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

#include <Math.h>

Public Member Functions
	Math (unsigned int trigTableSize=4096)
	Default constructor. More...

	~Math ()
	Default destructor. More...

Static Public Member Functions
static int	iabs (int iValue)

static int	iceil (real fValue)

static int	ifloor (real fValue)

static int	isign (int iValue)

static real	abs (real fValue)

static real	acos (real fValue)

static real	asin (real fValue)

static real	atan (real fValue)

static real	atan2 (real fY, real fX)

static real	ceil (real fValue)

static bool	isNaN (real f)

static real	cos (real fValue, bool useTables=false)
	Cosine function. More...

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 real	sin (real fValue, bool useTables=false)
	Sine function. More...

static real	sqr (real fValue)

static real	sqrt (real fValue)

static real	unitRandom ()

static real	rangeRandom (real fLow, real fHigh)

static real	symmetricRandom ()

static real	tan (real fValue, bool useTables=false)
	Tangent function. More...

static real	degreesToRadians (real degrees)

static real	radiansToDegrees (real radians)

static bool	pointInTri2D (const Vector2f &p, const Vector2f &a, const Vector2f &b, const Vector2f &c)
	Checks whether a given point is inside a triangle, in a 2-dimensional (Cartesian) space. More...

static bool	pointInTri3D (const Vector3f &p, const Vector3f &a, const Vector3f &b, const Vector3f &c, const Vector3f &normal)
	Checks whether a given 3D point is inside a triangle. More...

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

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

static std::pair< bool, real >	intersects (const Ray &ray, const AlignedBox3 &box)
	Ray / box intersection, returns boolean result and distance. More...

static bool	intersects (const Ray &ray, const AlignedBox3 &box, real d1, real d2)
	Ray / box intersection, returns boolean result and two intersection distance. More...

static std::pair< bool, real >	intersects (const Ray &ray, const Vector3f &a, const Vector3f &b, const Vector3f &c, const Vector3f &normal, bool positiveSide=true, bool negativeSide=true)
	Ray / triangle intersection, returns boolean result and distance. More...

static std::pair< bool, real >	intersects (const Ray &ray, const Vector3f &a, const Vector3f &b, const Vector3f &c, bool positiveSide=true, bool negativeSide=true)
	Ray / triangle intersection, returns boolean result and distance. More...

static bool	intersects (const Sphere &sphere, const AlignedBox3 &box)
	Sphere / box intersection test. More...

static bool	intersects (const Plane &plane, const AlignedBox3 &box)
	Plane / box intersection test. More...

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

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

static Vector3f	calculateTangentSpaceVector (const Vector3f &position1, const Vector3f &position2, const Vector3f &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. More...

static Matrix4f	buildReflectionMatrix (const Plane &p)
	Build a reflection matrix for the passed in plane. More...

static Vector4f	calculateFaceNormal (const Vector3f &v1, const Vector3f &v2, const Vector3f &v3)
	Calculate a face normal, including the w component which is the offset from the origin. More...

static Vector3f	calculateBasicFaceNormal (const Vector3f &v1, const Vector3f &v2, const Vector3f &v3)
	Calculate a face normal, no w-information. More...

static Vector4f	calculateFaceNormalWithoutNormalize (const Vector3f &v1, const Vector3f &v2, const Vector3f &v3)
	Calculate a face normal without normalize, including the w component which is the offset from the origin. More...

static Vector3f	calculateBasicFaceNormalWithoutNormalize (const Vector3f &v1, const Vector3f &v2, const Vector3f &v3)
	Calculate a face normal without normalize, no w-information. 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 real	Clamp (real val, real minval, real maxval)
	Clamp a value within an inclusive range. More...

static AffineTransform3	makeViewMatrix (const Vector3f &position, const Quaternion &orientation)

static Matrix4f	makePerspectiveMatrix (float fov, float aspect, float nearZ, float farZ)

static real	boundingRadiusFromAABB (const AlignedBox3 &aabb)
	Get a bounding radius value from a bounding box. More...

static Quaternion	buildRotation (const Vector3f &a, const Vector3f &b, const Vector3f &fallbackAxis)
	Compute a quaternion rotation transforming vector a to vector b. More...

static Vector3f	quaternionToEuler (const Quaternion &quat)
	Converts a quaternion to euler angles (pitch, yaw, roll) More...

static Quaternion	quaternionFromEuler (const Vector3f &pitchYawRoll)

static Ray	unproject (const Vector2f &point, const AffineTransform3 &modelview, const Transform3 &projection, const Rect &viewport)

static Ray	unprojectNormalized (const Vector2f &point, const AffineTransform3 &modelview, const Transform3 &projection)

static Vector3f	project (const Vector3f &point, const AffineTransform3 &modelview, const Transform3 &projection, const Rect &viewport)

static Vector3f	normal (const Vector3f &aa, const Vector3f &bb, const Vector3f &cc)

static AffineTransform3	computeMatchingPointsTransform (const Vectors3f &src, const Vectors3f &dst)

static void	swapMinMax (real &min, real &max)

Static Public Attributes
static const real	Log2Base
	Stored value of log(2) for frequent use. More...

static const real	PositiveInfinity

static const real	NegativeInfinity

static const float	Pi

static const real	TwoPi

static const real	HalfPi

static const real	DegToRad

static const real	RadToDeg

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

Static Protected Member Functions
static real	SinTable (real fValue)

static real	TanTable (real fValue)

Static Protected Attributes
static int	mTrigTableSize
	Size of the trig tables as determined by constructor. More...

static real	mTrigTableFactor
	Radian -> index factor value ( mTrigTableSize / 2 * Pi ) More...

static real *	mSinTable

static real *	mTanTable

Detailed Description

Class to provide access to common mathematical functions.

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

Note: This is based on MgcMath.h from Wild Magic.

Constructor & Destructor Documentation

omicron::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

omicron::Math::~Math ( )

Default destructor.

Member Function Documentation

static real omicron::Math::abs ( real fValue )

inlinestatic

static real omicron::Math::acos ( real fValue )

static

static real omicron::Math::asin ( real fValue )

static

static real omicron::Math::atan ( real fValue )

inlinestatic

static real omicron::Math::atan2	(	real	fY,
		real	fX
	)

inlinestatic

static real omicron::Math::boundingRadiusFromAABB ( const AlignedBox3 & aabb )

static

Get a bounding radius value from a bounding box.

static Matrix4f omicron::Math::buildReflectionMatrix ( const Plane & p )

static

Build a reflection matrix for the passed in plane.

static Quaternion omicron::Math::buildRotation	(	const Vector3f &	a,
		const Vector3f &	b,
		const Vector3f &	fallbackAxis
	)

static

Compute a quaternion rotation transforming vector a to vector b.

void omicron::Math::buildTrigTables ( )

protected

Private function to build trig tables.

static Vector3f omicron::Math::calculateBasicFaceNormal	(	const Vector3f &	v1,
		const Vector3f &	v2,
		const Vector3f &	v3
	)

static

Calculate a face normal, no w-information.

static Vector3f omicron::Math::calculateBasicFaceNormalWithoutNormalize	(	const Vector3f &	v1,
		const Vector3f &	v2,
		const Vector3f &	v3
	)

static

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

static Vector4f omicron::Math::calculateFaceNormal	(	const Vector3f &	v1,
		const Vector3f &	v2,
		const Vector3f &	v3
	)

static

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

static Vector4f omicron::Math::calculateFaceNormalWithoutNormalize	(	const Vector3f &	v1,
		const Vector3f &	v2,
		const Vector3f &	v3
	)

static

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

static Vector3f omicron::Math::calculateTangentSpaceVector	(	const Vector3f &	position1,
		const Vector3f &	position2,
		const Vector3f &	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 omicron::Math::ceil ( real fValue )

inlinestatic

static real omicron::Math::Clamp	(	real	val,
		real	minval,
		real	maxval
	)

inlinestatic

Clamp a value within an inclusive range.

static AffineTransform3 omicron::Math::computeMatchingPointsTransform	(	const Vectors3f &	src,
		const Vectors3f &	dst
	)

static

static real omicron::Math::cos	(	real	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.

static real omicron::Math::degreesToRadians ( real degrees )

inlinestatic

static real omicron::Math::exp ( real fValue )

inlinestatic

static bool omicron::Math::floatEqual	(	real	a,
		real	b,
		real	tolerance = `std::numeric_limits< real >::epsilon()`
	)

static

Compare 2 reals, using tolerance for inaccuracies.

static real omicron::Math::floor ( real fValue )

inlinestatic

static real omicron::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 int omicron::Math::iabs ( int iValue )

inlinestatic

static int omicron::Math::iceil ( real fValue )

inlinestatic

static int omicron::Math::ifloor ( real fValue )

inlinestatic

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

static

Ray / plane intersection, returns boolean result and distance.

static std::pair<bool, real> omicron::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> omicron::Math::intersects	(	const Ray &	ray,
		const AlignedBox3 &	box
	)

static

Ray / box intersection, returns boolean result and distance.

static bool omicron::Math::intersects	(	const Ray &	ray,
		const AlignedBox3 &	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.

static std::pair<bool, real> omicron::Math::intersects	(	const Ray &	ray,
		const Vector3f &	a,
		const Vector3f &	b,
		const Vector3f &	c,
		const Vector3f &	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.

static std::pair<bool, real> omicron::Math::intersects	(	const Ray &	ray,
		const Vector3f &	a,
		const Vector3f &	b,
		const Vector3f &	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.

static bool omicron::Math::intersects	(	const Sphere &	sphere,
		const AlignedBox3 &	box
	)

static

Sphere / box intersection test.

static bool omicron::Math::intersects	(	const Plane &	plane,
		const AlignedBox3 &	box
	)

static

Plane / box intersection test.

static std::pair<bool, real> omicron::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

static std::pair<bool, real> omicron::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

static bool omicron::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 int omicron::Math::isign ( int iValue )

static

static bool omicron::Math::isNaN ( real f )

inlinestatic

static real omicron::Math::log ( real fValue )

inlinestatic

static real omicron::Math::log2 ( real fValue )

inlinestatic

static real omicron::Math::logN	(	real	base,
		real	fValue
	)

inlinestatic

static Matrix4f omicron::Math::makePerspectiveMatrix	(	float	fov,
		float	aspect,
		float	nearZ,
		float	farZ
	)

static

static AffineTransform3 omicron::Math::makeViewMatrix	(	const Vector3f &	position,
		const Quaternion &	orientation
	)

static

static Vector3f omicron::Math::normal	(	const Vector3f &	aa,
		const Vector3f &	bb,
		const Vector3f &	cc
	)

static

static bool omicron::Math::pointInTri2D	(	const Vector2f &	p,
		const Vector2f &	a,
		const Vector2f &	b,
		const Vector2f &	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.

static bool omicron::Math::pointInTri3D	(	const Vector3f &	p,
		const Vector3f &	a,
		const Vector3f &	b,
		const Vector3f &	c,
		const Vector3f &	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.

static real omicron::Math::pow	(	real	fBase,
		real	fExponent
	)

inlinestatic

static Vector3f omicron::Math::project	(	const Vector3f &	point,
		const AffineTransform3 &	modelview,
		const Transform3 &	projection,
		const Rect &	viewport
	)

static

static Quaternion omicron::Math::quaternionFromEuler ( const Vector3f & pitchYawRoll )

static

static Vector3f omicron::Math::quaternionToEuler ( const Quaternion & quat )

static

Converts a quaternion to euler angles (pitch, yaw, roll)

static real omicron::Math::radiansToDegrees ( real radians )

inlinestatic

static real omicron::Math::rangeRandom	(	real	fLow,
		real	fHigh
	)

static

static real omicron::Math::sign ( real fValue )

static

static real omicron::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.

static real omicron::Math::SinTable ( real fValue )

staticprotected

static real omicron::Math::sqr ( real fValue )

inlinestatic

static real omicron::Math::sqrt ( real fValue )

inlinestatic

static void omicron::Math::swapMinMax	(	real &	min,
		real &	max
	)

static

static real omicron::Math::symmetricRandom ( )

static

static real omicron::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.

static real omicron::Math::TanTable ( real fValue )

staticprotected

static real omicron::Math::unitRandom ( )

static

static Ray omicron::Math::unproject	(	const Vector2f &	point,
		const AffineTransform3 &	modelview,
		const Transform3 &	projection,
		const Rect &	viewport
	)

static

static Ray omicron::Math::unprojectNormalized	(	const Vector2f &	point,
		const AffineTransform3 &	modelview,
		const Transform3 &	projection
	)

static

Member Data Documentation

const real omicron::Math::DegToRad

static

const real omicron::Math::HalfPi

static

const real omicron::Math::Log2Base

static

Stored value of log(2) for frequent use.

real* omicron::Math::mSinTable

staticprotected

real* omicron::Math::mTanTable

staticprotected

real omicron::Math::mTrigTableFactor

staticprotected

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

int omicron::Math::mTrigTableSize

staticprotected

Size of the trig tables as determined by constructor.

const real omicron::Math::NegativeInfinity

static

const float omicron::Math::Pi

static

const real omicron::Math::PositiveInfinity

static

const real omicron::Math::RadToDeg

static

const real omicron::Math::TwoPi

static

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

C:/dev/omegalib/release/src/omicron/include/omicron/math/Math.h

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Static Protected Member Functions

Static Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation