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

#include <OgreMath.h>

Classes
class	RandomValueProvider
	This class is used to provide an external random value provider. More...

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. More...

	~Math ()
	Default destructor. More...

Static Public Member Functions
static Degree	Abs (const Degree &dValue)
	Absolute value function. More...

static Radian	Abs (const Radian &rValue)
	Absolute value function. More...

static Real	Abs (Real fValue)
	Absolute value function. More...

static Radian	ACos (Real fValue)
	Arc cosine function. More...

static float	AngleUnitsToDegrees (float units)
	Convert from the current AngleUnit to degrees. More...

static float	AngleUnitsToRadians (float units)
	Convert from the current AngleUnit to radians. More...

static Radian	ASin (Real fValue)
	Arc sine function. More...

static Radian	ATan (float fValue)
	Arc tangent function. More...

static Radian	ATan2 (float fY, float fX)
	Arc tangent between two values function. More...

static Real	boundingRadiusFromAABB (const AxisAlignedBox &aabb)
	Get the radius of the origin-centered bounding sphere from the bounding box. More...

static Real	boundingRadiusFromAABBCentered (const AxisAlignedBox &aabb)
	Get the radius of the bbox-centered bounding sphere from the bounding box. More...

static Affine3	buildReflectionMatrix (const Plane &p)
	Build a reflection matrix for the passed in plane. More...

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

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

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. More...

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. More...

static Vector3	calculateTangentSpaceVector (const Vector3 &position1, const Vector3 &position2, const Vector3 &position3, Real u1, Real v1, Real u2, Real v2, Real u3, Real v3)

static Real	Ceil (Real fValue)
	Ceiling function Returns the smallest following integer. More...

template<typename T >
static T	Clamp (T val, T minval, T maxval)
	Clamp a value within an inclusive range. More...

static float	Cos (const Radian &fValue, bool useTables=false)
	Cosine function. More...

static float	Cos (float fValue, bool useTables=false)
	Cosine function. More...

static float	DegreesToAngleUnits (float degrees)
	Convert from degrees to the current AngleUnit. More...

static float	DegreesToRadians (float degrees)

static Real	Exp (Real fValue)

static Real	Floor (Real fValue)
	Floor function Returns the largest previous integer. More...

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. More...

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

static int	IAbs (int iValue)

static int	ICeil (float fValue)

static int	IFloor (float fValue)

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

static RayTestResult	intersects (const Ray &ray, const AxisAlignedBox &box)
	Ray / box intersection. More...

static bool	intersects (const Ray &ray, const AxisAlignedBox &box, Real d1, Real d2)
	Ray / box intersection, returns boolean result and two intersection distance. More...

static RayTestResult	intersects (const Ray &ray, const Plane &plane)
	Ray / plane intersection. More...

static RayTestResult	intersects (const Ray &ray, const Sphere &sphere, bool discardInside=true)
	Ray / sphere intersection. More...

static RayTestResult	intersects (const Ray &ray, const std::list< Plane > &planeList, bool normalIsOutside)

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

static RayTestResult	intersects (const Ray &ray, const Vector3 &a, const Vector3 &b, const Vector3 &c, bool positiveSide=true, bool negativeSide=true)
	Ray / triangle intersection [12], returns boolean result and distance. More...

static RayTestResult	intersects (const Ray &ray, const Vector3 &a, const Vector3 &b, const Vector3 &c, const Vector3 &normal, bool positiveSide=true, bool negativeSide=true)

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

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

static Real	InvSqrt (Real fValue)
	Inverse square root i.e. More...

static int	ISign (int iValue)

static bool	isNaN (Real f)

template<typename V , typename T >
static V	lerp (const V &v0, const V &v1, const T &t)
	Simulate the shader function lerp which performers linear interpolation. More...

static Real	Log (Real fValue)

static Real	Log2 (Real fValue)

static Real	LogN (Real base, Real fValue)

static Matrix3	lookRotation (const Vector3 &direction, const Vector3 &yaw)
	Create a rotation matrix from direction and yaw. More...

static Matrix4	makePerspectiveMatrix (Real left, Real right, Real bottom, Real top, Real zNear, Real zFar)
	This creates 'uniform' perspective projection matrix, which depth range [-1,1], right-handed rules. More...

static Affine3	makeViewMatrix (const Vector3 &position, const Quaternion &orientation, const Affine3 *reflectMatrix=0)
	This creates a view matrix. More...

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. More...

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. More...

static Real	Pow (Real fBase, Real fExponent)

static float	RadiansToAngleUnits (float radians)
	Convert from radians to the current AngleUnit . More...

static float	RadiansToDegrees (float radians)

static float	RangeRandom (float fLow, float fHigh)
	Generate a random number within the range provided. More...

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

static double	saturate (double t)

static float	saturate (float t)
	Simulate the shader function saturate that clamps a parameter value between 0 and 1. More...

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

static void	SetRandomValueProvider (RandomValueProvider *provider)

static Degree	Sign (const Degree &dValue)

static Radian	Sign (const Radian &rValue)

static Real	Sign (Real fValue)

static float	Sin (const Radian &fValue, bool useTables=false)
	Sine function. More...

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

static Real	Sqr (Real fValue)
	Squared function. More...

static Degree	Sqrt (const Degree &fValue)
	Square root function. More...

static Radian	Sqrt (const Radian &fValue)
	Square root function. More...

static Real	Sqrt (Real fValue)
	Square root function. More...

static float	SymmetricRandom ()
	Generate a random number in the range [-1,1]. More...

static float	Tan (const Radian &fValue, bool useTables=false)
	Tangent function. More...

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

static uint16	uint16Cast (size_t t)
	saturated cast of size_t to uint16 More...

static float	UnitRandom ()
	Generate a random number of unit length. More...

Static Public Attributes
static constexpr float	fDeg2Rad = PI / Real(180.0)

static constexpr float	fRad2Deg = Real(180.0) / PI

static constexpr Real	HALF_PI = Real( 0.5 * PI )

static constexpr Real	LOG2 = static_cast<Real> (0.69314718055994530942)
	Stored value of log(2) for frequent use. More...

static constexpr Real	NEG_INFINITY = -std::numeric_limits<Real>::infinity()

static constexpr Real	PI = static_cast<Real> (3.14159265358979323846)

static constexpr Real	POS_INFINITY = std::numeric_limits<Real>::infinity()

static constexpr Real	TWO_PI = Real( 2.0 * PI )

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.

Member Enumeration Documentation

◆ AngleUnit

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

Enumerator
AU_DEGREE
AU_RADIAN

Constructor & Destructor Documentation

◆ Math()

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

◆ ~Math()

Ogre::Math::~Math ( )

Default destructor.

Member Function Documentation

◆ IAbs()

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

inlinestatic

◆ ICeil()

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

inlinestatic

◆ IFloor()

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

inlinestatic

◆ ISign()

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

inlinestatic

◆ Abs() [1/3]

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

inlinestatic

Absolute value function.

Parameters

fValue The value whose absolute value will be returned.

Referenced by Ogre::VectorBase< 3, Real >::absDotProduct(), Ogre::VectorBase< 3, Real >::directionEquals(), Ogre::Quaternion::equals(), Ogre::VectorBase< 3, Real >::getRotationTo(), Ogre::Ray::intersects(), Ogre::Sphere::intersects(), Ogre::Volume::OctreeNode::isIsoSurfaceNear(), Ogre::VectorBase< 3, Real >::perpendicular(), Ogre::VectorBase< 3, Real >::primaryAxis(), and Ogre::AxisAlignedBox::transform().

◆ Abs() [2/3]

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

inlinestatic

Absolute value function.

Parameters

dValue The value, in degrees, whose absolute value will be returned.

References Ogre::Degree::valueDegrees().

◆ Abs() [3/3]

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

inlinestatic

Absolute value function.

Parameters

rValue The value, in radians, whose absolute value will be returned.

References Ogre::Radian::valueRadians().

◆ ACos()

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

static

Arc cosine function.

Parameters

fValue The value whose arc cosine will be returned.

Referenced by Ogre::Vector< dims, T >::angleBetween(), Ogre::VectorBase< 3, Real >::directionEquals(), and Ogre::Quaternion::equals().

◆ ASin()

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

static

Arc sine function.

Parameters

fValue The value whose arc sine will be returned.

◆ ATan()

static Radian Ogre::Math::ATan ( float fValue )

inlinestatic

Arc tangent function.

Parameters

fValue The value whose arc tangent will be returned.

◆ ATan2()

static Radian Ogre::Math::ATan2	(	float	fY,
		float	fX
	)

inlinestatic

Arc tangent between two values function.

Parameters

fY	The first value to calculate the arc tangent with.
fX	The second value to calculate the arc tangent with.

◆ Ceil()

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

inlinestatic

Ceiling function Returns the smallest following integer.

(example: Ceil(1.1) = 2)

Parameters

fValue The value to round up to the nearest integer.

◆ isNaN()

static bool Ogre::Math::isNaN ( Real f )

inlinestatic

Referenced by Ogre::DualQuaternion::isNaN(), Ogre::Quaternion::isNaN(), and Ogre::Vector< dims, T >::isNaN().

◆ Cos() [1/2]

static float Ogre::Math::Cos	(	const Radian &	fValue,
		bool	useTables = `false`
	)

inlinestatic

Cosine function.

Parameters

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

References Ogre::Radian::valueRadians().

Referenced by Ogre::VectorBase< 2, Real >::randomDeviant().

◆ Cos() [2/2]

static float Ogre::Math::Cos	(	float	fValue,
		bool	useTables = `false`
	)

inlinestatic

Cosine function.

Parameters

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

◆ Exp()

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

inlinestatic

◆ Floor()

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

inlinestatic

Floor function Returns the largest previous integer.

(example: Floor(1.9) = 1)

Parameters

fValue The value to round down to the nearest integer.

◆ Log()

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

inlinestatic

◆ Log2()

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

inlinestatic

◆ LogN()

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

inlinestatic

◆ Pow()

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

inlinestatic

◆ Sign() [1/3]

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

inlinestatic

◆ Sign() [2/3]

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

inlinestatic

References Ogre::Radian::valueRadians().

◆ Sign() [3/3]

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

inlinestatic

References Ogre::Degree::valueDegrees().

◆ saturate() [1/2]

static float Ogre::Math::saturate ( float t )

inlinestatic

Simulate the shader function saturate that clamps a parameter value between 0 and 1.

◆ saturate() [2/2]

static double Ogre::Math::saturate ( double t )

inlinestatic

◆ uint16Cast()

static uint16 Ogre::Math::uint16Cast ( size_t t )

inlinestatic

saturated cast of size_t to uint16

◆ lerp()

template<typename V , typename T >

static V Ogre::Math::lerp	(	const V &	v0,
		const V &	v1,
		const T &	t
	)

inlinestatic

Simulate the shader function lerp which performers linear interpolation.

given 3 parameters v0, v1 and t the function returns the value of (1 - t)* v0 + t * v1. where v0 and v1 are matching vector or scalar types and t can be either a scalar or a vector of the same type as a and b.

◆ Sin() [1/2]

static float Ogre::Math::Sin	(	const Radian &	fValue,
		bool	useTables = `false`
	)

inlinestatic

Sine function.

Parameters

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

References Ogre::Radian::valueRadians().

Referenced by Ogre::VectorBase< 2, Real >::randomDeviant().

◆ Sin() [2/2]

static float Ogre::Math::Sin	(	Real	fValue,
		bool	useTables = `false`
	)

inlinestatic

Sine function.

Parameters

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

◆ Sqr()

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

inlinestatic

Squared function.

Parameters

fValue The value to be squared (fValue^2)

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

◆ Sqrt() [1/3]

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

inlinestatic

Square root function.

Parameters

fValue The value whose square root will be calculated.

Referenced by Ogre::AxisAlignedBox::distance(), Ogre::VectorBase< 3, Real >::getRotationTo(), Ogre::Ray::intersects(), Ogre::Vector< dims, T >::length(), Ogre::Sphere::merge(), and Ogre::Quaternion::Norm().

◆ Sqrt() [2/3]

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

inlinestatic

Square root function.

Parameters

fValue The value, in radians, whose square root will be calculated.

Returns: The square root of the angle in radians.

References Ogre::Radian::valueRadians().

◆ Sqrt() [3/3]

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

inlinestatic

Square root function.

Parameters

fValue The value, in degrees, whose square root will be calculated.

Returns: The square root of the angle in degrees.

References Ogre::Degree::valueDegrees().

◆ InvSqrt()

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

inlinestatic

Inverse square root i.e.

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

Parameters

fValue The value whose inverse square root will be calculated.

◆ UnitRandom()

static float Ogre::Math::UnitRandom ( )

static

Generate a random number of unit length.

Returns: A random number in the range from [0,1].

Referenced by Ogre::VectorBase< 3, Real >::randomDeviant().

◆ RangeRandom()

static float Ogre::Math::RangeRandom	(	float	fLow,
		float	fHigh
	)

inlinestatic

Generate a random number within the range provided.

Parameters

fLow	The lower bound of the range.
fHigh	The upper bound of the range.

Returns: A random number in the range from [fLow,fHigh].

Referenced by Ogre::VectorBase< 2, Real >::randomDeviant().

◆ SymmetricRandom()

static float Ogre::Math::SymmetricRandom ( )

inlinestatic

Generate a random number in the range [-1,1].

Returns: A random number in the range from [-1,1].

◆ SetRandomValueProvider()

static void Ogre::Math::SetRandomValueProvider ( RandomValueProvider * provider )

static

◆ Tan() [1/2]

static float Ogre::Math::Tan	(	const Radian &	fValue,
		bool	useTables = `false`
	)

inlinestatic

Tangent function.

Parameters

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

References Ogre::Radian::valueRadians().

◆ Tan() [2/2]

static float Ogre::Math::Tan	(	Real	fValue,
		bool	useTables = `false`
	)

inlinestatic

Tangent function.

Parameters

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

◆ DegreesToRadians()

static float Ogre::Math::DegreesToRadians ( float degrees )

inlinestatic

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

◆ RadiansToDegrees()

static float Ogre::Math::RadiansToDegrees ( float radians )

inlinestatic

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

◆ setAngleUnit()

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.

◆ getAngleUnit()

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

static

Get the unit being used for angles.

◆ AngleUnitsToRadians()

static float Ogre::Math::AngleUnitsToRadians ( float units )

static

Convert from the current AngleUnit to radians.

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

◆ RadiansToAngleUnits()

static float Ogre::Math::RadiansToAngleUnits ( float radians )

static

Convert from radians to the current AngleUnit .

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

◆ AngleUnitsToDegrees()

static float Ogre::Math::AngleUnitsToDegrees ( float units )

static

Convert from the current AngleUnit to degrees.

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

◆ DegreesToAngleUnits()

static float Ogre::Math::DegreesToAngleUnits ( float degrees )

static

Convert from degrees to the current AngleUnit.

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

◆ pointInTri2D()

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

p	The point.
a	The triangle's first vertex.
b	The triangle's second vertex.
c	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.

◆ pointInTri3D()

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

p	p The point.
a	The triangle's first vertex.
b	The triangle's second vertex.
c	The triangle's third vertex.
normal	The 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.

◆ intersects() [1/7]

static RayTestResult Ogre::Math::intersects	(	const Ray &	ray,
		const AxisAlignedBox &	box
	)

static

Ray / box intersection.

◆ intersects() [2/7]

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

ray	The ray.
box	The box.
d1	A real pointer to retrieve the near intersection distance from the ray origin, maybe null which means don't care about the near intersection distance.
d2	A 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.

◆ intersects() [3/7]

static RayTestResult 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 [12], returns boolean result and distance.

Parameters

ray	The ray.
a	The triangle's first vertex.
b	The triangle's second vertex.
c	The triangle's third vertex.
positiveSide	Intersect with "positive side" of the triangle (as determined by vertex winding)
negativeSide	Intersect with "negative side" of the triangle (as determined by vertex winding)

◆ intersects() [4/7]

static RayTestResult Ogre::Math::intersects	(	const Ray &	ray,
		const Vector3 &	a,
		const Vector3 &	b,
		const Vector3 &	c,
		const Vector3 &	normal,
		bool	positiveSide = `true`,
		bool	negativeSide = `true`
	)

inlinestatic

Deprecated:: normal parameter is not used any more

◆ intersects() [5/7]

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

static

Sphere / box intersection test.

◆ intersects() [6/7]

static RayTestResult 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
planeList	List of planes which form a convex volume
normalIsOutside	Does the normal point outside the volume

◆ intersects() [7/7]

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

static

Deprecated:: migrate to PlaneList

◆ RealEqual()

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

inlinestatic

Compare 2 reals, using tolerance for inaccuracies.

Referenced by Ogre::VectorBase< 3, Real >::getRotationTo(), Ogre::Matrix3::hasScale(), and Ogre::Vector< dims, T >::positionEquals().

◆ calculateTangentSpaceVector()

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

Deprecated:: use TangentSpaceCalc

◆ buildReflectionMatrix()

static Affine3 Ogre::Math::buildReflectionMatrix ( const Plane & p )

static

Build a reflection matrix for the passed in plane.

◆ gaussianDistribution()

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.

◆ Clamp()

template<typename T >

static T Ogre::Math::Clamp	(	T	val,
		T	minval,
		T	maxval
	)

inlinestatic

Clamp a value within an inclusive range.

Referenced by Ogre::Vector< dims, T >::angleBetween().

◆ makeViewMatrix()

static Affine3 Ogre::Math::makeViewMatrix	(	const Vector3 &	position,
		const Quaternion &	orientation,
		const Affine3 *	reflectMatrix = `0`
	)

static

This creates a view matrix.

[ Lx Uy Dz Tx ] [ Lx Uy Dz Ty ] [ Lx Uy Dz Tz ] [ 0 0 0 1 ]

Where T = -(Transposed(Rot) * Pos)

◆ makePerspectiveMatrix()

static Matrix4 Ogre::Math::makePerspectiveMatrix	(	Real	left,
		Real	right,
		Real	bottom,
		Real	top,
		Real	zNear,
		Real	zFar
	)

static

This creates 'uniform' perspective projection matrix, which depth range [-1,1], right-handed rules.

[ A 0 C 0 ] [ 0 B D 0 ] [ 0 0 q qn ] [ 0 0 -1 0 ]

A = 2 * near / (right - left) B = 2 * near / (top - bottom) C = (right + left) / (right - left) D = (top + bottom) / (top - bottom) q = - (far + near) / (far - near) qn = - 2 * (far * near) / (far - near)

◆ boundingRadiusFromAABB()

static Real Ogre::Math::boundingRadiusFromAABB ( const AxisAlignedBox & aabb )

static

Get the radius of the origin-centered bounding sphere from the bounding box.

◆ boundingRadiusFromAABBCentered()

static Real Ogre::Math::boundingRadiusFromAABBCentered ( const AxisAlignedBox & aabb )

static

Get the radius of the bbox-centered bounding sphere from the bounding box.

Member Data Documentation

◆ LOG2

constexpr Real Ogre::Math::LOG2 = static_cast<Real> (0.69314718055994530942)

staticconstexpr

Stored value of log(2) for frequent use.

◆ POS_INFINITY

constexpr Real Ogre::Math::POS_INFINITY = std::numeric_limits<Real>::infinity()

staticconstexpr

Referenced by Ogre::AxisAlignedBox::getHalfSize(), Ogre::AxisAlignedBox::getSize(), and Ogre::AxisAlignedBox::volume().

◆ NEG_INFINITY

constexpr Real Ogre::Math::NEG_INFINITY = -std::numeric_limits<Real>::infinity()

staticconstexpr

◆ PI

constexpr Real Ogre::Math::PI = static_cast<Real> (3.14159265358979323846)

staticconstexpr

◆ TWO_PI

constexpr Real Ogre::Math::TWO_PI = Real( 2.0 * PI )

staticconstexpr

Referenced by Ogre::VectorBase< 2, Real >::angleTo(), and Ogre::VectorBase< 3, Real >::randomDeviant().

◆ HALF_PI

constexpr Real Ogre::Math::HALF_PI = Real( 0.5 * PI )

staticconstexpr

◆ fDeg2Rad

constexpr float Ogre::Math::fDeg2Rad = PI / Real(180.0)

staticconstexpr

◆ fRad2Deg

constexpr float Ogre::Math::fRad2Deg = Real(180.0) / PI

staticconstexpr

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

Classes

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Enumeration Documentation

◆ AngleUnit

Constructor & Destructor Documentation

◆ Math()

◆ ~Math()

Member Function Documentation

◆ IAbs()

◆ ICeil()

◆ IFloor()

◆ ISign()

◆ Abs() [1/3]

◆ Abs() [2/3]

◆ Abs() [3/3]

◆ ACos()

◆ ASin()

◆ ATan()

◆ ATan2()

◆ Ceil()

◆ isNaN()

◆ Cos() [1/2]

◆ Cos() [2/2]

◆ Exp()

◆ Floor()

◆ Log()

◆ Log2()

◆ LogN()

◆ Pow()

◆ Sign() [1/3]

◆ Sign() [2/3]

◆ Sign() [3/3]

◆ saturate() [1/2]

◆ saturate() [2/2]

◆ uint16Cast()

◆ lerp()

◆ Sin() [1/2]

◆ Sin() [2/2]

◆ Sqr()

◆ Sqrt() [1/3]

◆ Sqrt() [2/3]

◆ Sqrt() [3/3]

◆ InvSqrt()

◆ UnitRandom()

◆ RangeRandom()

◆ SymmetricRandom()

◆ SetRandomValueProvider()

◆ Tan() [1/2]

◆ Tan() [2/2]

◆ DegreesToRadians()

◆ RadiansToDegrees()

◆ setAngleUnit()

◆ getAngleUnit()

◆ AngleUnitsToRadians()

◆ RadiansToAngleUnits()

◆ AngleUnitsToDegrees()

◆ DegreesToAngleUnits()

◆ pointInTri2D()

◆ pointInTri3D()

◆ intersects() [1/7]

◆ intersects() [2/7]

◆ intersects() [3/7]

◆ intersects() [4/7]

◆ intersects() [5/7]

◆ intersects() [6/7]

◆ intersects() [7/7]

◆ RealEqual()

◆ calculateTangentSpaceVector()

◆ buildReflectionMatrix()

◆ gaussianDistribution()

◆ Clamp()

◆ makeViewMatrix()

◆ makePerspectiveMatrix()

◆ boundingRadiusFromAABB()

◆ boundingRadiusFromAABBCentered()

Member Data Documentation