Mathematic functions (Trigonometric, exponential, rounding, etc.). More...

Collaboration diagram for Murl::Math Functions:

Functions
template<class DataType >
DataType	Murl::Math::Abs (DataType value)
	Get the absolute value. More...

template<class DataType >
DataType	Murl::Math::Sgn (DataType value)
	Get the sign of a value. More...

template<class DataType >
const DataType &	Murl::Math::Min (const DataType &x, const DataType &y)
	Get the minimum of two values. More...

template<class DataType >
const DataType &	Murl::Math::Min (const DataType &x, const DataType &y, const DataType &z)
	Get the minimum of three values. More...

template<class DataType >
const DataType &	Murl::Math::Min (const DataType &x, const DataType &y, const DataType &z, const DataType &w)
	Get the minimum of four values. More...

template<class DataType >
const DataType &	Murl::Math::Max (const DataType &x, const DataType &y)
	Get the maximum of two values. More...

template<class DataType >
const DataType &	Murl::Math::Max (const DataType &x, const DataType &y, const DataType &z)
	Get the maximum of three values. More...

template<class DataType >
const DataType &	Murl::Math::Max (const DataType &x, const DataType &y, const DataType &z, const DataType &w)
	Get the maximum of four values. More...

template<class DataType >
const DataType &	Murl::Math::Clamp (const DataType &val, const DataType &min, const DataType &max)
	Clamp a value. More...

template<class DataType >
Bool	Murl::Math::IsNaN (DataType value)
	Check if a value is not a number (NaN). More...

template<class DataType >
Bool	Murl::Math::IsInfinite (DataType value)
	Check if a value is infinite (either positive infinity or negative infinity). More...

template<class DataType >
Bool	Murl::Math::IsFinite (DataType value)
	Check if a value is finite. More...

template<class DataType >
DataType	Murl::Math::Exp (DataType value)
	Get the the e number raised to the power of a value. More...

template<class DataType >
DataType	Murl::Math::Log (DataType value)
	Get the natural logarithm of a value. More...

template<class DataType >
DataType	Murl::Math::Log2 (DataType value)
	Get the base 2 logarithm of a value. More...

template<class DataType >
DataType	Murl::Math::Log10 (DataType value)
	Get the base 10 logarithm of a value. More...

template<class DataType >
DataType	Murl::Math::Sqrt (DataType value)
	Get the square root of a value. More...

template<class DataType >
DataType	Murl::Math::Pow (DataType base, DataType exponent)
	Get a base raised to the power of an exponent. More...

template<class DataType >
DataType	Murl::Math::Fmod (DataType numerator, DataType denominator)
	Get the remainder of a numerator divided by a denominator. More...

template<class DataType >
DataType	Murl::Math::ModF (DataType value, DataType &intPart)
	Get the integer part and the fractional part of a value. More...

template<class DataType >
DataType	Murl::Math::Remainder (DataType numerator, DataType denominator)
	Get the IEEE remainder of a numerator divided by a denominator. More...

template<class DataType >
DataType	Murl::Math::Sin (DataType radAngle)
	Get the sine of an angle value. More...

template<class DataType >
DataType	Murl::Math::Cos (DataType radAngle)
	Get the cosine of an angle value. More...

template<class DataType >
DataType	Murl::Math::Tan (DataType radAngle)
	Get the tangent of an angle value. More...

template<class DataType >
DataType	Murl::Math::ArcSin (DataType value)
	Get the arc sine of a value. More...

template<class DataType >
DataType	Murl::Math::ArcCos (DataType value)
	Get the arc cosine of a value. More...

template<class DataType >
DataType	Murl::Math::ArcTan (DataType value)
	Get the arc tangent of a value. More...

template<class DataType >
DataType	Murl::Math::ArcTan2 (DataType y, DataType x)
	Get the arc tangent of y divided by x. More...

template<class DataType >
DataType	Murl::Math::SinHyp (DataType value)
	Get the hyperbolic sine of an value. More...

template<class DataType >
DataType	Murl::Math::CosHyp (DataType value)
	Get the hyperbolic cosine of an value. More...

template<class DataType >
DataType	Murl::Math::TanHyp (DataType value)
	Get the hyperbolic tangent of an value. More...

template<class DataType >
DataType	Murl::Math::ArcSinHyp (DataType value)
	Get the hyperbolic arc sine of an value. More...

template<class DataType >
DataType	Murl::Math::ArcCosHyp (DataType value)
	Get the hyperbolic arc cosine of an value. More...

template<class DataType >
DataType	Murl::Math::ArcTanHyp (DataType value)
	Get the hyperbolic arc tangent of an value. More...

template<class DataType >
DataType	Murl::Math::Floor (DataType value)
	Round down to an integral value. More...

template<class DataType >
DataType	Murl::Math::Ceil (DataType value)
	Round up to an integral value. More...

template<class DataType >
DataType	Murl::Math::Round (DataType value)
	Round to an integral value, regardless of the rounding direction. More...

template<class DataType >
Bool	Murl::Math::IsEqual (const DataType &a, const DataType &b, const DataType &epsilon=Limits< DataType >::Epsilon())
	Check if two values are equal within an epsilon range. More...

template<class DataType >
DataType	Murl::Math::DegToRad (DataType degrees)
	Convert degrees into radiants. More...

template<class DataType >
DataType	Murl::Math::RadToDeg (DataType radiants)
	Convert radiants into degrees. More...

template<class DataType >
DataType	Murl::Math::MapAngle (DataType angle)
	Map an angle into range [-PI . More...

template<class DataType >
DataType	Murl::Math::AddAngle (DataType angle1, DataType angle2)
	Calculate the sum of two angles. More...

template<class DataType >
DataType	Murl::Math::SubAngle (DataType angle1, DataType angle2)
	Calculate the difference between two angles. More...

UInt16	Murl::Math::FloatToHalfFloat (Float value)
	Convert a given 32bit float value to 16bit ("half float"), represented by a UInt16 integer. More...

UInt16	Murl::Math::IntToHalfFloat (UInt8 value)
	Convert a given 8bit unsigned integer value to a 16bit floating point value ("half float"), represented by a UInt16 integer. More...

Float	Murl::Math::HalfFloatToFloat (UInt16 value)
	Convert a given 16bit half float value stored in a UInt16 to a 32bit float value. More...

UInt8	Murl::Math::HalfFloatToInt (UInt16 value)
	Convert a given 16bit half float value stored in a UInt16 to a 8bit unsigned integer value. More...

UInt16	Murl::Math::FloatToPackedFloat11 (Float value)
	Convert a given 32bit float value to an 11bit packed float, represented by a UInt16 integer. More...

Float	Murl::Math::PackedFloat11ToFloat (UInt16 value)
	Convert a given packed 11bit float value stored in a UInt16 to a 32bit float value. More...

UInt16	Murl::Math::FloatToPackedFloat10 (Float value)
	Convert a given 32bit float value to an 10bit packed float, represented by a UInt16 integer. More...

Float	Murl::Math::PackedFloat10ToFloat (UInt16 value)
	Convert a given packed 10bit float value stored in a UInt16 to a 32bit float value. More...

template<class DataTypeV , class DataTypeT >
DataTypeV	Murl::Math::Lerp (const DataTypeV &startValue, const DataTypeV &endValue, DataTypeT t)
	The linear interpolation template function. More...

template<class DataTypeT >
Double	Murl::Math::Lerp (Double startValue, Double endValue, DataTypeT t)
	The linear interpolation template function for Double. More...

template<class DataTypeV , class DataTypeT >
DataTypeT	Murl::Math::GetCubicBezierParameter (DataTypeV x0, DataTypeV x1, DataTypeV x2, DataTypeV x3, DataTypeV x)
	Get the cubic bezier parameter t for a given X value. More...

template<class DataTypeV , class DataTypeT >
DataTypeV	Murl::Math::CubicBezier (DataTypeV x0, DataTypeV x1, DataTypeV x2, DataTypeV x3, DataTypeT t)
	Evaluate a cubic bezier curve for a given parameter t. More...

template<class DataTypeV >
DataTypeV	Murl::Math::CubicBezierAt (DataTypeV x0, DataTypeV x1, DataTypeV x2, DataTypeV x3, DataTypeV y0, DataTypeV y1, DataTypeV y2, DataTypeV y3, DataTypeV x)
	Evaluate a cubic bezier curve at a given X value. More...

template<class DataType >
Easing< DataType >::Interpolate	Murl::Math::GetEasingFunction (IEnums::Interpolation interpolation)
	Get the Easing::Interpolate function for a specified interpolation. More...

template<class DataType >
DataType	Murl::Math::Interpolation (IEnums::Interpolation interpolation, DataType x)
	The interpolation template function calculates the IEnums::Interpolation curve (easing function). More...

Detailed Description

Mathematic functions (Trigonometric, exponential, rounding, etc.).

Basic mathematical functions available for Float and Double data type.

Function Documentation

◆ Abs()

template<class DataType >

DataType Murl::Math::Abs ( DataType value )

Get the absolute value.

Parameters

value The input value.

Returns: The absolute value.

Referenced by Murl::Math::Vector< DataType >::Abs(), Murl::Math::Vector< DataType >::AbsSelf(), Murl::Util::BoxFilter::Apply(), Murl::Util::BilinearFilter::Apply(), Murl::Util::GaussianFilter::Apply(), Murl::Math::Vector< DataType >::GetBaseNormals(), Murl::Math::GetCubicBezierParameter(), Murl::Math::Matrix< DataType >::Invert(), Murl::Math::IsEqual(), Murl::Math::Matrix< DataType >::IsEqual(), Murl::Math::Quaternion< DataType >::IsEqual(), Murl::Math::Rectangle< DataType >::IsEqual(), Murl::Math::Vector< DataType >::IsEqual(), Murl::Math::Cone< DataType >::Set(), Murl::Math::Sphere< DataType >::SetBounding(), Murl::Math::Sphere< DataType >::SetContaining(), and Murl::Math::Matrix< DataType >::Solve().

◆ Sgn()

template<class DataType >

DataType Murl::Math::Sgn ( DataType value )

Get the sign of a value.

Parameters

value The input value.

Returns: 1 if the value is positive, -1 if the value is negative or zero if the value is zero.

◆ Min() [1/3]

template<class DataType >

const DataType& Murl::Math::Min	(	const DataType &	x,
		const DataType &	y
	)

Get the minimum of two values.

If both are equivalent, x is returned.

Parameters

x	The 1st value.
y	The 2nd value.

Returns: The lesser value of x and y.

Referenced by Murl::Math::Clamp(), Murl::IAttributes::GetEnumValuesByIndex(), Murl::Math::Rectangle< DataType >::Include(), Murl::Math::Rectangle< DataType >::Intersect(), Murl::Math::Min(), Murl::Math::MinMax< DataType, LimitsType >::Reset(), Murl::Math::Rectangle< DataType >::Unite(), and Murl::Math::Sphere< DataType >::Unite().

◆ Min() [2/3]

template<class DataType >

const DataType& Murl::Math::Min	(	const DataType &	x,
		const DataType &	y,
		const DataType &	z
	)

Get the minimum of three values.

If all are equivalent, x is returned.

Parameters

x	The 1st value.
y	The 2nd value.
z	The 3rd value.

Returns: The lowest value of x, y and z.

References Murl::Math::Min().

◆ Min() [3/3]

template<class DataType >

const DataType& Murl::Math::Min	(	const DataType &	x,
		const DataType &	y,
		const DataType &	z,
		const DataType &	w
	)

Get the minimum of four values.

If all are equivalent, x is returned.

Parameters

x	The 1st value.
y	The 2nd value.
z	The 3rd value.
w	The 4th value.

Returns: The lowest value of x, y, z and w.

References Murl::Math::Min().

◆ Max() [1/3]

template<class DataType >

const DataType& Murl::Math::Max	(	const DataType &	x,
		const DataType &	y
	)

Get the maximum of two values.

If both are equivalent, x is returned.

Parameters

x	The 1st value.
y	The 2nd value.

Returns: The greater value of x and y.

Referenced by Murl::Math::Clamp(), Murl::Math::Rectangle< DataType >::GetSizeX(), Murl::Math::Rectangle< DataType >::GetSizeY(), Murl::Math::Sphere< DataType >::Include(), Murl::Math::Rectangle< DataType >::Include(), Murl::Math::Rectangle< DataType >::Intersect(), Murl::Math::Max(), Murl::Math::MinMax< DataType, LimitsType >::Reset(), Murl::Math::Quaternion< DataType >::Set(), Murl::Array< DataType >::SetCountAndReserve(), Murl::Math::Rectangle< DataType >::Unite(), and Murl::Math::Sphere< DataType >::Unite().

◆ Max() [2/3]

template<class DataType >

const DataType& Murl::Math::Max	(	const DataType &	x,
		const DataType &	y,
		const DataType &	z
	)

Get the maximum of three values.

If all are equivalent, x is returned.

Parameters

x	The 1st value.
y	The 2nd value.
z	The 3rd value.

Returns: The highest value of x, y and z.

References Murl::Math::Max().

◆ Max() [3/3]

template<class DataType >

const DataType& Murl::Math::Max	(	const DataType &	x,
		const DataType &	y,
		const DataType &	z,
		const DataType &	w
	)

Get the maximum of four values.

If all are equivalent, x is returned.

Parameters

x	The 1st value.
y	The 2nd value.
z	The 3rd value.
w	The 4th value.

Returns: The highest value of x, y, z and w.

References Murl::Math::Max().

◆ Clamp()

template<class DataType >

const DataType& Murl::Math::Clamp	(	const DataType &	val,
		const DataType &	min,
		const DataType &	max
	)

Clamp a value.

Parameters

val	The value to clamp.
min	The minimum value.
max	The maximum value.

Returns: The value clamped in range [min .. max].

References Murl::Math::Max(), and Murl::Math::Min().

Referenced by Murl::Math::FloatToHalfFloat(), Murl::Math::FloatToPackedFloat10(), Murl::Math::FloatToPackedFloat11(), Murl::Math::GetCubicBezierParameter(), Murl::Math::HalfFloatToFloat(), Murl::Math::HalfFloatToInt(), Murl::Math::Quaternion< DataType >::Interpolate(), Murl::Math::SplineBase< DataType >::Interpolate(), Murl::Math::PackedFloat10ToFloat(), and Murl::Math::PackedFloat11ToFloat().

◆ IsNaN()

template<class DataType >

Bool Murl::Math::IsNaN ( DataType value )

Check if a value is not a number (NaN).

The NaN values are used to identify undefined or non-representable values for floating-point elements, such as the result of 0/0.

Parameters

value The value to check.

Returns: true if the value is not a number (NaN).

◆ IsInfinite()

template<class DataType >

Bool Murl::Math::IsInfinite ( DataType value )

Check if a value is infinite (either positive infinity or negative infinity).

Parameters

value The value to check.

Returns: true if the value is an infinity value.

◆ IsFinite()

template<class DataType >

Bool Murl::Math::IsFinite ( DataType value )

Check if a value is finite.

A finite value is any floating-point value that is neither infinite nor NaN.

Parameters

value The value to check.

Returns: true if the value is finite.

◆ Exp()

template<class DataType >

DataType Murl::Math::Exp ( DataType value )

Get the the e number raised to the power of a value.

Parameters

value The input value.

Returns: The the e number raised to the power of the value.

Referenced by Murl::Util::GaussianFilter::Apply().

◆ Log()

template<class DataType >

DataType Murl::Math::Log ( DataType value )

Get the natural logarithm of a value.

Parameters

value The input value.

Returns: The natural logarithm of the value.

◆ Log2()

template<class DataType >

DataType Murl::Math::Log2 ( DataType value )

Get the base 2 logarithm of a value.

Parameters

value The input value.

Returns: The base 2 logarithm of the value.

◆ Log10()

template<class DataType >

DataType Murl::Math::Log10 ( DataType value )

Get the base 10 logarithm of a value.

Parameters

value The input value.

Returns: The base 10 logarithm of the value.

◆ Sqrt()

template<class DataType >

DataType Murl::Math::Sqrt ( DataType value )

Get the square root of a value.

Parameters

value The input value.

Returns: The square root of the value.

Referenced by Murl::Math::Easing< DataType >::EaseCircularHelper(), Murl::Math::Easing< DataType >::EaseCircularIn(), Murl::Math::Easing< DataType >::EaseCircularOut(), Murl::Util::GaussianFilter::GaussianFilter(), Murl::Math::Vector< DataType >::GetAngle2D(), Murl::Math::Matrix< DataType >::GetEulerRotation(), Murl::Math::Vector< DataType >::GetLength(), Murl::Math::Matrix< DataType >::GetScalingComponent(), Murl::Math::Matrix< DataType >::GetScalingComponentX(), Murl::Math::Matrix< DataType >::GetScalingComponentY(), Murl::Math::Matrix< DataType >::GetScalingComponentZ(), Murl::Math::Sphere< DataType >::Include(), Murl::Math::Quaternion< DataType >::Normalize(), Murl::Math::Plane< DataType >::NormalizeSelf(), Murl::Math::Quaternion< DataType >::NormalizeSelf(), Murl::Math::Cylinder< DataType >::Set(), Murl::Math::Cone< DataType >::Set(), Murl::Math::Quaternion< DataType >::Set(), and Murl::Math::Vector< DataType >::Set().

◆ Pow()

template<class DataType >

DataType Murl::Math::Pow	(	DataType	base,
		DataType	exponent
	)

Get a base raised to the power of an exponent.

Parameters

base	The base input value.
exponent	The exponent input value.

Returns: The base raised to the power of the exponent.

Referenced by Murl::Math::Easing< DataType >::EaseElasticIn(), and Murl::Math::Easing< DataType >::EaseExponentialIn().

◆ Fmod()

template<class DataType >

DataType Murl::Math::Fmod	(	DataType	numerator,
		DataType	denominator
	)

Get the remainder of a numerator divided by a denominator.

Parameters

numerator	The numerator input value.
denominator	The denominator input value.

Returns: The remainder of the numerator divided by the denominator.

Referenced by Murl::Math::SplineBase< DataType >::Interpolate(), and Murl::Math::MapAngle().

◆ ModF()

template<class DataType >

DataType Murl::Math::ModF	(	DataType	value,
		DataType &	intPart
	)

Get the integer part and the fractional part of a value.

Parameters

value	The input value.
intPart	The integer part return value.

Returns: The fractional part of the value.

◆ Remainder()

template<class DataType >

DataType Murl::Math::Remainder	(	DataType	numerator,
		DataType	denominator
	)

Get the IEEE remainder of a numerator divided by a denominator.

Parameters

numerator	The numerator input value.
denominator	The denominator input value.

Returns: The IEEE remainder of the numerator divided by the denominator.

◆ Sin()

template<class DataType >

DataType Murl::Math::Sin ( DataType radAngle )

Get the sine of an angle value.

Parameters

radAngle The angle value in radiants.

Returns: The sine of the angle value.

Referenced by Murl::Math::Cone< DataType >::Cone(), Murl::Math::Easing< DataType >::EaseBackIn(), Murl::Math::Easing< DataType >::EaseElasticIn(), Murl::Math::Matrix< DataType >::GetEulerRotation(), Murl::Math::Quaternion< DataType >::Interpolate(), Murl::Math::Quaternion< DataType >::Quaternion(), Murl::Math::Cone< DataType >::Set(), Murl::Math::Matrix< DataType >::SetRotationComponentAxisAngle(), Murl::Math::Matrix< DataType >::SetRotationComponentX(), Murl::Math::Matrix< DataType >::SetRotationComponentXYZ(), Murl::Math::Matrix< DataType >::SetRotationComponentY(), and Murl::Math::Matrix< DataType >::SetRotationComponentZ().

◆ Cos()

template<class DataType >

DataType Murl::Math::Cos ( DataType radAngle )

Get the cosine of an angle value.

Parameters

radAngle The angle value in radiants.

Returns: The cosine of the angle value.

Referenced by Murl::Math::Cone< DataType >::Cone(), Murl::Math::Matrix< DataType >::GetEulerRotation(), Murl::Math::Quaternion< DataType >::Quaternion(), Murl::Math::Cone< DataType >::Set(), Murl::Math::Matrix< DataType >::SetRotationComponentAxisAngle(), Murl::Math::Matrix< DataType >::SetRotationComponentX(), Murl::Math::Matrix< DataType >::SetRotationComponentXYZ(), Murl::Math::Matrix< DataType >::SetRotationComponentY(), and Murl::Math::Matrix< DataType >::SetRotationComponentZ().

◆ Tan()

template<class DataType >

DataType Murl::Math::Tan ( DataType radAngle )

Get the tangent of an angle value.

Parameters

radAngle The angle value in radiants.

Returns: The tangent of the angle value.

Referenced by Murl::Math::Cone< DataType >::Cone().

◆ ArcSin()

template<class DataType >

DataType Murl::Math::ArcSin ( DataType value )

Get the arc sine of a value.

Parameters

value The input value.

Returns: The arc sine of the value in radiants.

◆ ArcCos()

template<class DataType >

DataType Murl::Math::ArcCos ( DataType value )

Get the arc cosine of a value.

Parameters

value The input value.

Returns: The arc cosine of the value in radiants.

Referenced by Murl::Math::Vector< DataType >::GetAngle2D(), Murl::Math::Quaternion< DataType >::Interpolate(), and Murl::Math::Vector< DataType >::Set().

◆ ArcTan()

template<class DataType >

DataType Murl::Math::ArcTan ( DataType value )

Get the arc tangent of a value.

Parameters

value The input value.

Returns: The arc tangent of the value in radiants.

Referenced by Murl::Math::Cone< DataType >::Set().

◆ ArcTan2()

template<class DataType >

DataType Murl::Math::ArcTan2	(	DataType	y,
		DataType	x
	)

Get the arc tangent of y divided by x.

The function uses the sign of both arguments to determine the quadrant.

Parameters

y	The y input value.
x	The x input value.

Returns: The arc tangent of y divided by x in radiants.

Referenced by Murl::Math::Matrix< DataType >::GetEulerRotation().

◆ SinHyp()

template<class DataType >

DataType Murl::Math::SinHyp ( DataType value )

Get the hyperbolic sine of an value.

Parameters

value The input value.

Returns: The hyperbolic sine of the value.

◆ CosHyp()

template<class DataType >

DataType Murl::Math::CosHyp ( DataType value )

Get the hyperbolic cosine of an value.

Parameters

value The input value.

Returns: The hyperbolic cosine of the value.

◆ TanHyp()

template<class DataType >

DataType Murl::Math::TanHyp ( DataType value )

Get the hyperbolic tangent of an value.

Parameters

value The input value.

Returns: The hyperbolic tangent of the value.

◆ ArcSinHyp()

template<class DataType >

DataType Murl::Math::ArcSinHyp ( DataType value )

Get the hyperbolic arc sine of an value.

Parameters

value The input value.

Returns: The hyperbolic arc sine of the value.

◆ ArcCosHyp()

template<class DataType >

DataType Murl::Math::ArcCosHyp ( DataType value )

Get the hyperbolic arc cosine of an value.

Parameters

value The input value.

Returns: The hyperbolic arc cosine of the value.

◆ ArcTanHyp()

template<class DataType >

DataType Murl::Math::ArcTanHyp ( DataType value )

Get the hyperbolic arc tangent of an value.

Parameters

value The input value.

Returns: The hyperbolic arc tangent of the value.

◆ Floor()

template<class DataType >

DataType Murl::Math::Floor ( DataType value )

Round down to an integral value.

Parameters

value The input value.

Returns: The round down integral value.

Referenced by Murl::Math::Round().

◆ Ceil()

template<class DataType >

DataType Murl::Math::Ceil ( DataType value )

Round up to an integral value.

Parameters

value The input value.

Returns: The round up integral value.

Referenced by Murl::Math::Round().

◆ Round()

template<class DataType >

DataType Murl::Math::Round ( DataType value )

Round to an integral value, regardless of the rounding direction.

Rounding half-way cases away from zero.

Parameters

value The input value.

Returns: The rounded integral value.

References Murl::Math::Ceil(), and Murl::Math::Floor().

◆ IsEqual()

template<class DataType >

Bool Murl::Math::IsEqual	(	const DataType &	a,
		const DataType &	b,
		const DataType &	epsilon = `Limits<DataType>::Epsilon()`
	)

Check if two values are equal within an epsilon range.

Parameters

a	The 1st value.
b	The 2nd value.
epsilon	The epsilon value.

Returns: true if Abs(a - b) is within epsilon range.

References Murl::Math::Abs().

◆ DegToRad()

template<class DataType >

DataType Murl::Math::DegToRad ( DataType degrees )

Convert degrees into radiants.

Parameters

degrees The degrees to convert.

Returns: The radiants.

References Murl::Math::DEG_TO_RAD.

◆ RadToDeg()

template<class DataType >

DataType Murl::Math::RadToDeg ( DataType radiants )

Convert radiants into degrees.

Parameters

radiants The radiants to convert.

Returns: The degrees.

References Murl::Math::RAD_TO_DEG.

◆ MapAngle()

template<class DataType >

DataType Murl::Math::MapAngle ( DataType angle )

Map an angle into range [-PI .

. PI).

Parameters

angle The angle value in radiants.

Returns: The mapped angle in range [-PI .. PI).

References Murl::Math::Fmod(), Murl::Math::PI, and Murl::Math::TWO_PI.

Referenced by Murl::Math::AddAngle(), and Murl::Math::SubAngle().

◆ AddAngle()

template<class DataType >

DataType Murl::Math::AddAngle	(	DataType	angle1,
		DataType	angle2
	)

Calculate the sum of two angles.

Parameters

angle1	The first angle value in radiants.
angle2	The second angle value in radiants.

Returns: The result of (angle1 + angle2) in range [-PI .. PI).

References Murl::Math::MapAngle().

◆ SubAngle()

template<class DataType >

DataType Murl::Math::SubAngle	(	DataType	angle1,
		DataType	angle2
	)

Calculate the difference between two angles.

Parameters

angle1	The first angle value in radiants.
angle2	The second angle value in radiants.

Returns: The result of (angle1 - angle2) in range [-PI .. PI).

References Murl::Math::MapAngle().

◆ FloatToHalfFloat()

UInt16 Murl::Math::FloatToHalfFloat ( Float value )

inline

Convert a given 32bit float value to 16bit ("half float"), represented by a UInt16 integer.

Parameters

value The 32bit float value to convert

Returns: The half float value as an UInt16.

References Murl::Math::Clamp().

Referenced by Murl::Math::IntToHalfFloat().

◆ IntToHalfFloat()

UInt16 Murl::Math::IntToHalfFloat ( UInt8 value )

inline

Convert a given 8bit unsigned integer value to a 16bit floating point value ("half float"), represented by a UInt16 integer.

The input value is divided by 255.

Parameters

value The 8bit unsigned integer value to convert

Returns: The half float value as an UInt16.

References Murl::Math::FloatToHalfFloat().

◆ HalfFloatToFloat()

Float Murl::Math::HalfFloatToFloat ( UInt16 value )

inline

Convert a given 16bit half float value stored in a UInt16 to a 32bit float value.

Parameters

value The 16bit float value to convert

Returns: The converted 32bit float value

References Murl::Math::Clamp().

Referenced by Murl::Math::HalfFloatToInt().

◆ HalfFloatToInt()

UInt8 Murl::Math::HalfFloatToInt ( UInt16 value )

inline

Convert a given 16bit half float value stored in a UInt16 to a 8bit unsigned integer value.

The output value is first clamped to the range [0..1] and then multiplied by 255.

Parameters

value The 16bit float value to convert

Returns: The converted 8bit unsigned integer value

References Murl::Math::Clamp(), and Murl::Math::HalfFloatToFloat().

◆ FloatToPackedFloat11()

UInt16 Murl::Math::FloatToPackedFloat11 ( Float value )

inline

Convert a given 32bit float value to an 11bit packed float, represented by a UInt16 integer.

Parameters

value The 32bit float value to convert

Returns: The packed 11bit float value as an UInt16.

References Murl::Math::Clamp().

◆ PackedFloat11ToFloat()

Float Murl::Math::PackedFloat11ToFloat ( UInt16 value )

inline

Convert a given packed 11bit float value stored in a UInt16 to a 32bit float value.

Parameters

value The packed 11bit float value to convert

Returns: The converted 32bit float value

References Murl::Math::Clamp().

◆ FloatToPackedFloat10()

UInt16 Murl::Math::FloatToPackedFloat10 ( Float value )

inline

Convert a given 32bit float value to an 10bit packed float, represented by a UInt16 integer.

Parameters

value The 32bit float value to convert

Returns: The packed 10bit float value as an UInt16.

References Murl::Math::Clamp().

◆ PackedFloat10ToFloat()

Float Murl::Math::PackedFloat10ToFloat ( UInt16 value )

inline

Convert a given packed 10bit float value stored in a UInt16 to a 32bit float value.

Parameters

value The packed 10bit float value to convert

Returns: The converted 32bit float value

References Murl::Math::Clamp().

◆ Lerp() [1/2]

template<class DataTypeV , class DataTypeT >

DataTypeV Murl::Math::Lerp	(	const DataTypeV &	startValue,
		const DataTypeV &	endValue,
		DataTypeT	t
	)

The linear interpolation template function.

Parameters

startValue	The start value to interpolate.
endValue	The end value to interpolate.
t	The parameter to interpolate in range [0 .. 1].

Returns: The interpolation between the inputs startValue and endValue for a parameter t in the closed unit interval [0 .. 1].

Referenced by Murl::Logic::Animation< DataType >::OnEvaluate().

◆ Lerp() [2/2]

template<class DataTypeT >

Double Murl::Math::Lerp	(	Double	startValue,
		Double	endValue,
		DataTypeT	t
	)

The linear interpolation template function for Double.

Parameters

startValue	The start value to interpolate.
endValue	The end value to interpolate.
t	The parameter to interpolate in range [0 .. 1].

Returns: The interpolation between the inputs startValue and endValue for a parameter t in the closed unit interval [0 .. 1].

◆ GetCubicBezierParameter()

template<class DataTypeV , class DataTypeT >

DataTypeT Murl::Math::GetCubicBezierParameter	(	DataTypeV	x0,
		DataTypeV	x1,
		DataTypeV	x2,
		DataTypeV	x3,
		DataTypeV	x
	)

Get the cubic bezier parameter t for a given X value.

This function interpolates the bezier parameter t (in the range [0..1] for a given target X value and the X values of the four curve control points.

Parameters

x0	The X value of the starting point (first control point)
x1	The X value of the second control point
x2	The X value of the third control point
x3	The X value of the end point (fourth control point)
x	The target X value

Returns: The interpolated curve parameter in the range [0..1].

References Murl::Math::Abs(), and Murl::Math::Clamp().

◆ CubicBezier()

template<class DataTypeV , class DataTypeT >

DataTypeV Murl::Math::CubicBezier	(	DataTypeV	x0,
		DataTypeV	x1,
		DataTypeV	x2,
		DataTypeV	x3,
		DataTypeT	t
	)

Evaluate a cubic bezier curve for a given parameter t.

This function returns the interpolated value of a cubic bezier curve defined via four control points and a given parameter t in the range [0..1].

Parameters

x0	The starting point (first control point)
x1	The second control point
x2	The third control point
x3	The end point (fourth control point)
t	The curve parameter in the range [0..1]

Returns: The interpolated X value.

◆ CubicBezierAt()

template<class DataTypeV >

DataTypeV Murl::Math::CubicBezierAt	(	DataTypeV	x0,
		DataTypeV	x1,
		DataTypeV	x2,
		DataTypeV	x3,
		DataTypeV	y0,
		DataTypeV	y1,
		DataTypeV	y2,
		DataTypeV	y3,
		DataTypeV	x
	)

Evaluate a cubic bezier curve at a given X value.

This function returns the interpolated Y value of a cubic bezier curve defined via four (X,Y) control point pairs and a given target X value. If the target X value is outside the range [x0..x3], it is clamped to that range.

Parameters

x0	The X value of the starting point (first control point)
x1	The X value of the second control point
x2	The X value of the third control point
x3	The X value of the end point (fourth control point)
y0	The Y value of the starting point (first control point)
y1	The Y value of the second control point
y2	The Y value of the third control point
y3	The Y value of the end point (fourth control point)
x	The target X value

Returns: The interpolated Y value

◆ GetEasingFunction()

template<class DataType >

Easing<DataType>::Interpolate Murl::Math::GetEasingFunction ( IEnums::Interpolation interpolation )

Get the Easing::Interpolate function for a specified interpolation.

Parameters

interpolation The interpolation.

Returns: The corresponding Easing::Interpolate function, or Easing::Linear() if the interpolation is invalid.

◆ Interpolation()

template<class DataType >

DataType Murl::Math::Interpolation	(	IEnums::Interpolation	interpolation,
		DataType	x
	)

The interpolation template function calculates the IEnums::Interpolation curve (easing function).

Parameters

interpolation	The interpolation.
x	The value to interpolate in range [0 .. 1].

Returns: The easing function result.

Referenced by Murl::Logic::Animation< DataType >::OnEvaluate(), and Murl::Logic::Animation< DataType >::SetIntermediateKeys().