standard math lib More...

#include <ParaMath.h>

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.

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 float	Abs (float fValue)

static double	Abs (double fValue)

static int	Abs (int nValue)

static Degree	Abs (const Degree &dValue)

static Radian	Abs (const Radian &rValue)

static Radian	ACos (float fValue)

static Radian	ASin (float fValue)

static Radian	ATan (float fValue)

static Radian	ATan2 (float fY, float fX)

static float	Ceil (float fValue)

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	Exp (float fValue)

static float	Floor (float fValue)

static float	Log (float fValue)

static float	Pow (float fBase, float fExponent)

static float	Sign (float fValue)

static Radian	Sign (const Radian &rValue)

static Degree	Sign (const Degree &dValue)

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

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

static float	Sqr (float fValue)

static float	Sqrt (float fValue)

static double	Sqr (double fValue)

static double	Sqrt (double fValue)

static Radian	Sqrt (const Radian &fValue)

static Degree	Sqrt (const Degree &fValue)

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

static float	UnitRandom ()

static float	RangeRandom (float fLow, float fHigh)

static float	SymmetricRandom ()

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

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

static float	DegreesToRadians (float degrees)

static float	RadiansToDegrees (float radians)

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

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

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

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

static float	DegreesToAngleUnits (float degrees)
	Convert from degrees to the current AngleUnit. 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 std::pair< bool, float >	intersects (const Ray &ray, const Plane &plane)
	Ray / plane intersection, returns boolean result and distance. More...

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

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

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

static std::pair< bool, float >	intersects (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. More...

static std::pair< bool, float >	intersects (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. More...

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

static bool	intersects (const CShapeSphere &sphere, const CShapeBox &box)

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

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

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

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

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

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

static Matrix4	buildReflectionMatrix (const Plane &p)
	Build a reflection matrix for the passed in plane. 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 Vector3	calculateBasicFaceNormal (const Vector3 &v1, const Vector3 &v2, const Vector3 &v3)
	Calculate a face normal, no w-information. 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	calculateBasicFaceNormalWithoutNormalize (const Vector3 &v1, const Vector3 &v2, const Vector3 &v3)
	Calculate a face normal without normalize, no w-information. More...

static float	gaussianDistribution (float x, float offset=0.0f, float scale=1.0f)
	Generates a value based on the Gaussian (normal) distribution function with the given offset and scale parameters.

template<class T >
static T	Clamp (const T X, const T Min, const T Max)
	Clamps X to be between Min and Max, inclusive.

static Matrix4	makeViewMatrix (const Vector3 &position, const Quaternion &orientation, const Matrix4 *reflectMatrix=0)

static bool	IsEquivalent (float f1, float f2)
	Returns whether two floating-point values are equivalent within a given tolerance. More...

static bool	IsEquivalent (float f1, float f2, float tolerance)
	Returns whether two floating-point values are equivalent within a given tolerance. More...

static bool	IsEquivalent (double f1, double f2)
	Returns whether two double-sized floating-point values are equivalent. More...

static bool	IsEquivalent (double f1, double f2, double tolerance)
	Returns whether two double-sized floating-point values are equivalent within a given tolerance. More...

template<class T >
static bool	IsEquivalent (const T al, size_t acount, const T bl, size_t bcount)
	Returns whether two constant-sized arrays are equivalent. More...

static int	log2 (unsigned int x)
	this is a fast version of log2. More...

static int	log2_ceil (unsigned int x)
	this is a fast version of log2. More...

template<class T >
static T	Max (const T A, const T B)
	Returns higher value in a generic way.

template<class T >
static T	Min (const T A, const T B)
	Returns lower value in a generic way.

static int32	Trunc (float F)
	Converts a float to an integer with truncation towards zero. More...

static float	TruncFloat (float F)
	Converts a float to an integer value with truncation towards zero. More...

static float	Fractional (float Value)
	Returns the fractional part of a float. More...

static float	GridSnap (float Location, float Grid)
	Snaps a value to the nearest grid multiple.

template<class T >
static T	DivideAndRoundUp (T Dividend, T Divisor)
	Divides two integers and rounds up.

template<class T >
static T	Max3 (const T A, const T B, const T C)
	Returns highest of 3 values.

template<class T >
static T	Min3 (const T A, const T B, const T C)
	Returns lowest of 3 values.

template<class T , class U >
static T	Lerp (const T &A, const T &B, const U &Alpha)
	Performs a linear interpolation between two values, Alpha ranges from 0-1.

static int32	Rand ()
	Returns a random integer between 0 and RAND_MAX, inclusive.

static void	RandInit (int32 Seed)
	Seeds global random number functions Rand() and FRand()

static float	FRand ()
	Returns a random float between 0 and 1, inclusive. More...

static void	SRandInit (int32 Seed)
	Seeds future calls to SRand()

static float	SRand ()
	Returns a seeded random float in the range [0,1), using the seed from SRandInit(). More...

static float	FloatSelect (float Comparand, float ValueGEZero, float ValueLTZero)
	Returns value based on comparand. More...

static bool	SmoothMoveFloat1 (float &src, const float dest, const float fMaxStep)
	change src from src to dest, by a maximum of fMaxStep. More...

static bool	SmoothMoveAngle1 (float &src, const float dest, const float fMaxStep)
	change src from src to dest, by a maximum of fMaxStep. More...

static bool	SmoothMoveVec3 (Vector3 *result, const Vector3 &vPosTarget, const Vector3 &vPos, FLOAT fIncrease, FLOAT fTolerance)
	linearly (smoothly) move vPos to vPosTarget by the amount fIncrease return true if we have reached the target. More...

static float	ToStandardAngle (float fAngle)
	make sure that the angle is in the range (-Pi,Pi]

static double	ToStandardAngle (double fAngle)

static bool	MatchString (const std::string &matchPattern, const std::string &matchStr)
	check if the matchStr matches the string pattern in matchPattern More...

static bool	ComputeFacingTarget (const Vector3 &target, const Vector3 &source, FLOAT &fFacing)
	facing target in xz plane fFacing: [out] it is in the range [0, 2PI] return true if target!=source(a valid facing can be computed)

static bool	ComputeFacingTarget (const DVector3 &target, const DVector3 &source, float &fFacing)

static int	Round (float fValue)
	get the closest integer near the specified float number. More...

static float	MinVec3 (const Vector3 &v)
	Returns MIN(x, y, z);.

static float	MaxVec3 (const Vector3 &v)
	Returns MAX(x, y, z);.

template<class T >
static bool	CompareXZ (const T &a, const T &b)
	return true if equal. More...

template<class T >
static bool	CompareXZ (const T &a, const T &b, float epsilon)
	return true if equal. More...

static bool	FuzzyCompare (double p1, double p2)

static bool	FuzzyCompare (float p1, float p2)

static bool	FuzzyIsNull (double d)

static bool	FuzzyIsNull (float f)

static bool	IsNull (double d)

static bool	IsNull (float f)

template<typename T >
static bool	is_nan (T value)
	whether value is not a number, T is usually float or double

template<typename T >
static bool	is_infinity (T value)
	whether value is infinity, T is usually float or double

static void	GetMatrixScaling (const Matrix4 &globalMat, float fScalingX, float fScalingY, float *fScalingZ)
	Get the scaling factor from globalMat. More...

static Matrix4 *	CreateBillboardMatrix (Matrix4 pOut, const Matrix4 matModelview, const Vector3 *vBillboardPos, bool bAxisAligned=false)
	create a billboard matrix More...

static void	CameraRotMatrixYawPitch (Matrix4 &out, float fYaw, float fPitch)

static int	NextPowerOf2 (int x)
	get nearest power of two of x

Static Public Attributes
static const float	POS_INFINITY = std::numeric_limits<float>::infinity()

static const float	NEG_INFINITY = -std::numeric_limits<float>::infinity()

static const float	PI = float( 4.0f * atan( 1.0f ) )

static const float	TWO_PI = float( 2.0f * PI )

static const float	HALF_PI = float( 0.5 * PI )

static const float	fDeg2Rad = PI / float(180.0)

static const float	fRad2Deg = float(180.0) / PI

Protected Member Functions
void	buildTrigTables ()
	Private function to build trig tables.

Static Protected Member Functions
static float	SinTable (float fValue)

static float	TanTable (float fValue)

Static Protected Attributes
static AngleUnit	msAngleUnit

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

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

static float *	mSinTable = NULL

static float *	mTanTable = NULL

Detailed Description

standard math lib

Member Enumeration Documentation

§ AngleUnit

enum ParaEngine::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

Constructor & Destructor Documentation

§ Math()

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

Member Function Documentation

§ AngleUnitsToDegrees()

float Math::AngleUnitsToDegrees ( float units )

static

Convert from the current AngleUnit to degrees.

§ AngleUnitsToRadians()

float Math::AngleUnitsToRadians ( float units )

static

Convert from the current AngleUnit to radians.

§ buildReflectionMatrix()

Matrix4 Math::buildReflectionMatrix ( const Plane & p )

static

Build a reflection matrix for the passed in plane.

§ calculateBasicFaceNormal()

Vector3 Math::calculateBasicFaceNormal	(	const Vector3 &	v1,
		const Vector3 &	v2,
		const Vector3 &	v3
	)

static

Calculate a face normal, no w-information.

§ calculateBasicFaceNormalWithoutNormalize()

Vector3 Math::calculateBasicFaceNormalWithoutNormalize	(	const Vector3 &	v1,
		const Vector3 &	v2,
		const Vector3 &	v3
	)

static

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

§ calculateFaceNormal()

Vector4 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.

§ calculateFaceNormalWithoutNormalize()

Vector4 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.

§ calculateTangentSpaceVector()

Vector3 Math::calculateTangentSpaceVector	(	const Vector3 &	position1,
		const Vector3 &	position2,
		const Vector3 &	position3,
		float	u1,
		float	v1,
		float	u2,
		float	v2,
		float	u3,
		float	v3
	)

static

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

§ CameraRotMatrixYawPitch()

void ParaEngine::Math::CameraRotMatrixYawPitch	(	Matrix4 &	out,
		float	fYaw,
		float	fPitch
	)

static

LXZ: 2009.6.26. for unknown reasons, ParaMatrixRotationYawPitchRoll sometimes yields invalid matrix. So I need to emulate it with standard multiplication. The order of transformations is roll first, then pitch, then yaw, where:

Yaw around the y-axis, in radians.
Pitch around the x-axis, in radians.
Roll around the z-axis, in radians. ParaMatrixRotationYawPitchRoll( &mCameraRot, m_fCameraYawAngle, m_fCameraPitchAngle, 0 );

§ CompareXZ() [1/2]

template<class T >

static bool ParaEngine::Math::CompareXZ	(	const T &	a,
		const T &	b
	)

inlinestatic

return true if equal.

T is a 3D vector, such as Vector3

§ CompareXZ() [2/2]

template<class T >

static bool ParaEngine::Math::CompareXZ	(	const T &	a,
		const T &	b,
		float	epsilon
	)

inlinestatic

return true if equal.

T is a 3D vector, such as Vector3

§ Cos() [1/2]

static float ParaEngine::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.

§ Cos() [2/2]

static float ParaEngine::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.

§ CreateBillboardMatrix()

Matrix4 * ParaEngine::Math::CreateBillboardMatrix	(	Matrix4 *	pOut,
		const Matrix4 *	matModelview,
		const Vector3 *	vBillboardPos,
		bool	bAxisAligned = `false`
	)

static

create a billboard matrix

Parameters

pOut	[out], the output billboard matrix
matModelview	the current model view matrix. if NULL, the current model and view matrix on the global stack is used
vBillboardPos	the billboard position in model space. if NULL, (0,0,0) is used.
bAxisAligned	if true, it will create a billboard with Y (up) axis fixed. Default to false.

Returns: pOut is returned.

§ DegreesToAngleUnits()

float Math::DegreesToAngleUnits ( float degrees )

static

Convert from degrees to the current AngleUnit.

§ FloatSelect()

static float ParaEngine::Math::FloatSelect	(	float	Comparand,
		float	ValueGEZero,
		float	ValueLTZero
	)

inlinestatic

Returns value based on comparand.

The main purpose of this function is to avoid branching based on floating point comparison which can be avoided via compiler intrinsics.

Please note that we don't define what happens in the case of NaNs as there might be platform specific differences.

Parameters

Comparand	Comparand the results are based on
ValueGEZero	Return value if Comparand >= 0
ValueLTZero	Return value if Comparand < 0

Returns: ValueGEZero if Comparand >= 0, ValueLTZero otherwise

§ Fractional()

static float ParaEngine::Math::Fractional ( float Value )

inlinestatic

Returns the fractional part of a float.

Parameters

Value Floating point value to convert

Returns: A float between >=0 and < 1.

§ FRand()

static float ParaEngine::Math::FRand ( )

inlinestatic

Returns a random float between 0 and 1, inclusive.

§ getAngleUnit()

Math::AngleUnit Math::getAngleUnit ( void )

static

Get the unit being used for angles.

§ GetMatrixScaling()

void Math::GetMatrixScaling	(	const Matrix4 &	globalMat,
		float *	fScalingX,
		float *	fScalingY,
		float *	fScalingZ
	)

static

Get the scaling factor from globalMat.

since we need to create separate physics mesh with different scaling factors even for the same mesh model. it is assumed that components of globalMat satisfies the following equation: |(globalMat._11, globalMat._12, globalMat._13)| = 1; |(globalMat._21, globalMat._22, globalMat._23)| = 1; |(globalMat._31, globalMat._32, globalMat._33)| = 1;

Parameters

globalMat	the input matrix
fScalingX	[out] maybe NULL
fScalingY	[out] maybe NULL
fScalingZ	[out] maybe NULL

§ intersects() [1/11]

std::pair< bool, float > Math::intersects	(	const Ray &	ray,
		const Plane &	plane
	)

static

Ray / plane intersection, returns boolean result and distance.

§ intersects() [2/11]

std::pair< bool, float > Math::intersects	(	const Ray &	ray,
		const Sphere &	sphere,
		bool	discardInside = `true`
	)

static

Ray / sphere intersection, returns boolean result and distance.

§ intersects() [3/11]

std::pair< bool, float > Math::intersects	(	const Ray &	ray,
		const AxisAlignedBox &	box
	)

static

Ray / box intersection, returns boolean result and distance.

§ intersects() [4/11]

bool Math::intersects	(	const Ray &	ray,
		const AxisAlignedBox &	box,
		float *	d1,
		float *	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() [5/11]

std::pair< bool, float > 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

ray	The ray.
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), doesn't need normalised since we don't care.
positiveSide	Intersect with "positive side" of the triangle
negativeSide	Intersect 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.

§ intersects() [6/11]

std::pair< bool, float > 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

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
negativeSide	Intersect 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.

§ intersects() [7/11]

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

static

Sphere / box intersection test.

§ intersects() [8/11]

bool Math::intersects	(	const Plane &	plane,
		const AxisAlignedBox &	box
	)

static

Plane / box intersection test.

§ intersects() [9/11]

std::pair< bool, float > 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

§ intersects() [10/11]

std::pair< bool, float > 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

§ intersects() [11/11]

bool 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!

§ InvSqrt()

float Math::InvSqrt ( float fValue )

static

Inverse square root i.e.

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

§ IsEquivalent() [1/5]

static bool ParaEngine::Math::IsEquivalent	(	float	f1,
		float	f2
	)

inlinestatic

Returns whether two floating-point values are equivalent within a given tolerance.

Parameters

f1	A first floating-point value.
f2	A second floating-point value.

§ IsEquivalent() [2/5]

static bool ParaEngine::Math::IsEquivalent	(	float	f1,
		float	f2,
		float	tolerance
	)

inlinestatic

Returns whether two floating-point values are equivalent within a given tolerance.

Parameters

f1	A first floating-point value.
f2	A second floating-point value.
tolerance	The tolerance in which to accept the two floating-point values as equivalent.

§ IsEquivalent() [3/5]

static bool ParaEngine::Math::IsEquivalent	(	double	f1,
		double	f2
	)

inlinestatic

Returns whether two double-sized floating-point values are equivalent.

Parameters

f1	A first double-sized floating-point value.
f2	A second double-sized floating-point value.

§ IsEquivalent() [4/5]

static bool ParaEngine::Math::IsEquivalent	(	double	f1,
		double	f2,
		double	tolerance
	)

inlinestatic

Returns whether two double-sized floating-point values are equivalent within a given tolerance.

Parameters

f1	A first double-sized floating-point value.
f2	A second double-sized floating-point value.
tolerance	The tolerance in which to accept the two double-sized floating-point values as equivalent.

§ IsEquivalent() [5/5]

template<class T >

static bool ParaEngine::Math::IsEquivalent	(	const T *	al,
		size_t	acount,
		const T *	bl,
		size_t	bcount
	)

inlinestatic

Returns whether two constant-sized arrays are equivalent.

Parameters

al	A first constant-sized array.
acount	The number of elements in the first array.
bl	A second constant-sized array.
bcount	The number of elements in the second array.

Returns: Whether the two arrays are equivalent.

§ log2()

int Math::log2 ( unsigned int x )

static

this is a fast version of log2.

return the smaller

§ log2_ceil()

static int ParaEngine::Math::log2_ceil ( unsigned int x )

inlinestatic

this is a fast version of log2.

return the bigger

§ MatchString()

bool Math::MatchString	(	const std::string &	matchPattern,
		const std::string &	matchStr
	)

static

check if the matchStr matches the string pattern in matchPattern

Parameters

matchPattern	the match pattern. It may end with "" in which case "" will match any character(s). e.g "Li*" will match both "LiXizhi" and "LiTC", whereas "Li" will only match "Li"
matchStr	the match string.

Returns: : return true if the two string matches.

§ pointInTri2D()

bool 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()

bool 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	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.

§ RadiansToAngleUnits()

float Math::RadiansToAngleUnits ( float radians )

static

Convert from radians to the current AngleUnit .

§ Round()

int ParaEngine::Math::Round ( float fValue )

inlinestatic

get the closest integer near the specified float number.

E.g. Round(1.49)==1, Round(1.51)==2, ToInt(

§ setAngleUnit()

void Math::setAngleUnit ( Math::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.

§ Sin() [1/2]

static float ParaEngine::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.

§ Sin() [2/2]

static float ParaEngine::Math::Sin	(	float	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.

§ SmoothMoveAngle1()

bool Math::SmoothMoveAngle1	(	float &	src,
		const float	dest,
		const float	fMaxStep
	)

static

change src from src to dest, by a maximum of fMaxStep.

If dest has been reached, return true; otherwise return false.

§ SmoothMoveFloat1()

bool Math::SmoothMoveFloat1	(	float &	src,
		const float	dest,
		const float	fMaxStep
	)

static

change src from src to dest, by a maximum of fMaxStep.

If dest has been reached, return true; otherwise return false.

§ SmoothMoveVec3()

bool Math::SmoothMoveVec3	(	Vector3 *	result,
		const Vector3 &	vPosTarget,
		const Vector3 &	vPos,
		FLOAT	fIncrease,
		FLOAT	fTolerance
	)

static

linearly (smoothly) move vPos to vPosTarget by the amount fIncrease return true if we have reached the target.

if the distance between target and the pos is within fTolerance, result is set to target

§ SRand()

float Math::SRand ( )

static

Returns a seeded random float in the range [0,1), using the seed from SRandInit().

§ Tan() [1/2]

static float ParaEngine::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.

§ Tan() [2/2]

static float ParaEngine::Math::Tan	(	float	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.

§ Trunc()

static int32 ParaEngine::Math::Trunc ( float F )

inlinestatic

Converts a float to an integer with truncation towards zero.

Parameters

F	Floating point value to convert

Returns: Truncated integer.

§ TruncFloat()

static float ParaEngine::Math::TruncFloat ( float F )

inlinestatic

Converts a float to an integer value with truncation towards zero.

Parameters

F	Floating point value to convert

Returns: Truncated integer value.

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

Client/trunk/ParaEngineClient/math/ParaMath.h
Client/trunk/ParaEngineClient/Engine/MathLib.h
Client/trunk/ParaEngineClient/math/ParaMath.cpp

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Static Protected Member Functions

Static Protected Attributes

Detailed Description

Member Enumeration Documentation

§ AngleUnit

Constructor & Destructor Documentation

§ Math()

Member Function Documentation

§ AngleUnitsToDegrees()

§ AngleUnitsToRadians()

§ buildReflectionMatrix()

§ calculateBasicFaceNormal()

§ calculateBasicFaceNormalWithoutNormalize()

§ calculateFaceNormal()

§ calculateFaceNormalWithoutNormalize()

§ calculateTangentSpaceVector()

§ CameraRotMatrixYawPitch()

§ CompareXZ() [1/2]

§ CompareXZ() [2/2]

§ Cos() [1/2]

§ Cos() [2/2]

§ CreateBillboardMatrix()

§ DegreesToAngleUnits()

§ FloatSelect()

§ Fractional()

§ FRand()

§ getAngleUnit()

§ GetMatrixScaling()

§ intersects() [1/11]

§ intersects() [2/11]

§ intersects() [3/11]

§ intersects() [4/11]

§ intersects() [5/11]

§ intersects() [6/11]

§ intersects() [7/11]

§ intersects() [8/11]

§ intersects() [9/11]

§ intersects() [10/11]

§ intersects() [11/11]

§ InvSqrt()

§ IsEquivalent() [1/5]

§ IsEquivalent() [2/5]

§ IsEquivalent() [3/5]

§ IsEquivalent() [4/5]

§ IsEquivalent() [5/5]

§ log2()

§ log2_ceil()

§ MatchString()

§ pointInTri2D()

§ pointInTri3D()

§ RadiansToAngleUnits()

§ Round()

§ setAngleUnit()

§ Sin() [1/2]

§ Sin() [2/2]

§ SmoothMoveAngle1()

§ SmoothMoveFloat1()

§ SmoothMoveVec3()

§ SRand()

§ Tan() [1/2]

§ Tan() [2/2]

§ Trunc()

§ TruncFloat()