Public Types | Public Member Functions | Static Public Member Functions | Static Public Attributes | Protected Member Functions | Static Protected Member Functions | Static Protected Attributes
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

static int IAbs (int iValue)
static int ICeil (float fValue)
static int IFloor (float fValue)
static int ISign (int iValue)
static Real Abs (Real fValue)
static Degree Abs (const Degree &dValue)
static Radian Abs (const Radian &rValue)
static Radian ACos (Real fValue)
static Radian ASin (Real fValue)
static Radian ATan (Real fValue)
static Radian ATan2 (Real fY, Real fX)
static Real Ceil (Real fValue)
static bool isNaN (Real f)
static Real Cos (const Radian &fValue, bool useTables=false)
 Cosine function.
static Real Cos (Real fValue, bool useTables=false)
 Cosine function.
static Real Exp (Real fValue)
static Real Floor (Real fValue)
static Real Log (Real fValue)
static Real Log2 (Real fValue)
static Real LogN (Real base, Real fValue)
static Real Pow (Real fBase, Real fExponent)
static Real Sign (Real fValue)
static Radian Sign (const Radian &rValue)
static Degree Sign (const Degree &dValue)
static Real Sin (const Radian &fValue, bool useTables=false)
 Sine function.
static Real Sin (Real fValue, bool useTables=false)
 Sine function.
static Real Sqr (Real fValue)
static Real Sqrt (Real fValue)
static Radian Sqrt (const Radian &fValue)
static Degree Sqrt (const Degree &fValue)
static Real InvSqrt (Real fValue)
 Inverse square root i.e.
static Real UnitRandom ()
static Real RangeRandom (Real fLow, Real fHigh)
static Real SymmetricRandom ()
static Real Tan (const Radian &fValue, bool useTables=false)
 Tangent function.
static Real Tan (Real fValue, bool useTables=false)
 Tangent function.
static Real DegreesToRadians (Real degrees)
static Real RadiansToDegrees (Real radians)
static void setAngleUnit (AngleUnit unit)
 These functions used to set the assumed angle units (radians or degrees) expected when using the Angle type.
static AngleUnit getAngleUnit (void)
 Get the unit being used for angles.
static Real AngleUnitsToRadians (Real units)
 Convert from the current AngleUnit to radians.
static Real RadiansToAngleUnits (Real radians)
 Convert from radians to the current AngleUnit .
static Real AngleUnitsToDegrees (Real units)
 Convert from the current AngleUnit to degrees.
static Real DegreesToAngleUnits (Real degrees)
 Convert from degrees to the current AngleUnit.
static bool pointInTri2D (const Vector2 &p, const Vector2 &a, const Vector2 &b, const Vector2 &c)
 Checks whether a given point is inside a triangle, in a 2-dimensional (Cartesian) space.
static bool pointInTri3D (const Vector3 &p, const Vector3 &a, const Vector3 &b, const Vector3 &c, const Vector3 &normal)
 Checks whether a given 3D point is inside a triangle.
static std::pair< bool, Realintersects (const Ray &ray, const Plane &plane)
 Ray / plane intersection, returns boolean result and distance.
static std::pair< bool, Realintersects (const Ray &ray, const Sphere &sphere, bool discardInside=true)
 Ray / sphere intersection, returns boolean result and distance.
static std::pair< bool, Realintersects (const Ray &ray, const AxisAlignedBox &box)
 Ray / box intersection, returns boolean result and distance.
static bool intersects (const Ray &ray, const AxisAlignedBox &box, Real *d1, Real *d2)
 Ray / box intersection, returns boolean result and two intersection distance.
static std::pair< bool, Realintersects (const Ray &ray, const Vector3 &a, const Vector3 &b, const Vector3 &c, const Vector3 &normal, bool positiveSide=true, bool negativeSide=true)
 Ray / triangle intersection, returns boolean result and distance.
static std::pair< bool, Realintersects (const Ray &ray, const Vector3 &a, const Vector3 &b, const Vector3 &c, bool positiveSide=true, bool negativeSide=true)
 Ray / triangle intersection, returns boolean result and distance.
static bool intersects (const Sphere &sphere, const AxisAlignedBox &box)
 Sphere / box intersection test.
static bool intersects (const Plane &plane, const AxisAlignedBox &box)
 Plane / box intersection test.
static std::pair< bool, Realintersects (const Ray &ray, const vector< Plane >::type &planeList, bool normalIsOutside)
 Ray / convex plane list intersection test.
static std::pair< bool, Realintersects (const Ray &ray, const list< Plane >::type &planeList, bool normalIsOutside)
 Ray / convex plane list intersection test.
static bool intersects (const Sphere &sphere, const Plane &plane)
 Sphere / plane intersection test.
static bool RealEqual (Real a, Real b, Real tolerance=std::numeric_limits< Real >::epsilon())
 Compare 2 reals, using tolerance for inaccuracies.
static 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.
static Matrix4 buildReflectionMatrix (const Plane &p)
 Build a reflection matrix for the passed in plane.
static 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.
static Vector3 calculateBasicFaceNormal (const Vector3 &v1, const Vector3 &v2, const Vector3 &v3)
 Calculate a face normal, no w-information.
static 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.
static Vector3 calculateBasicFaceNormalWithoutNormalize (const Vector3 &v1, const Vector3 &v2, const Vector3 &v3)
 Calculate a face normal without normalize, no w-information.
static Real gaussianDistribution (Real x, Real offset=0.0f, Real scale=1.0f)
 Generates a value based on the Gaussian (normal) distribution function with the given offset and scale parameters.
template<typename T >
static T Clamp (T val, T minval, T maxval)
 Clamp a value within an inclusive range.
static Matrix4 makeViewMatrix (const Vector3 &position, const Quaternion &orientation, const Matrix4 *reflectMatrix=0)
static Real boundingRadiusFromAABB (const AxisAlignedBox &aabb)
 Get a bounding radius value from a bounding box.

Static Public Attributes

static const Real LOG2
 Stored value of log(2) for frequent use.
static const Real POS_INFINITY
static const Real NEG_INFINITY
static const Real PI
static const Real TWO_PI
static const Real HALF_PI
static const Real fDeg2Rad
static const Real fRad2Deg

Protected Member Functions

void buildTrigTables ()
 Private function to build trig tables.

Static Protected Member Functions

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

Static Protected Attributes

static AngleUnit msAngleUnit
static int mTrigTableSize
 Size of the trig tables as determined by constructor.
static Real mTrigTableFactor
 Radian -> index factor value ( mTrigTableSize / 2 * PI )
static RealmSinTable
static RealmTanTable

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 190 of file OgreMath.h.


Member Enumeration Documentation

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

Enumerator:
AU_DEGREE 
AU_RADIAN 

Definition at line 198 of file OgreMath.h.


Constructor & Destructor Documentation

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

Default constructor.

Parameters:
trigTableSizeOptional parameter to set the size of the tables used to implement Sin, Cos, Tan
Ogre::Math::~Math ( )

Default destructor.


Member Function Documentation

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

Definition at line 240 of file OgreMath.h.

References Ogre::Degree::valueDegrees().

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

Definition at line 241 of file OgreMath.h.

References Ogre::Radian::valueRadians().

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

Convert from the current AngleUnit to degrees.

Referenced by Ogre::Angle::operator Degree().

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

Convert from the current AngleUnit to radians.

Referenced by Ogre::Angle::operator Radian().

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

Definition at line 244 of file OgreMath.h.

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

Definition at line 245 of file OgreMath.h.

static Real Ogre::Math::boundingRadiusFromAABB ( const AxisAlignedBox aabb) [static]

Get a bounding radius value from a bounding box.

static 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.

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

Calculate a face normal, no w-information.

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

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

static 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.

static 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.

static 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.

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

Definition at line 246 of file OgreMath.h.

template<typename T >
static T Ogre::Math::Clamp ( val,
minval,
maxval 
) [static]

Clamp a value within an inclusive range.

Definition at line 576 of file OgreMath.h.

Referenced by Ogre::Vector3::angleBetween().

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

Cosine function.

Parameters:
fValueAngle in radians
useTablesIf true, uses lookup tables rather than calculation - faster but less accurate.

Definition at line 261 of file OgreMath.h.

References Ogre::Radian::valueRadians().

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

Cosine function.

Parameters:
fValueAngle in radians
useTablesIf true, uses lookup tables rather than calculation - faster but less accurate.

Definition at line 271 of file OgreMath.h.

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

Convert from degrees to the current AngleUnit.

Referenced by Ogre::Degree::valueAngleUnits().

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

Definition at line 361 of file OgreMath.h.

Referenced by Ogre::Degree::valueRadians().

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

Definition at line 275 of file OgreMath.h.

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

Definition at line 277 of file OgreMath.h.

static Real Ogre::Math::gaussianDistribution ( Real  x,
Real  offset = 0.0f,
Real  scale = 1.0f 
) [static]

Generates a value based on the Gaussian (normal) distribution function with the given offset and scale parameters.

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

Get the unit being used for angles.

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

Definition at line 234 of file OgreMath.h.

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

Definition at line 235 of file OgreMath.h.

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

Definition at line 236 of file OgreMath.h.

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

Ray / convex plane list intersection test.

Parameters:
rayThe ray to test with
plaeListList of planes which form a convex volume
normalIsOutsideDoes the normal point outside the volume
static std::pair<bool, Real> Ogre::Math::intersects ( const Ray ray,
const Vector3 a,
const Vector3 b,
const Vector3 c,
bool  positiveSide = true,
bool  negativeSide = true 
) [static]

Ray / triangle intersection, returns boolean result and distance.

Parameters:
rayThe ray.
aThe triangle's first vertex.
bThe triangle's second vertex.
cThe triangle's third vertex.
positiveSideIntersect with "positive side" of the triangle
negativeSideIntersect with "negative side" of the triangle
Returns:
If the ray is intersects the triangle, a pair of true and the distance between intersection point and ray origin returned.
If the ray isn't intersects the triangle, a pair of false and 0 returned.
static std::pair<bool, Real> Ogre::Math::intersects ( const Ray ray,
const Plane plane 
) [static]

Ray / plane intersection, returns boolean result and distance.

Referenced by Ogre::Sphere::intersects(), Ogre::Ray::intersects(), Ogre::PlaneBoundedVolume::intersects(), and Ogre::AxisAlignedBox::intersects().

static 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.

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

Ray / box intersection, returns boolean result and distance.

static bool Ogre::Math::intersects ( const Ray ray,
const AxisAlignedBox box,
Real d1,
Real d2 
) [static]

Ray / box intersection, returns boolean result and two intersection distance.

Parameters:
rayThe ray.
boxThe box.
d1A real pointer to retrieve the near intersection distance from the ray origin, maybe null which means don't care about the near intersection distance.
d2A real pointer to retrieve the far intersection distance from the ray origin, maybe null which means don't care about the far intersection distance.
Returns:
If the ray is intersects the box, true is returned, and the near intersection distance is return by d1, the far intersection distance is return by d2. Guarantee 0 <= d1 <= d2.
If the ray isn't intersects the box, false is returned, and d1 and d2 is unmodified.
static std::pair<bool, Real> Ogre::Math::intersects ( const Ray ray,
const Vector3 a,
const Vector3 b,
const Vector3 c,
const Vector3 normal,
bool  positiveSide = true,
bool  negativeSide = true 
) [static]

Ray / triangle intersection, returns boolean result and distance.

Parameters:
rayThe ray.
aThe triangle's first vertex.
bThe triangle's second vertex.
cThe triangle's third vertex.
normalThe triangle plane's normal (passed in rather than calculated on demand since the caller may already have it), doesn't need normalised since we don't care.
positiveSideIntersect with "positive side" of the triangle
negativeSideIntersect with "negative side" of the triangle
Returns:
If the ray is intersects the triangle, a pair of true and the distance between intersection point and ray origin returned.
If the ray isn't intersects the triangle, a pair of false and 0 returned.
static bool Ogre::Math::intersects ( const Sphere sphere,
const AxisAlignedBox box 
) [static]

Sphere / box intersection test.

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

Plane / box intersection test.

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

Ray / convex plane list intersection test.

Parameters:
rayThe ray to test with
plaeListList of planes which form a convex volume
normalIsOutsideDoes the normal point outside the volume
static 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!
static Real Ogre::Math::InvSqrt ( Real  fValue) [static]

Inverse square root i.e.

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

static int Ogre::Math::ISign ( int  iValue) [static]
static bool Ogre::Math::isNaN ( Real  f) [static]
static Real Ogre::Math::Log ( Real  fValue) [static]

Definition at line 279 of file OgreMath.h.

static Real Ogre::Math::Log2 ( Real  fValue) [static]

Definition at line 284 of file OgreMath.h.

static Real Ogre::Math::LogN ( Real  base,
Real  fValue 
) [static]

Definition at line 286 of file OgreMath.h.

static Matrix4 Ogre::Math::makeViewMatrix ( const Vector3 position,
const Quaternion orientation,
const Matrix4 reflectMatrix = 0 
) [static]
static bool Ogre::Math::pointInTri2D ( const Vector2 p,
const Vector2 a,
const Vector2 b,
const Vector2 c 
) [static]

Checks whether 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:
pThe point.
aThe triangle's first vertex.
bThe triangle's second vertex.
cThe 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.
static bool Ogre::Math::pointInTri3D ( const Vector3 p,
const Vector3 a,
const Vector3 b,
const Vector3 c,
const Vector3 normal 
) [static]

Checks whether a given 3D point is inside a triangle.

Remarks:
The vertices of the triangle must be given in either trigonometrical (anticlockwise) or inverse trigonometrical (clockwise) order, and the point must be guaranteed to be in the same plane as the triangle
Parameters:
pThe point.
aThe triangle's first vertex.
bThe triangle's second vertex.
cThe triangle's third vertex.
normalThe triangle plane's normal (passed in rather than calculated on demand since the caller may already have it)
Returns:
If the point resides in the triangle, true is returned.
If the point is outside the triangle, false is returned.
static Real Ogre::Math::Pow ( Real  fBase,
Real  fExponent 
) [static]

Definition at line 288 of file OgreMath.h.

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

Convert from radians to the current AngleUnit .

Referenced by Ogre::Radian::valueAngleUnits().

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

Definition at line 362 of file OgreMath.h.

Referenced by Ogre::Radian::valueDegrees().

static Real Ogre::Math::RangeRandom ( Real  fLow,
Real  fHigh 
) [static]
static bool Ogre::Math::RealEqual ( Real  a,
Real  b,
Real  tolerance = std::numeric_limits< Real >::epsilon() 
) [static]
static 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.
static Real Ogre::Math::Sign ( Real  fValue) [static]
static Degree Ogre::Math::Sign ( const Degree dValue) [static]

Definition at line 295 of file OgreMath.h.

References Ogre::Degree::valueDegrees().

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

Definition at line 291 of file OgreMath.h.

References Ogre::Radian::valueRadians().

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

Sine function.

Parameters:
fValueAngle in radians
useTablesIf true, uses lookup tables rather than calculation - faster but less accurate.

Definition at line 317 of file OgreMath.h.

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

Sine function.

Parameters:
fValueAngle in radians
useTablesIf true, uses lookup tables rather than calculation - faster but less accurate.

Definition at line 307 of file OgreMath.h.

References Ogre::Radian::valueRadians().

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

Definition at line 321 of file OgreMath.h.

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

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

Definition at line 325 of file OgreMath.h.

References Ogre::Radian::valueRadians().

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

Definition at line 327 of file OgreMath.h.

References Ogre::Degree::valueDegrees().

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

Tangent function.

Parameters:
fValueAngle in radians
useTablesIf true, uses lookup tables rather than calculation - faster but less accurate.

Definition at line 357 of file OgreMath.h.

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

Tangent function.

Parameters:
fValueAngle in radians
useTablesIf true, uses lookup tables rather than calculation - faster but less accurate.

Definition at line 347 of file OgreMath.h.

References Ogre::Radian::valueRadians().

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

Member Data Documentation

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

Definition at line 595 of file OgreMath.h.

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

Definition at line 596 of file OgreMath.h.

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

Definition at line 594 of file OgreMath.h.

const Real Ogre::Math::LOG2 [static]

Stored value of log(2) for frequent use.

Definition at line 282 of file OgreMath.h.

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

Definition at line 206 of file OgreMath.h.

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

Definition at line 213 of file OgreMath.h.

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

Definition at line 214 of file OgreMath.h.

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

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

Definition at line 212 of file OgreMath.h.

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

Size of the trig tables as determined by constructor.

Definition at line 209 of file OgreMath.h.

Definition at line 591 of file OgreMath.h.

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

Definition at line 592 of file OgreMath.h.

Referenced by Ogre::Vector3::getRotationTo().

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

Definition at line 593 of file OgreMath.h.

Referenced by Ogre::Vector3::randomDeviant(), and Ogre::Vector2::randomDeviant().


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 3.0 Unported License.
Last modified Sat Jan 14 2012 18:40:49