 

Ray / plane intersection, returns boolean result and distance.

Real Ogre::Math::InvSqrt (  Real  fValue  )  [static]
 

Inverse square root i.e.

1 / Sqrt(x), good for vector normalisation.

int Ogre::Math::ISign (  int  iValue  )  [static]
 

Real Ogre::Math::Log (  Real  fValue  )  [static]
 

Definition at line 248 of file OgreMath.h.

References Ogre::Real.

bool Ogre::Math::pointInTri2D (  Real  px,
Real  pz,
Real  ax,
Real  az,
Real  bx,
Real  bz,
Real  cx,
Real  cz
)  [static]
 

Checks wether a given point is inside a triangle, in a 2-dimensional (Cartesian) space.

Remarks:
The vertices of the triangle must be given in either trigonometrical (anticlockwise) or inverse trigonometrical (clockwise) order.
Parameters:
px The X-coordinate of the point.
py The Y-coordinate of the point.
ax The X-coordinate of the triangle's first vertex.
ay The Y-coordinate of the triangle's first vertex.
bx The X-coordinate of the triangle's second vertex.
by The Y-coordinate of the triangle's second vertex.
cx The X-coordinate of the triangle's third vertex.
cy The Y-coordinate of the triangle's third vertex.
Returns:
If the point resides in the triangle, true is returned.
If the point is outside the triangle, false is returned.

Real Ogre::Math::Pow (  Real  fBase,
Real  fExponent
)  [static]
 

Definition at line 250 of file OgreMath.h.

References Ogre::Real.

Real Ogre::Math::RadiansToAngleUnits (  Real  radians  )  [static]
 

Convert from radians to the current AngleUnit .

Real Ogre::Math::RadiansToDegrees (  Real  radians  )  [static]
 

Definition at line 324 of file OgreMath.h.

References Ogre::Real.

Real Ogre::Math::RangeRandom (  Real  fLow,
Real  fHigh
)  [static]
 

bool Ogre::Math::RealEqual (  Real  a,
Real  b,
Real  tolerance = std::numeric_limits< Real >::epsilon()
)  [static]
 

Compare 2 reals, using tolerance for inaccuracies.

void Ogre::Math::setAngleUnit (  AngleUnit  unit  )  [static]
 

These functions used to set the assumed angle units (radians or degrees) expected when using the Angle type.

You can set this directly after creating a new Root, and also before/after resource creation, depending on whether you want the change to affect resource files.

Degree Ogre::Math::Sign (  const Degree &  dValue  )  [static]
 

Definition at line 257 of file OgreMath.h.

References Ogre::Degree::valueDegrees().

Radian Ogre::Math::Sign (  const Radian &  rValue  )  [static]
 

Definition at line 253 of file OgreMath.h.

References Ogre::Radian::valueRadians().

Real Ogre::Math::Sign (  Real  fValue  )  [static]
 

Real Ogre::Math::Sin (  Real  fValue,
bool  useTables = false
)  [static]
 

Sine function.

Parameters:
fValue Angle in radians
useTables If true, uses lookup tables rather than calculation - faster but less accurate.

Definition at line 279 of file OgreMath.h.

References Ogre::Real.

Real Ogre::Math::Sin (  const Radian &  fValue,
bool  useTables = false
)  [static]
 

Sine function.

Parameters:
fValue Angle in radians
useTables If true, uses lookup tables rather than calculation - faster but less accurate.

Definition at line 269 of file OgreMath.h.

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

Real Ogre::Math::SinTable (  Real  fValue  )  [static, protected]
 

Real Ogre::Math::Sqr (  Real  fValue  )  [static]
 

Definition at line 283 of file OgreMath.h.

References Ogre::Real.

Degree Ogre::Math::Sqrt (  const Degree &  fValue  )  [static]
 

Definition at line 289 of file OgreMath.h.

References Ogre::Degree::valueDegrees().

Radian Ogre::Math::Sqrt (  const Radian &  fValue  )  [static]
 

Definition at line 287 of file OgreMath.h.

References Ogre::Radian::valueRadians().

Real Ogre::Math::Sqrt (  Real  fValue  )  [static]
 

Definition at line 285 of file OgreMath.h.

References Ogre::Real.

Real Ogre::Math::SymmetricRandom (   )  [static]
 

Real Ogre::Math::Tan (  Real  fValue,
bool  useTables = false
)  [static]
 

Tangent function.

Parameters:
fValue Angle in radians
useTables If true, uses lookup tables rather than calculation - faster but less accurate.

Definition at line 319 of file OgreMath.h.

References Ogre::Real.

Real Ogre::Math::Tan (  const Radian &  fValue,
bool  useTables = false
)  [static]
 

Tangent function.

Parameters:
fValue Angle in radians
useTables If true, uses lookup tables rather than calculation - faster but less accurate.

Definition at line 309 of file OgreMath.h.

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

Real Ogre::Math::TanTable (  Real  fValue  )  [static, protected]
 

Real Ogre::Math::UnitRandom (   )  [static]
 

Member Data Documentation

const Real Ogre::Math::fDeg2Rad [static]
 

Definition at line 440 of file OgreMath.h.

const Real Ogre::Math::fRad2Deg [static]
 

Definition at line 441 of file OgreMath.h.

const Real Ogre::Math::HALF_PI [static]
 

Definition at line 439 of file OgreMath.h.

AngleUnit Ogre::Math::msAngleUnit [static, protected]
 

Definition at line 181 of file OgreMath.h.

Real* Ogre::Math::mSinTable [static, protected]
 

Definition at line 188 of file OgreMath.h.

Real* Ogre::Math::mTanTable [static, protected]
 

Definition at line 189 of file OgreMath.h.

Real Ogre::Math::mTrigTableFactor [static, protected]
 

Radian -> index factor value ( mTrigTableSize / 2 * PI ).

Definition at line 187 of file OgreMath.h.

int Ogre::Math::mTrigTableSize [static, protected]
 

Size of the trig tables as determined by constructor.

Definition at line 184 of file OgreMath.h.

const Real Ogre::Math::NEG_INFINITY [static]
 

Definition at line 436 of file OgreMath.h.

const Real Ogre::Math::PI [static]
 

Definition at line 437 of file OgreMath.h.

const Real Ogre::Math::POS_INFINITY [static]
 

Definition at line 435 of file OgreMath.h.

const Real Ogre::Math::TWO_PI [static]
 

Definition at line 438 of file OgreMath.h.

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

Copyright © 2000-2005 by The OGRE Team
Last modified Sun Nov 20 12:37:17 2005