Maths classes and functions. More...

Classes
struct	gf::Matrix< T, ROWS, COLS >
	General purpose math matrix. More...

struct	gf::Matrix< T, 2, 2 >
	A 2x2 matrix. More...

struct	gf::Matrix< T, 3, 3 >
	A 3x3 matrix. More...

struct	gf::Matrix< T, 4, 4 >
	A 4x4 matrix. More...

struct	gf::Range< T >
	A half-open range of values. More...

struct	gf::Range< T >::Iterator
	A range iterator. More...

struct	gf::PositionRange< T >
	A 2D range. More...

struct	gf::PositionRange< T >::Iterator
	An iterator for a 2D range. More...

struct	gf::NeighborSquareRange< T >
	A 2D range. More...

struct	gf::NeighborSquareRange< T >::Iterator
	An iterator for a 2D range. More...

struct	gf::NeighborDiamondRange< T >
	A 2D range. More...

struct	gf::NeighborDiamondRange< T >::Iterator
	An iterator for a 2D range. More...

struct	gf::Vector< T, N >
	General purpose math vector. More...

struct	gf::Vector< T, 2 >
	A 2D vector. More...

struct	gf::Vector< T, 3 >
	A 3D vector. More...

struct	gf::Vector< T, 4 >
	A 4D vector. More...

Typedefs
template<typename T >
using	gf::Step = T(*)(T)
	A step is a function with special features. More...

using	gf::Matrix2f = Matrix< float, 2, 2 >
	A float square matrix of size 2. More...

using	gf::Matrix2d = Matrix< double, 2, 2 >
	A double square matrix of size 2. More...

using	gf::Matrix3f = Matrix< float, 3, 3 >
	A float square matrix of size 3. More...

using	gf::Matrix3d = Matrix< double, 3, 3 >
	A double square matrix of size 3. More...

using	gf::Matrix4f = Matrix< float, 4, 4 >
	A float square matrix of size 4. More...

using	gf::Matrix4d = Matrix< double, 4, 4 >
	A double square matrix of size 4. More...

using	gf::RangeF = Range< float >
	A float range. More...

using	gf::RangeI = Range< int >
	A int range. More...

using	gf::RangeU = Range< unsigned >
	A unsigned range. More...

using	gf::RangeZ = Range< std::size_t >
	A `std::size_t` range. More...

using	gf::Vector2f = Vector< float, 2 >
	A float vector with 2 components. More...

using	gf::Vector3f = Vector< float, 3 >
	A float vector with 3 components. More...

using	gf::Vector4f = Vector< float, 4 >
	A float vector with 4 components. More...

using	gf::Vector2d = Vector< double, 2 >
	A double vector with 2 components. More...

using	gf::Vector3d = Vector< double, 3 >
	A double vector with 3 components. More...

using	gf::Vector4d = Vector< double, 4 >
	A double vector with 4 components. More...

using	gf::Vector2i = Vector< int, 2 >
	A int vector with 2 components. More...

using	gf::Vector3i = Vector< int, 3 >
	A int vector with 3 components. More...

using	gf::Vector4i = Vector< int, 4 >
	A int vector with 4 components. More...

using	gf::Vector2u = Vector< unsigned, 2 >
	A unsigned vector with 2 components. More...

using	gf::Vector3u = Vector< unsigned, 3 >
	A unsigned vector with 3 components. More...

using	gf::Vector4u = Vector< unsigned, 4 >
	A unsigned vector with 4 components. More...

using	gf::Vector2z = Vector< std::size_t, 2 >
	A std::size_t vector with 2 components. More...

using	gf::Vector3z = Vector< std::size_t, 3 >
	A std::size_t vector with 3 components. More...

using	gf::Vector4z = Vector< std::size_t, 4 >
	A std::size_t vector with 4 components. More...

using	gf::Vector2b = Vector< bool, 2 >
	A bool vector with 2 components. More...

using	gf::Vector3b = Vector< bool, 3 >
	A bool vector with 3 components. More...

using	gf::Vector4b = Vector< bool, 4 >
	A bool vector with 4 components. More...

template<typename T >
using	gf::Color3 = Vector< T, 3 >
	A color vector with 3 components. More...

template<typename T >
using	gf::Color4 = Vector< T, 4 >
	A color vector with 4 components. More...

using	gf::Color3f = Color3< float >
	A float color vector with 3 components. More...

using	gf::Color4f = Color4< float >
	A float color vector with 4 components. More...

using	gf::Color3d = Color3< double >
	A double color vector with 3 components. More...

using	gf::Color4d = Color4< double >
	A double color vector with 4 components. More...

using	gf::Color3u = Color3< uint8_t >
	A uint8_t color vector with 3 components. More...

using	gf::Color4u = Color4< uint8_t >
	A uint8_t color vector with 4 components. More...

template<typename T , std::size_t N>
using	gf::Distance = T(*)(Vector< T, N >, Vector< T, N >)
	A distance function. More...

template<typename T >
using	gf::Distance2 = Distance< T, 2 >
	A distance function for 2D vectors. More...

template<typename T >
using	gf::Distance3 = Distance< T, 3 >
	A distance function for 3D vectors. More...

Functions
template<typename T >
constexpr T	gf::pi ()
	Templated value of \( \pi \). More...

template<typename T >
constexpr bool	gf::almostEquals (T a, T b, T epsilon=std::numeric_limits< T >::epsilon())
	Compare two floats. More...

template<typename T >
constexpr T	gf::degreesToRadians (T degrees)
	Convert degrees to radians. More...

template<typename T >
constexpr T	gf::radiansToDegrees (T radians)
	Convert radians to degrees. More...

template<typename T >
constexpr T	gf::linearStep (T t)
	Linear step. More...

template<typename T >
constexpr T	gf::cubicStep (T t)
	Cubic step (smoothstep) More...

template<typename T >
constexpr T	gf::quinticStep (T t)
	Quintic step (smootherstep) More...

template<typename T >
T	gf::cosineStep (T t)
	Cosine step. More...

template<typename T , typename U >
constexpr T	gf::lerp (T lhs, T rhs, U t)
	Linear interpolation function. More...

template<typename T >
constexpr T	gf::clamp (T val, T lo, T hi)
	Clamping function. More...

template<typename T >
constexpr T	gf::square (T val)
	Square function. More...

template<typename T >
constexpr T	gf::cube (T val)
	Cube function. More...

template<typename T >
constexpr int	gf::sign (T val)
	Sign function. More...

template<typename T >
constexpr T	gf::absdiff (T lhs, T rhs)
	Absolute difference of two values. More...

Variables
constexpr float	gf::Pi = pi<float>()
	The \( \pi \) constant. More...

constexpr float	gf::Pi2 = Pi / 2
	The \( \frac{\pi}{2} \) constant. More...

constexpr float	gf::Pi3 = Pi / 3
	The \( \frac{\pi}{3} \) constant. More...

constexpr float	gf::Pi4 = Pi / 4
	The \( \frac{\pi}{4} \) constant. More...

constexpr float	gf::Pi6 = Pi / 6
	The \( \frac{\pi}{6} \) constant. More...

constexpr float	gf::Sqrt2 = 1.41421356237309504880f
	The \( \sqrt{2} \) constant. More...

constexpr float	gf::InvSqrt2 = 1 / Sqrt2
	The \( \frac{1}{\sqrt{2}} \) constant. More...

constexpr float	gf::Sqrt3 = 1.7320508075688772935f
	The \( \sqrt{3} \) constant. More...

constexpr float	gf::Epsilon = std::numeric_limits<float>::epsilon()
	Machine epsilon. More...

Detailed Description

Maths classes and functions.

Typedef Documentation

◆ Color3

template<typename T >

using gf::Color3 = typedef Vector<T, 3>

A color vector with 3 components.

See also: gf::Vector, gf::Vector<T, 4>

◆ Color3d

using gf::Color3d = typedef Color3<double>

A double color vector with 3 components.

See also: gf::Vector, gf::Vector<T, 3>

◆ Color3f

using gf::Color3f = typedef Color3<float>

A float color vector with 3 components.

See also: gf::Vector, gf::Vector<T, 3>

◆ Color3u

using gf::Color3u = typedef Color3<uint8_t>

A uint8_t color vector with 3 components.

See also: gf::Vector, gf::Vector<T, 3>

◆ Color4

template<typename T >

using gf::Color4 = typedef Vector<T, 4>

A color vector with 4 components.

See also: gf::Vector, gf::Vector<T, 4>

◆ Color4d

using gf::Color4d = typedef Color4<double>

A double color vector with 4 components.

See also: gf::Vector, gf::Vector<T, 4>

◆ Color4f

using gf::Color4f = typedef Color4<float>

A float color vector with 4 components.

See also: gf::Vector, gf::Vector<T, 4>

◆ Color4u

using gf::Color4u = typedef Color4<uint8_t>

A uint8_t color vector with 4 components.

See also: gf::Vector, gf::Vector<T, 4>

◆ Distance

template<typename T , std::size_t N>

using gf::Distance = typedef T (*)(Vector<T, N>, Vector<T, N>)

A distance function.

A distance function is a function that gives the distance between two vectors.

gf::Distance<float, 3> distFn = gf::manhattanDistance<float, 3>;
Vector3f vec1 = ...;
Vector3f vec2 = ...;
 
float distance = distFn(vec1, vec2);

See also: manhattanDistance(), squareDistance(), euclideanDistance(), chebyshevDistance(); gf::Distance2, gf::Distance3

◆ Distance2

template<typename T >

using gf::Distance2 = typedef Distance<T, 2>

A distance function for 2D vectors.

See also: gf::Distance

◆ Distance3

template<typename T >

using gf::Distance3 = typedef Distance<T, 3>

A distance function for 3D vectors.

See also: gf::Distance

◆ Matrix2d

using gf::Matrix2d = typedef Matrix<double, 2, 2>

A double square matrix of size 2.

See also: gf::Matrix, gf::Matrix<T, 2, 2>

◆ Matrix2f

using gf::Matrix2f = typedef Matrix<float, 2, 2>

A float square matrix of size 2.

See also: gf::Matrix, gf::Matrix<T, 2, 2>

◆ Matrix3d

using gf::Matrix3d = typedef Matrix<double, 3, 3>

A double square matrix of size 3.

See also: gf::Matrix, gf::Matrix<T, 3, 3>

◆ Matrix3f

using gf::Matrix3f = typedef Matrix<float, 3, 3>

A float square matrix of size 3.

See also: gf::Matrix, gf::Matrix<T, 3, 3>

◆ Matrix4d

using gf::Matrix4d = typedef Matrix<double, 4, 4>

A double square matrix of size 4.

See also: gf::Matrix, gf::Matrix<T, 4, 4>

◆ Matrix4f

using gf::Matrix4f = typedef Matrix<float, 4, 4>

A float square matrix of size 4.

See also: gf::Matrix, gf::Matrix<T, 4, 4>

◆ RangeF

using gf::RangeF = typedef Range<float>

A float range.

See also: gf::Range

◆ RangeI

using gf::RangeI = typedef Range<int>

A int range.

See also: gf::Range

◆ RangeU

using gf::RangeU = typedef Range<unsigned>

A unsigned range.

See also: gf::Range

◆ RangeZ

using gf::RangeZ = typedef Range<std::size_t>

A std::size_t range.

See also: gf::Range

◆ Step

template<typename T >

using gf::Step = typedef T (*)(T)

A step is a function with special features.

A step \( f \) is a (mathematical) function which has the following properties:

\( f(0) = 0 \)
\( f(1) = 1 \)

It can be used to smooth a linear interpolation.

gf::Vector2f point1 = ...;
gf::Vector2f point2 = ...;
float t = ...;
gf::Step<float> step = gf::cubicStep<float>;
 
gf::Vector2f interpolatedPoint = gf::lerp(point1, point2, t);
gf::Vector2f smoothedInterpolatedPoint = gf::lerp(point1, point2, step(t));

See also: linearStep(), cubicStep(), quinticStep(), cosineStep()

◆ Vector2b

using gf::Vector2b = typedef Vector<bool, 2>

A bool vector with 2 components.

See also: gf::Vector, gf::Vector<T, 2>

◆ Vector2d

using gf::Vector2d = typedef Vector<double, 2>

A double vector with 2 components.

See also: gf::Vector, gf::Vector<T, 2>

◆ Vector2f

using gf::Vector2f = typedef Vector<float, 2>

A float vector with 2 components.

See also: gf::Vector, gf::Vector<T, 2>

◆ Vector2i

using gf::Vector2i = typedef Vector<int, 2>

A int vector with 2 components.

See also: gf::Vector, gf::Vector<T, 2>

◆ Vector2u

using gf::Vector2u = typedef Vector<unsigned, 2>

A unsigned vector with 2 components.

See also: gf::Vector, gf::Vector<T, 2>

◆ Vector2z

using gf::Vector2z = typedef Vector<std::size_t, 2>

A std::size_t vector with 2 components.

See also: gf::Vector, gf::Vector<T, 2>

◆ Vector3b

using gf::Vector3b = typedef Vector<bool, 3>

A bool vector with 3 components.

See also: gf::Vector, gf::Vector<T, 3>

◆ Vector3d

using gf::Vector3d = typedef Vector<double, 3>

A double vector with 3 components.

See also: gf::Vector, gf::Vector<T, 3>

◆ Vector3f

using gf::Vector3f = typedef Vector<float, 3>

A float vector with 3 components.

See also: gf::Vector, gf::Vector<T, 3>

◆ Vector3i

using gf::Vector3i = typedef Vector<int, 3>

A int vector with 3 components.

See also: gf::Vector, gf::Vector<T, 3>

◆ Vector3u

using gf::Vector3u = typedef Vector<unsigned, 3>

A unsigned vector with 3 components.

See also: gf::Vector, gf::Vector<T, 3>

◆ Vector3z

using gf::Vector3z = typedef Vector<std::size_t, 3>

A std::size_t vector with 3 components.

See also: gf::Vector, gf::Vector<T, 3>

◆ Vector4b

using gf::Vector4b = typedef Vector<bool, 4>

A bool vector with 4 components.

See also: gf::Vector, gf::Vector<T, 4>

◆ Vector4d

using gf::Vector4d = typedef Vector<double, 4>

A double vector with 4 components.

See also: gf::Vector, gf::Vector<T, 4>

◆ Vector4f

using gf::Vector4f = typedef Vector<float, 4>

A float vector with 4 components.

See also: gf::Vector, gf::Vector<T, 4>

◆ Vector4i

using gf::Vector4i = typedef Vector<int, 4>

A int vector with 4 components.

See also: gf::Vector, gf::Vector<T, 4>

◆ Vector4u

using gf::Vector4u = typedef Vector<unsigned, 4>

A unsigned vector with 4 components.

See also: gf::Vector, gf::Vector<T, 4>

◆ Vector4z

using gf::Vector4z = typedef Vector<std::size_t, 4>

A std::size_t vector with 4 components.

See also: gf::Vector, gf::Vector<T, 4>

Function Documentation

◆ absdiff()

template<typename T >

constexpr T gf::absdiff	(	T	lhs,
		T	rhs
	)

constexpr

Absolute difference of two values.

This function is defined as:

\[ \text{absdiff}(a, b) = | a - b | \]

Parameters

lhs	The first value
rhs	The second value

Returns: The absolute difference between the two values

◆ almostEquals()

template<typename T >

constexpr bool gf::almostEquals	(	T	a,
		T	b,
		T	epsilon = `std::numeric_limits<T>::epsilon()`
	)

constexpr

Compare two floats.

Parameters

a	The first float
b	The second float
epsilon	A small value that controls the equality comparison

See also: Comparison - The Floating-Point Guide

◆ clamp()

template<typename T >

constexpr T gf::clamp	(	T	val,
		T	lo,
		T	hi
	)

constexpr

Clamping function.

This function takes a value and returns it if it is in a specified range. If not, the returned value is the nearest value in the range.

Parameters

val	The value to clamp
lo	The minimum accepted value
hi	The maximum accepted value

Returns: The clamped value

◆ cosineStep()

template<typename T >

T gf::cosineStep ( T t )

inline

Cosine step.

\[ f(t) = (1 - \cos(\pi * t)) * 0.5 \]

See also: gf::Step

◆ cube()

template<typename T >

constexpr T gf::cube ( T val )

constexpr

Cube function.

For a value \( x \), the cube value is \( x^3 \).

Parameters

val A value

Returns: The cube of the value

◆ cubicStep()

template<typename T >

constexpr T gf::cubicStep ( T t )

constexpr

Cubic step (smoothstep)

\[ f(t) = -2 * t^3 + 3 * t^2 \]

Compared to a step, it has the following properties:

\( f'(0) = 0 \)
\( f'(1) = 0 \)

This function is also known as smoothstep

See also: gf::Step

◆ degreesToRadians()

template<typename T >

constexpr T gf::degreesToRadians ( T degrees )

constexpr

Convert degrees to radians.

Parameters

degrees An angle in degrees

Returns: The angle in radians

See also: radiansToDegrees()

◆ lerp()

template<typename T , typename U >

constexpr T gf::lerp	(	T	lhs,
		T	rhs,
		U	t
	)

constexpr

Linear interpolation function.

This functions returns an interpolated value between two values lhs and rhs according to a parameter \( t \). When \( t = 0 \) then lhs is returned, and when \( t = 1 \) then rhs is returned.

Parameters

lhs	The first value
rhs	The second value
t	The interpolation parameter, generally in the interval \( [0,1] \)

Returns: A value between the first and second value

◆ linearStep()

template<typename T >

constexpr T gf::linearStep ( T t )

constexpr

Linear step.

\[ f(t) = t \]

See also: gf::Step

◆ pi()

template<typename T >

constexpr T gf::pi ( )

constexpr

Templated value of \( \pi \).

◆ quinticStep()

template<typename T >

constexpr T gf::quinticStep ( T t )

constexpr

Quintic step (smootherstep)

\[ f(t) = 6 * t^5 - 15 * t^4 + 10 * t^3 \]

Compared to a step, it has the following properties:

\( f'(0) = 0 \)
\( f'(1) = 0 \)
\( f''(0) = 0 \)
\( f''(1) = 0 \)

This function is also known as smootherstep

See also: gf::Step

◆ radiansToDegrees()

template<typename T >

constexpr T gf::radiansToDegrees ( T radians )

constexpr

Convert radians to degrees.

Parameters

radians An angle in radians

Returns: The angle in degrees

See also: degreesToRadians()

◆ sign()

template<typename T >

constexpr int gf::sign ( T val )

constexpr

Sign function.

The sign function of \( x \) is:

\( -1 \) if \( x < 0 \)
\( 0 \) if \( x = 0 \)
\( 1 \) if \( x > 0 \)

Parameters

val A value

Returns: The sign of the value

See also: Sign function

◆ square()

template<typename T >

constexpr T gf::square ( T val )

constexpr

Square function.

For a value \( x \), the square value is \( x^2 \).

Parameters

val A value

Returns: The square of the value

Variable Documentation

◆ Epsilon

constexpr float gf::Epsilon = std::numeric_limits<float>::epsilon()

constexpr

Machine epsilon.

◆ InvSqrt2

constexpr float gf::InvSqrt2 = 1 / Sqrt2

constexpr

The \( \frac{1}{\sqrt{2}} \) constant.

◆ Pi

constexpr float gf::Pi = pi<float>()

constexpr

The \( \pi \) constant.

◆ Pi2

constexpr float gf::Pi2 = Pi / 2

constexpr

The \( \frac{\pi}{2} \) constant.

◆ Pi3

constexpr float gf::Pi3 = Pi / 3

constexpr

The \( \frac{\pi}{3} \) constant.

◆ Pi4

constexpr float gf::Pi4 = Pi / 4

constexpr

The \( \frac{\pi}{4} \) constant.

◆ Pi6

constexpr float gf::Pi6 = Pi / 6

constexpr

The \( \frac{\pi}{6} \) constant.

◆ Sqrt2

constexpr float gf::Sqrt2 = 1.41421356237309504880f

constexpr

The \( \sqrt{2} \) constant.

◆ Sqrt3

constexpr float gf::Sqrt3 = 1.7320508075688772935f

constexpr

The \( \sqrt{3} \) constant.

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ Color3

◆ Color3d

◆ Color3f

◆ Color3u

◆ Color4

◆ Color4d

◆ Color4f

◆ Color4u

◆ Distance

◆ Distance2

◆ Distance3

◆ Matrix2d

◆ Matrix2f

◆ Matrix3d

◆ Matrix3f

◆ Matrix4d

◆ Matrix4f

◆ RangeF

◆ RangeI

◆ RangeU

◆ RangeZ

◆ Step

◆ Vector2b

◆ Vector2d

◆ Vector2f

◆ Vector2i

◆ Vector2u

◆ Vector2z

◆ Vector3b

◆ Vector3d

◆ Vector3f

◆ Vector3i

◆ Vector3u

◆ Vector3z

◆ Vector4b

◆ Vector4d

◆ Vector4f

◆ Vector4i

◆ Vector4u

◆ Vector4z

Function Documentation

◆ absdiff()

◆ almostEquals()

◆ clamp()

◆ cosineStep()

◆ cube()

◆ cubicStep()

◆ degreesToRadians()

◆ lerp()

◆ linearStep()

◆ pi()

◆ quinticStep()

◆ radiansToDegrees()

◆ sign()

◆ square()

Variable Documentation

◆ Epsilon

◆ InvSqrt2

◆ Pi

◆ Pi2

◆ Pi3

◆ Pi4

◆ Pi6

◆ Sqrt2

◆ Sqrt3