Mathematics utilitarian functions and classes. More...

Data Structures
class	AngleAxis
	The angle-axis rotation representation ( angle rotated around axis ). More...
class	Box
	An axis aligned 3D box. More...
class	Matrix
	A 4x4 matrix. More...
class	OrientedBox
	This is an oriented (rotated) bounding box, used for early collision tests. More...
class	Plane
	A 3D infinite plane. More...
class	Quaternion
	The mighty quaternion, holding rotation. More...
class	Ray
	A ray, stored as first point and direction. More...
class	Vector3D
	A 3D vector. More...
Functions
template<class T >
void	swapValues (T &rA, T &rB)
	swap variables of any type
template<class T >
T	clampValue (T aA, T aMin, T aMax)
	clamp variables of any type
NYTRO_EXPORT float32	getCos2D (float32 x1, float32 y1, float32 x2, float32 y2)
NYTRO_EXPORT Vector3D	getHermitePoint (Vector3D &rA, Vector3D &rAN, Vector3D &rBN, Vector3D &rB, float32 aTime)
	compute hermite point using control points rA,rB incoming tangent rAN, outgoing rBN, at interpolation point aTime [0..1]
NYTRO_EXPORT void	getShadowMatrix (float32 aShadowMat[4][4], float32 aGroundPlane[4], float32 aLightPos[4])
	compute a shadow matrix
NYTRO_EXPORT void	getReflectedPoint (Vector3D &rN, Vector3D &rL, Vector3D &rR)
NYTRO_EXPORT void	getRefractedPoint (Vector3D &rN, Vector3D &rL, Vector3D &rR, float32 aCoef)
NYTRO_EXPORT void	getProjectedPoint (Vector3D &rP1, Vector3D &rP2, Vector3D &rP3, Vector3D &rP, Vector3D &rProj)
NYTRO_EXPORT void	setRandomSeed (int32 aSeed)
	set the random seed
NYTRO_EXPORT int32	getRandomInteger (int32 aMax)
NYTRO_EXPORT float32	getRandomFloat (float32 aLow, float32 aHigh)
NYTRO_EXPORT bool	sphereIntersect (Vector3D &rSphereCenter1, Vector3D &rSphereCenter2, Vector3D &rVelocity1, Vector3D &rVelocity2, float32 aRadius1, float32 aRadius2, float32 &rTimeIn, float32 &rTimeOut)
	intersect spheres with centers aSphereCenter1 and aSphereCenter2, with velocities aVelocity1, aVelocity2, with radiuses aRadius1, aRadius2, into rTimeIn and rTimeOut
NYTRO_EXPORT bool	triangleLineIntersect (Vector3D &rP1, Vector3D &rP2, Vector3D &rP3, Vector3D &rL1, Vector3D &rL2, Vector3D &rIntersection, float32 &rTime, bool bAcceptBackface=true)
	intersect triangle [rP1,rP2,rP3] and line [rL1,rL2], put into rIntersection the intersection point at rTime [0..1]
NYTRO_EXPORT bool	lineLineIntersect (Vector3D &rLA1, Vector3D &rLA2, Vector3D &rLB1, Vector3D &rLB2, Vector3D &rL1, Vector3D &rL2, float32 &rT1, float32 &rT2, float32 aTolerance=0.0001)
	intersect two infinite 3D lines rLA1, rLB1 and rLA2, rLB2 resulting a segment rL1,rL2 which is the smallest segment between the two lines it will also return the rT1 on line 1, and rT2 on line 2 (the actual rL1 and rL2), aTolerance is the error threshold used to detect intersection
NYTRO_EXPORT bool	segmentSegmentIntersect (Vector3D &rLA1, Vector3D &rLA2, Vector3D &rLB1, Vector3D &rLB2, Vector3D &rL1, Vector3D &rL2, float32 &rT1, float32 &rT2, float32 aSmallestDistance=0, float32 aTolerance=0.0001)
	intersect two finite 3D segment lines rLA1, rLB1 and rLA2, rLB2 resulting a segment rL1,rL2 which is the smallest segment between the two lines it will also return the rT1 on line 1, and rT2 on line 2 (the actual rL1 and rL2), aTolerance is the error threshold used to detect intersection
NYTRO_EXPORT bool	linePolylineIntersect (Vector3D &rA, Vector3D &rB, vector< Vector3D > &rPolyline, float32 aSmallestDistance=1, float32 aTolerance=0.0001)
	intersect a line with a polyline
NYTRO_EXPORT float32	getEasedValue (float32 aPrevious, float32 aCurrent, float32 aNext, float32 aEaseFrom, float32 aEaseTo)
	ease a value
NYTRO_EXPORT float32	getRandomNormalizedFloat ()
NYTRO_EXPORT Vector3D	getClosestPointOnLineSegment (Vector3D &rA, Vector3D &rB, Vector3D &rP, bool &rEdge)
NYTRO_EXPORT Vector3D	getClosestPointOnLine (Vector3D &rA, Vector3D &rB, Vector3D &rP)
NYTRO_EXPORT bool	isPointInsideEdge (Vector3D &rA, Vector3D &rB, Vector3D &rP)
NYTRO_EXPORT bool	intersectRaySphere (Vector3D &rCenter, float32 aRadius, Ray &rRay, float32 &rHitTime, Vector3D &rHitPosIn, Vector3D &rHitPosOut)
	intersect a ray/line with a sphere
Variables
const float64	kConst_2PI = 6.283185307f
const float64	kConst_PI = 3.141592654f
const float64	kConst_HalfPI = 1.570796327f
const float64	kConst_Eps = 0.001f
const float64	kConst_Epsilon = 1.0e-6
const float64	kConst_PIOver180 = kConst_PI / 180.0f
const float64	kConst_180OverPI = 180.0f / kConst_PI
const float64	kConst_PIx180 = kConst_PI * 180.0f
const float32	kMeterUnit = 1.0f
	how many world units is 1 meter
const float32	kFeetUnit = kMeterUnit * 0.3048f
const float32	kOneKm = kMeterUnit*1000.0f
const float32	kOneMile = kOneKm*1.609344f
const float32	kOneNauticalMile = kOneKm*1.852f
const float64	M_PI = kConst_PI
const float64	PI = kConst_PI

Detailed Description

Mathematics utilitarian functions and classes.

Function Documentation

template<class T >

T Nytro::Math::clampValue	(	T	aA,
		T	aMin,
		T	aMax
	)			`[inline]`

clamp variables of any type

Definition at line 87 of file nyMath.h.

NYTRO_EXPORT Vector3D Nytro::Math::getClosestPointOnLine	(	Vector3D &	rA,
		Vector3D &	rB,
		Vector3D &	rP
	)

Returns:: closest point on line

NYTRO_EXPORT Vector3D Nytro::Math::getClosestPointOnLineSegment	(	Vector3D &	rA,
		Vector3D &	rB,
		Vector3D &	rP,
		bool &	rEdge
	)

Returns:: the closest point on a limited line segment

NYTRO_EXPORT float32 Nytro::Math::getCos2D	(	float32	x1,
		float32	y1,
		float32	x2,
		float32	y2
	)

Returns:: the 2D cosinus (dot) between the lines formed by x1,y1 and x2,y2, with origin in 0,0

NYTRO_EXPORT float32 Nytro::Math::getEasedValue	(	float32	aPrevious,
		float32	aCurrent,
		float32	aNext,
		float32	aEaseFrom,
		float32	aEaseTo
	)

ease a value

NYTRO_EXPORT Vector3D Nytro::Math::getHermitePoint	(	Vector3D &	rA,
		Vector3D &	rAN,
		Vector3D &	rBN,
		Vector3D &	rB,
		float32	aTime
	)

compute hermite point using control points rA,rB incoming tangent rAN, outgoing rBN, at interpolation point aTime [0..1]

NYTRO_EXPORT void Nytro::Math::getProjectedPoint	(	Vector3D &	rP1,
		Vector3D &	rP2,
		Vector3D &	rP3,
		Vector3D &	rP,
		Vector3D &	rProj
	)

Returns:: point rP projected onto plane made by rP1,rP2,rP3 into rProj

NYTRO_EXPORT float32 Nytro::Math::getRandomFloat	(	float32	aLow,
		float32	aHigh
	)

Returns:: a random float32 between aLow and aHigh

NYTRO_EXPORT int32 Nytro::Math::getRandomInteger ( int32 aMax )

Returns:: a random integer smaller than aMax

NYTRO_EXPORT float32 Nytro::Math::getRandomNormalizedFloat ( )

Returns:: a random float32 between [0..1]

NYTRO_EXPORT void Nytro::Math::getReflectedPoint	(	Vector3D &	rN,
		Vector3D &	rL,
		Vector3D &	rR
	)

Returns:: the reflected vector rL around normal rN into rR

NYTRO_EXPORT void Nytro::Math::getRefractedPoint	(	Vector3D &	rN,
		Vector3D &	rL,
		Vector3D &	rR,
		float32	aCoef
	)

Returns:: the refracted vector rL around normal rN, into rR, using refraction index aCoef

NYTRO_EXPORT void Nytro::Math::getShadowMatrix	(	float32	aShadowMat[4][4],
		float32	aGroundPlane[4],
		float32	aLightPos[4]
	)

compute a shadow matrix

NYTRO_EXPORT bool Nytro::Math::intersectRaySphere	(	Vector3D &	rCenter,
		float32	aRadius,
		Ray &	rRay,
		float32 &	rHitTime,
		Vector3D &	rHitPosIn,
		Vector3D &	rHitPosOut
	)

intersect a ray/line with a sphere

NYTRO_EXPORT bool Nytro::Math::isPointInsideEdge	(	Vector3D &	rA,
		Vector3D &	rB,
		Vector3D &	rP
	)

Returns:: true if point is inside an edge/line

NYTRO_EXPORT bool Nytro::Math::lineLineIntersect	(	Vector3D &	rLA1,
		Vector3D &	rLA2,
		Vector3D &	rLB1,
		Vector3D &	rLB2,
		Vector3D &	rL1,
		Vector3D &	rL2,
		float32 &	rT1,
		float32 &	rT2,
		float32	aTolerance = `0.0001`
	)

intersect two infinite 3D lines rLA1, rLB1 and rLA2, rLB2 resulting a segment rL1,rL2 which is the smallest segment between the two lines
it will also return the rT1 on line 1, and rT2 on line 2 (the actual rL1 and rL2), aTolerance is the error threshold used to detect intersection

NYTRO_EXPORT bool Nytro::Math::linePolylineIntersect	(	Vector3D &	rA,
		Vector3D &	rB,
		vector< Vector3D > &	rPolyline,
		float32	aSmallestDistance = `1`,
		float32	aTolerance = `0.0001`
	)

intersect a line with a polyline

Returns:: true if the line touches one of the polyline's segments

NYTRO_EXPORT bool Nytro::Math::segmentSegmentIntersect	(	Vector3D &	rLA1,
		Vector3D &	rLA2,
		Vector3D &	rLB1,
		Vector3D &	rLB2,
		Vector3D &	rL1,
		Vector3D &	rL2,
		float32 &	rT1,
		float32 &	rT2,
		float32	aSmallestDistance = `0`,
		float32	aTolerance = `0.0001`
	)

intersect two finite 3D segment lines rLA1, rLB1 and rLA2, rLB2 resulting a segment rL1,rL2 which is the smallest segment between the two lines
it will also return the rT1 on line 1, and rT2 on line 2 (the actual rL1 and rL2), aTolerance is the error threshold used to detect intersection

NYTRO_EXPORT void Nytro::Math::setRandomSeed ( int32 aSeed )

set the random seed

NYTRO_EXPORT bool Nytro::Math::sphereIntersect	(	Vector3D &	rSphereCenter1,
		Vector3D &	rSphereCenter2,
		Vector3D &	rVelocity1,
		Vector3D &	rVelocity2,
		float32	aRadius1,
		float32	aRadius2,
		float32 &	rTimeIn,
		float32 &	rTimeOut
	)

intersect spheres with centers aSphereCenter1 and aSphereCenter2, with velocities aVelocity1, aVelocity2, with radiuses aRadius1, aRadius2, into rTimeIn and rTimeOut

template<class T >

void Nytro::Math::swapValues	(	T &	rA,
		T &	rB
	)			`[inline]`

swap variables of any type

Definition at line 79 of file nyMath.h.

NYTRO_EXPORT bool Nytro::Math::triangleLineIntersect	(	Vector3D &	rP1,
		Vector3D &	rP2,
		Vector3D &	rP3,
		Vector3D &	rL1,
		Vector3D &	rL2,
		Vector3D &	rIntersection,
		float32 &	rTime,
		bool	bAcceptBackface = `true`
	)