sp::math Namespace Reference

This namespace contains all mathematical basic functions such as sine, cosine, distance calculations etc. More...

Namespaces
namespace	CollisionLibrary
	Here you will find each function for collision detection, distance computation and intersection tests.
namespace	InterpolatorManager
namespace	Randomizer
	Namepsace for all random-generation functions.
namespace	Rasterizer
	Namespace for rasterization templates.
namespace	TriangleCutter
Classes
class	Interpolator
class	FunctionalInterpolator
class	UInt128
class	MD5CheckSum
class	RadianDegreeAngle
class	Degree
	Degree class. An instance of this class will always store a value in the range [0.0 .. 360.0). More...
class	Radian
	Radian class. An instance of this class will always store a value in the range [0.0 .. 2*pi). More...
class	RasterizerVertex
struct	SSplinePolynom
class	Spline
	Multi-dimensional spline class. More...
struct	STriangleCut
Typedefs
typedef FunctionalInterpolator < f32, f32,&Lerp >	LinearInterpolator
typedef FunctionalInterpolator < f32, f32,&LerpParabolic >	ParabolicInterpolator
typedef FunctionalInterpolator < f32, f32,&LerpSin >	SinInterpolator
typedef boost::function< void(s32 x, s32 y, void *UserData)	RenderPixelCallback )
	Callback function interface for rasterization without vertices.
typedef Spline< dim::point2df, f32, 2 >	Spline2D
typedef Spline< dim::vector3df, f32, 3 >	Spline3D
Enumerations
enum	ETriangleCutResults { TRIANGLECUT_NONE, TRIANGLECUT_QUAD_AND_TRIANGLE, TRIANGLECUT_TWO_TRIANGLES }
	Possible results of a triangle clip. More...
Functions
SP_EXPORT void	getVertexInterpolation (const dim::triangle3df &Triangle, const dim::vector3df &Pos, f32 &Vert, f32 &Horz)
SP_EXPORT dim::matrix4f	getTangentSpace (const dim::vector3df PosA, const dim::vector3df PosB, const dim::vector3df PosC, const dim::point2df MapA, const dim::point2df MapB, const dim::point2df MapC, dim::vector3df &Tangent, dim::vector3df &Binormal, dim::vector3df &Normal)
template<typename T >
T	getDistance (const dim::point2d< T > &PosA, const dim::point2d< T > &PosB)
	Returns the distance between the two given 2D points.
template<typename T >
T	getDistance (const dim::vector3d< T > &PosA, const dim::vector3d< T > &PosB)
	Returns the distance between the two given 3D points.
template<typename T >
T	getDistanceSq (const dim::point2d< T > &PosA, const dim::point2d< T > &PosB)
template<typename T >
T	getDistanceSq (const dim::vector3d< T > &PosA, const dim::vector3d< T > &PosB)
template<typename T >
T	getAngle (const dim::point2d< T > &A, const dim::point2d< T > &B)
template<typename T >
T	getAngle (const dim::point2d< T > &A, const dim::point2d< T > &B, const T &OffsetAngle)
template<typename T >
dim::vector3d< T >	getNormalVectorSq (const dim::vector3d< T > &PosA, const dim::vector3d< T > &PosB, const dim::vector3d< T > &PosC)
	Returns normal vector computed by the three specified coordinates.
template<typename T >
dim::vector3d< T >	getNormalVector (const dim::vector3d< T > &PosA, const dim::vector3d< T > &PosB, const dim::vector3d< T > &PosC)
	Returns normalized normal vector computed by the three specified coordinates.
template<typename T >
dim::vector3d< T >	getBarycentricCoord (const dim::triangle3d< T > &Triangle, const dim::vector3d< T > &Point)
template<typename T >
void	sortContainerConst (std::vector< T > &ObjectList, bool(*lpFuncCmp)(const T &obj1, const T &obj2))
template<typename T >
void	sortContainer (std::vector< T > &ObjectList, bool(*lpFuncCmp)(T &obj1, T &obj2))
template<class T >
T	getVertexInterpolation (const T &VertexA, const T &VertexB, const T &VertexC, const f32 Vert, const f32 Horz)
dim::vector4df	Convert (const video::color &Color)
	Returns color in form of a 4D vector. The color components R, G, B, and A are transformed to the range [0.0, 1.0].
video::color	Convert (const dim::vector4df &Color)
	Returns color in typical form. The color components R, G, B, and A are transformed to the range [0, 255].
template<typename T >
T	Abs (const T &Value)
	Returns the absolute value of the given parameter (5 -> 5 and -5 -> 5).
template<typename T >
T	Max (const T &A, const T &B)
	Returns the largest value of the specified variables.
template<typename T >
T	Min (const T &A, const T &B)
	Returns the smallest value of the specified variables.
template<typename T >
T	Max (const T &A, const T &B, const T &C)
	Returns the largest value of the specified variables.
template<typename T >
T	Min (const T &A, const T &B, const T &C)
	Returns the smallest value of the specified variables.
template<typename T >
void	Increase (T &Value, const T &PotNewValue)
	Increase the given value if the potentially new value is greater.
template<typename T >
void	Decrease (T &Value, const T &PotNewValue)
	Decrease the given value if the potentially new value is smaller.
template<typename T >
T	MinMax (const T &Value, const T &Min, const T &Max)
	Returns the input value if it is inside the range "Min" and "Max. Otherwise the clamped range.
template<typename T >
void	Clamp (T &Value, const T &Min, const T &Max)
	Clamps the variable "Value" to the range "Min" and "Max".
template<typename T >
void	Swap (T &A, T &B)
	Exchanges (or rather swaps) the content of the specified variables A and B.
template<typename T >
T	Sgn (const T &Value)
	Returns the signed value. Resulting values can only be 1, -1 or 0.
template<typename T >
T	Round (const T &Value, s32 Precision)
	Returns the rounded value to the specified precision.
template<typename T >
T	Pow2 (const T &Value)
	Returns the square of the specified value (Value * Value).
template<typename T >
T	Sin (const T &Value)
	Returns the sine of the specified value as degree.
template<typename T >
T	Cos (const T &Value)
	Returns the cosine of the specified value as degree.
template<typename T >
T	Tan (const T &Value)
	Returns the tangent of the specified value as degree.
template<typename T >
T	ASin (const T &Value)
	Returns the arcus sine of the specified value as degree.
template<typename T >
T	ACos (const T &Value)
	Returns arcus cosine of the specified value as degree.
template<typename T >
T	ATan (const T &Value)
	Returns arcus tangent of the specified value as degree.
template<typename T >
T	Log (const T &Value, const T &Base=T(10))
	Returns the logarithm with the specified base.
template<typename T , typename I >
void	Lerp (T &Result, const T &From, const T &To, const I &Factor)
template<typename T , typename I >
T	Lerp (const T &From, const T &To, const I &Factor)
	Overloaded function. For more information read the documentation of the first variant of this function.
template<typename T , typename I >
T	LerpParabolic (const T &From, const T &To, const I &Factor)
	Parabolic interpolation. This is equivalent to "Lerp(From, To, Factor*Factor)".
template<typename T , typename I >
T	LerpSin (const T &From, const T &To, const I &Factor)
	Sine interpolation. This is equivalent to "Lerp(From, To, Sin(Factor*90))".
s32	Round (f32 Value)
	Rounds the float value to the nearest integer value (e.g. 3.4 to 3 and 3.5 to 4).
s32	RoundPow2 (s32 Value)
	Rounds the given value to the nearest power of two value (e.g. 34 to 32 and 120 to 128).
bool	Equal (f32 A, f32 B, f32 Tolerance=ROUNDING_ERROR)
	Returns true if A and B are equal with the specified tolerance.
bool	Equal (s32 A, s32 B, s32 Tolerance=0)
bool	getBitR2L (u32 Integer, s32 Pos)
	Returns the bit inside the specified integer at the specified position (right to left).
void	setBitR2L (u32 &Integer, s32 Pos, bool Enable)
	Sets the bit inside the specified integer at the specified position (right to left).
bool	getBitL2R (u32 Integer, s32 Pos)
	Returns the bit inside the specified integer at the specified position (left to right).
void	setBitL2R (u32 &Integer, s32 Pos, bool Enable)
	Sets the bit inside the specified integer at the specified position (left to right).
bool	getBitR2L (u8 Integer, s32 Pos)
	Returns the bit inside the specified integer at the specified position (right to left).
void	setBitR2L (u8 &Integer, s32 Pos, bool Enable)
	Sets the bit inside the specified integer at the specified position (right to left).
bool	getBitL2R (u8 Integer, s32 Pos)
	Returns the bit inside the specified integer at the specified position (left to right).
void	setBitL2R (u8 &Integer, s32 Pos, bool Enable)
	Sets the bit inside the specified integer at the specified position (left to right).
template<typename T >
T	getTriangleArea2D (const T &x1, const T &y1, const T &x2, const T &y2, const T &x3, const T &y3)
template<typename T >
T	getBezierValue (const f32 t, const T &Pos1, const T &Pos2, const T &Radial1, const T &Radial2)
	Returns a bezier value used for bezier curves.
template<typename T >
T	getBernsteinValue (const f32 t, const T Points[4])
	Returns a bernstein value used for bezier patch generation.
template<typename T >
T	getGaussianValue (const T &X, const T &Mean, const T &StdDeviation)
	Returns a gaussian value used for gaussian blur.
template<typename T >
T	getHaltonSequence (s32 Index, s32 Base)
template<typename T >
T	ModularPow (T Base, T Exp, const T &Modulus)
Variables
const f32	DEG = PI / 180.0f
const f32	RAD = 180.0f / PI
const f64	DEG64 = PI64 / 180.0
const f64	RAD64 = 180.0 / PI64
const f64	SQRT2 = sqrt(2.0)
const f32	SQRT2F = sqrtf(2.0f)
const f64	STDASPECT = 4.0 / 3.0

---

Detailed Description

This namespace contains all mathematical basic functions such as sine, cosine, distance calculations etc.

---

Typedef Documentation

typedef FunctionalInterpolator<f32, f32, &Lerp> sp::math::LinearInterpolator

typedef FunctionalInterpolator<f32, f32, &LerpParabolic> sp::math::ParabolicInterpolator

typedef boost::function<void (s32 x, s32 y, void* UserData) sp::math::RenderPixelCallback)

Callback function interface for rasterization without vertices.

typedef FunctionalInterpolator<f32, f32, &LerpSin> sp::math::SinInterpolator

typedef Spline<dim::point2df, f32, 2> sp::math::Spline2D

typedef Spline<dim::vector3df, f32, 3> sp::math::Spline3D

---

Enumeration Type Documentation

enum sp::math::ETriangleCutResults

Possible results of a triangle clip.

Enumerator:

TRIANGLECUT_NONE	The triangle is not cut.
TRIANGLECUT_QUAD_AND_TRIANGLE	The cut brought out a quadrangle and a triangle.
TRIANGLECUT_TWO_TRIANGLES	The cut brought out two triangles.

---

Function Documentation

template<typename T >

T sp::math::Abs

(

const T &

Value

)

[inline]

Returns the absolute value of the given parameter (5 -> 5 and -5 -> 5).

template<typename T >

T sp::math::ACos

(

const T &

Value

)

[inline]

Returns arcus cosine of the specified value as degree.

template<typename T >

T sp::math::ASin

(

const T &

Value

)

[inline]

Returns the arcus sine of the specified value as degree.

template<typename T >

T sp::math::ATan

(

const T &

Value

)

[inline]

Returns arcus tangent of the specified value as degree.

template<typename T >

void sp::math::Clamp	(	T &	Value,
		const T &	Min,
		const T &	Max
	)			[inline]

Clamps the variable "Value" to the range "Min" and "Max".

dim::vector4df sp::math::Convert

(

const video::color &

Color

)

[inline]

Returns color in form of a 4D vector. The color components R, G, B, and A are transformed to the range [0.0, 1.0].

video::color sp::math::Convert

(

const dim::vector4df &

Color

)

[inline]

Returns color in typical form. The color components R, G, B, and A are transformed to the range [0, 255].

template<typename T >

T sp::math::Cos

(

const T &

Value

)

[inline]

Returns the cosine of the specified value as degree.

template<typename T >

void sp::math::Decrease	(	T &	Value,
		const T &	PotNewValue
	)			[inline]

Decrease the given value if the potentially new value is smaller.

bool sp::math::Equal	(	f32	A,
		f32	B,
		f32	Tolerance = ROUNDING_ERROR
	)			[inline]

Returns true if A and B are equal with the specified tolerance.

bool sp::math::Equal	(	s32	A,
		s32	B,
		s32	Tolerance = 0
	)			[inline]

Returns true if A and B are equal. The tolerance factor is only used to have the same interface like the floating-point version of this function.

template<typename T >

T sp::math::getAngle	(	const dim::point2d< T > &	A,
		const dim::point2d< T > &	B,
		const T &	OffsetAngle
	)

Returns the angle between the two given 2D points to the offset angle. This is in the range [-180.0 .. 180.0].

template<typename T >

T sp::math::getAngle	(	const dim::point2d< T > &	A,
		const dim::point2d< T > &	B
	)

Returns the angle between the two given 2D points.

Parameters:

[in]	A	Specifies the first 2D point.
[in]	B	Specifies the second 2D point.

Returns:

Angle between the two points. This is in the range [0.0 .. 360.0). If B.X >= A.X and B.Y >= A.Y then the return value is in the range [0.0 .. 90.0). If B.X >= A.X and B.Y < A.Y then the return value is in the range [90.0 .. 180.0). If B.X < A.X and B.Y < A.Y then the return value is in the range [180.0 .. 270.0). If B.X < A.X and B.Y >= A.Y then the return value is in the range [270.0 .. 360.0).

template<typename T >

dim::vector3d<T> sp::math::getBarycentricCoord	(	const dim::triangle3d< T > &	Triangle,
		const dim::vector3d< T > &	Point
	)

Returns the barycentric coordinate given by the cartesian point respectively to the given triangle.

Parameters:

[in]	Triangle	Specifies the 3D triangle.
[in]	Point	Specifies the cartesian point. This point must lie onto the triangle.

Returns:

Barycentric coordinate of the given point respectively to the given triangle.

template<typename T >

T sp::math::getBernsteinValue	(	const f32	t,
		const T	Points[4]
	)

Returns a bernstein value used for bezier patch generation.

template<typename T >

T sp::math::getBezierValue	(	const f32	t,
		const T &	Pos1,
		const T &	Pos2,
		const T &	Radial1,
		const T &	Radial2
	)

Returns a bezier value used for bezier curves.

bool sp::math::getBitL2R	(	u32	Integer,
		s32	Pos
	)			[inline]

Returns the bit inside the specified integer at the specified position (left to right).

bool sp::math::getBitL2R	(	u8	Integer,
		s32	Pos
	)			[inline]

Returns the bit inside the specified integer at the specified position (left to right).

bool sp::math::getBitR2L	(	u32	Integer,
		s32	Pos
	)			[inline]

Returns the bit inside the specified integer at the specified position (right to left).

bool sp::math::getBitR2L	(	u8	Integer,
		s32	Pos
	)			[inline]

Returns the bit inside the specified integer at the specified position (right to left).

template<typename T >

T sp::math::getDistance	(	const dim::vector3d< T > &	PosA,
		const dim::vector3d< T > &	PosB
	)			[inline]

Returns the distance between the two given 3D points.

template<typename T >

T sp::math::getDistance	(	const dim::point2d< T > &	PosA,
		const dim::point2d< T > &	PosB
	)			[inline]

Returns the distance between the two given 2D points.

template<typename T >

T sp::math::getDistanceSq	(	const dim::point2d< T > &	PosA,
		const dim::point2d< T > &	PosB
	)			[inline]

Returns:

Suqare distance between two 2D points (used for fast distance comparisions).

template<typename T >

T sp::math::getDistanceSq	(	const dim::vector3d< T > &	PosA,
		const dim::vector3d< T > &	PosB
	)			[inline]

Returns:

Suqare distance between two 3D points (used for fast distance comparisions).

template<typename T >

T sp::math::getGaussianValue	(	const T &	X,
		const T &	Mean,
		const T &	StdDeviation
	)

Returns a gaussian value used for gaussian blur.

template<typename T >

T sp::math::getHaltonSequence	(	s32	Index,
		s32	Base
	)

Returns the halton sequence for the given input and base. This is used for quasi-random values. For more details take a look at: http://orion.math.iastate.edu/reu/2001/voronoi/halton_sequence.html.

Parameters:

[in]	Index	Specifies the sequence index.
[in]	Base	Specifies the sequence base. This has to be a prime number! Usually beginning with 2, 3, etc.

Todo:

This is currently not used and has not been tested!

template<typename T >

dim::vector3d<T> sp::math::getNormalVector	(	const dim::vector3d< T > &	PosA,
		const dim::vector3d< T > &	PosB,
		const dim::vector3d< T > &	PosC
	)			[inline]

Returns normalized normal vector computed by the three specified coordinates.

template<typename T >

dim::vector3d<T> sp::math::getNormalVectorSq	(	const dim::vector3d< T > &	PosA,
		const dim::vector3d< T > &	PosB,
		const dim::vector3d< T > &	PosC
	)			[inline]

Returns normal vector computed by the three specified coordinates.

SP_EXPORT dim::matrix4f sp::math::getTangentSpace	(	const dim::vector3df	PosA,
		const dim::vector3df	PosB,
		const dim::vector3df	PosC,
		const dim::point2df	MapA,
		const dim::point2df	MapB,
		const dim::point2df	MapC,
		dim::vector3df &	Tangent,
		dim::vector3df &	Binormal,
		dim::vector3df &	Normal
	)

template<typename T >

T sp::math::getTriangleArea2D	(	const T &	x1,
		const T &	y1,
		const T &	x2,
		const T &	y2,
		const T &	x3,
		const T &	y3
	)			[inline]

Returns the 2D triangle area.

Note:

This is actually only used inside the dim::triangle3d::getBarycentricCoord function.

SP_EXPORT void sp::math::getVertexInterpolation	(	const dim::triangle3df &	Triangle,
		const dim::vector3df &	Pos,
		f32 &	Vert,
		f32 &	Horz
	)

Todo:

Develop this new

template<class T >

T sp::math::getVertexInterpolation	(	const T &	VertexA,
		const T &	VertexB,
		const T &	VertexC,
		const f32	Vert,
		const f32	Horz
	)

Deprecated:

template<typename T >

void sp::math::Increase	(	T &	Value,
		const T &	PotNewValue
	)			[inline]

Increase the given value if the potentially new value is greater.

template<typename T , typename I >

void sp::math::Lerp	(	T &	Result,
		const T &	From,
		const T &	To,
		const I &	Factor
	)			[inline]

Returns a linear-interpolation ('lerp') between the two given points ('From' and 'To').

Parameters:

[out]	Result	Specifies the resulting output point.
[in]	From	Specifies the start point.
[in]	To	Specifies the end point.
[in]	Factor	Specifies the interpolation factor. This should be in the range [0.0 .. 1.0].

Template Parameters:

	T	Specifies the type of the points (e.g. float, dim::point2df, dim::vector3df etc.).
	I	Specifies the interpolation data type. This should be a float or a double.

See also:

dim::point2d

dim::vector3d

template<typename T , typename I >

T sp::math::Lerp	(	const T &	From,
		const T &	To,
		const I &	Factor
	)			[inline]

Overloaded function. For more information read the documentation of the first variant of this function.

template<typename T , typename I >

T sp::math::LerpParabolic	(	const T &	From,
		const T &	To,
		const I &	Factor
	)			[inline]

Parabolic interpolation. This is equivalent to "Lerp(From, To, Factor*Factor)".

template<typename T , typename I >

T sp::math::LerpSin	(	const T &	From,
		const T &	To,
		const I &	Factor
	)			[inline]

Sine interpolation. This is equivalent to "Lerp(From, To, Sin(Factor*90))".

template<typename T >

T sp::math::Log	(	const T &	Value,
		const T &	Base = T(10)
	)			[inline]

Returns the logarithm with the specified base.

template<typename T >

T sp::math::Max	(	const T &	A,
		const T &	B
	)			[inline]

Returns the largest value of the specified variables.

template<typename T >

T sp::math::Max	(	const T &	A,
		const T &	B,
		const T &	C
	)			[inline]

Returns the largest value of the specified variables.

template<typename T >

T sp::math::Min	(	const T &	A,
		const T &	B,
		const T &	C
	)			[inline]

Returns the smallest value of the specified variables.

template<typename T >

T sp::math::Min	(	const T &	A,
		const T &	B
	)			[inline]

Returns the smallest value of the specified variables.

template<typename T >

T sp::math::MinMax	(	const T &	Value,
		const T &	Min,
		const T &	Max
	)			[inline]

Returns the input value if it is inside the range "Min" and "Max. Otherwise the clamped range.

template<typename T >

T sp::math::ModularPow	(	T	Base,
		T	Exp,
		const T &	Modulus
	)

Computes the efficient modular pow value.

Template Parameters:

T

This type must support the following operators: %, =, *= and >>=.

Parameters:

[in]	Base	Specifies the base value.
[in]	Exp	Specifies the exponent value.
[in]	Modulus	Specifies the modulus value.

Returns:

'Base' power of 'Exp' modulo 'Modulus'. This is equivalent to '(Base ^ Exp) % Modulus' but faster.

template<typename T >

T sp::math::Pow2

(

const T &

Value

)

[inline]

Returns the square of the specified value (Value * Value).

template<typename T >

T sp::math::Round	(	const T &	Value,
		s32	Precision
	)			[inline]

Returns the rounded value to the specified precision.

s32 sp::math::Round

(

f32

Value

)

[inline]

Rounds the float value to the nearest integer value (e.g. 3.4 to 3 and 3.5 to 4).

s32 sp::math::RoundPow2

(

s32

Value

)

[inline]

Rounds the given value to the nearest power of two value (e.g. 34 to 32 and 120 to 128).

void sp::math::setBitL2R	(	u32 &	Integer,
		s32	Pos,
		bool	Enable
	)			[inline]

Sets the bit inside the specified integer at the specified position (left to right).

void sp::math::setBitL2R	(	u8 &	Integer,
		s32	Pos,
		bool	Enable
	)			[inline]

Sets the bit inside the specified integer at the specified position (left to right).

void sp::math::setBitR2L	(	u8 &	Integer,
		s32	Pos,
		bool	Enable
	)			[inline]

Sets the bit inside the specified integer at the specified position (right to left).

void sp::math::setBitR2L	(	u32 &	Integer,
		s32	Pos,
		bool	Enable
	)			[inline]

Sets the bit inside the specified integer at the specified position (right to left).

template<typename T >

T sp::math::Sgn

(

const T &

Value

)

[inline]

Returns the signed value. Resulting values can only be 1, -1 or 0.

template<typename T >

T sp::math::Sin

(

const T &

Value

)

[inline]

Returns the sine of the specified value as degree.

template<typename T >

void sp::math::sortContainer	(	std::vector< T > &	ObjectList,
		bool(*)(T &obj1, T &obj2)	lpFuncCmp
	)

Deprecated:

template<typename T >

void sp::math::sortContainerConst	(	std::vector< T > &	ObjectList,
		bool(*)(const T &obj1, const T &obj2)	lpFuncCmp
	)

Deprecated:

template<typename T >

void sp::math::Swap	(	T &	A,
		T &	B
	)			[inline]

Exchanges (or rather swaps) the content of the specified variables A and B.

template<typename T >

T sp::math::Tan

(

const T &

Value

)

[inline]

Returns the tangent of the specified value as degree.

---

Variable Documentation

const f32 sp::math::DEG = PI / 180.0f

const f64 sp::math::DEG64 = PI64 / 180.0

const f32 sp::math::RAD = 180.0f / PI

const f64 sp::math::RAD64 = 180.0 / PI64

const f64 sp::math::SQRT2 = sqrt(2.0)

const f32 sp::math::SQRT2F = sqrtf(2.0f)

const f64 sp::math::STDASPECT = 4.0 / 3.0