Classes
class	pcl::Fact< T >
	Factorial function. More...

class	pcl::Pow10I< T >
	Exponential function 10**n, n being a signed integer. More...

class	pcl::Pow2I< T >
	Exponential function 2**n, n being a signed integer. More...

Functions
float	pcl::Abs (float x) noexcept

template<typename T >
constexpr T	pcl::Angle (int d, int m, T s) noexcept

template<typename T >
constexpr T	pcl::Angle (int d, T m) noexcept

template<typename T >
constexpr T	pcl::ArcCos (T x) noexcept

template<typename T >
constexpr T	pcl::ArcCosh (T x) noexcept

template<typename T >
constexpr T	pcl::ArcHav (T x) noexcept

template<typename T >
constexpr T	pcl::ArcSin (T x) noexcept

template<typename T >
constexpr T	pcl::ArcSinh (T x) noexcept

template<typename T >
constexpr T	pcl::ArcTan (T x) noexcept

template<typename T >
constexpr T	pcl::ArcTan (T y, T x) noexcept

template<typename T >
T	pcl::ArcTan2Pi (T y, T x) noexcept

template<typename T >
constexpr T	pcl::ArcTanh (T x) noexcept

template<typename T >
constexpr T	pcl::AsRad (T x) noexcept

void PCL_FUNC	pcl::CalendarTimeToJD (int &jdi, double &jdf, int year, int month, int day, double dayf=0) noexcept

double	pcl::CalendarTimeToJD (int year, int month, int day, double dayf=0) noexcept

template<typename T >
constexpr T	pcl::Ceil (T x) noexcept

template<typename T >
constexpr T	pcl::Cos (T x) noexcept

template<typename T >
constexpr T	pcl::Cosh (T x) noexcept

template<typename T >
constexpr T	pcl::Cotan (T x) noexcept

template<typename S1 , typename S2 , typename S3 , typename D >
void	pcl::DecimalToSexagesimal (int &sign, S1 &s1, S2 &s2, S3 &s3, const D &d) noexcept

template<typename T >
constexpr T	pcl::Deg (T x) noexcept

template<typename T >
constexpr T	pcl::Erf (T x) noexcept

template<typename T >
constexpr T	pcl::ErfInv (T x) noexcept

template<typename T >
constexpr T	pcl::Exp (T x) noexcept

double	pcl::Factorial (int n) noexcept

template<typename T >
constexpr T	pcl::Floor (T x) noexcept

template<typename T >
constexpr T	pcl::Frac (T x) noexcept

template<typename T >
void	pcl::Frexp (T x, T &m, int &p) noexcept

template<typename T >
constexpr T	pcl::Hav (T x) noexcept

void	pcl::JDToCalendarTime (int &year, int &month, int &day, double &dayf, double jd) noexcept

void PCL_FUNC	pcl::JDToCalendarTime (int &year, int &month, int &day, double &dayf, int jdi, double jdf) noexcept

template<typename T >
T	pcl::L1Norm (const T i, const T j) noexcept

template<typename T >
T	pcl::L2Norm (const T i, const T j) noexcept

template<typename T >
constexpr T	pcl::Ldexp (T m, int p) noexcept

template<typename T >
constexpr T	pcl::Ln (T x) noexcept

constexpr long double	pcl::Ln2 () noexcept

double	pcl::LnFactorial (int n) noexcept

template<typename T >
constexpr T	pcl::Log (T x) noexcept

constexpr long double	pcl::Log2 () noexcept

template<typename T >
constexpr T	pcl::Log2 (T x) noexcept

constexpr long double	pcl::Log2e () noexcept

constexpr long double	pcl::Log2T () noexcept

template<typename T >
constexpr T	pcl::LogN (T n, T x) noexcept

template<typename T >
constexpr T	pcl::MasRad (T x) noexcept

template<typename T >
constexpr T	pcl::MinRad (T x) noexcept

template<typename T >
constexpr T	pcl::Mod (T x, T y) noexcept

template<typename T >
constexpr T	pcl::Mod2Pi (T x) noexcept

template<typename T >
constexpr T	pcl::ModPi (T x) noexcept

template<typename T >
T	pcl::Norm (const T i, const T j) noexcept

template<typename T , typename P >
T	pcl::Norm (const T i, const T j, const P &p) noexcept

template<typename T >
constexpr T	pcl::Norm2Pi (T x) noexcept

constexpr long double	pcl::Pi () noexcept

template<typename T , typename C >
T	pcl::Poly (T x, C c, int n) noexcept

template<typename T >
T	pcl::Poly (T x, std::initializer_list< T > c) noexcept

template<typename T >
constexpr T	pcl::Pow (T x, T y) noexcept

template<typename T >
T	pcl::Pow10 (T x) noexcept

template<typename T >
constexpr T	pcl::Pow2 (T x) noexcept

template<typename T >
T	pcl::PowI (T x, int n) noexcept

template<typename T >
T	pcl::PowI10 (T x) noexcept

template<typename T >
T	pcl::PowI12 (T x) noexcept

template<typename T >
T	pcl::PowI4 (T x) noexcept

template<typename T >
T	pcl::PowI6 (T x) noexcept

template<typename T >
T	pcl::PowI8 (T x) noexcept

template<typename T >
constexpr T	pcl::Rad (T x) noexcept

template<typename T >
constexpr T	pcl::RadMin (T x) noexcept

template<typename T >
constexpr T	pcl::RadSec (T x) noexcept

template<typename T1 , typename T2 >
void	pcl::Rotate (int &x, int &y, T1 sa, T1 ca, T2 xc, T2 yc) noexcept

template<typename T1 , typename T2 >
void	pcl::Rotate (int64 &x, int64 &y, T1 sa, T1 ca, T2 xc, T2 yc) noexcept

template<typename T1 , typename T2 >
void	pcl::Rotate (long &x, long &y, T1 sa, T1 ca, T2 xc, T2 yc) noexcept

template<typename T , typename T1 , typename T2 >
void	pcl::Rotate (T &x, T &y, T1 a, T2 xc, T2 yc) noexcept

template<typename T , typename T1 , typename T2 >
void	pcl::Rotate (T &x, T &y, T1 sa, T1 ca, T2 xc, T2 yc) noexcept

template<typename T >
T	pcl::RotL (T x, uint32 n) noexcept

template<typename T >
T	pcl::RotR (T x, uint32 n) noexcept

double	pcl::Round (double x) noexcept

float	pcl::Round (float x) noexcept

long double	pcl::Round (long double x) noexcept

template<typename T >
T	pcl::Round (T x, int n) noexcept

template<typename T >
int	pcl::RoundI (T x) noexcept

template<typename T >
int	pcl::RoundInt (T x) noexcept

int64	pcl::RoundInt64 (double x) noexcept

int64	pcl::RoundInt64Arithmetic (double x) noexcept

template<typename T >
int	pcl::RoundIntArithmetic (T x) noexcept

template<typename T >
int	pcl::RoundIntBanker (T x) noexcept

template<typename T >
constexpr T	pcl::SecRad (T x) noexcept

template<typename S1 , typename S2 , typename S3 >
double	pcl::SexagesimalToDecimal (int sign, const S1 &s1, const S2 &s2=S2(0), const S3 &s3=S3(0)) noexcept

template<typename T >
constexpr int	pcl::Sign (T x) noexcept

template<typename T >
constexpr char	pcl::SignChar (T x) noexcept

template<typename T >
constexpr T	pcl::Sin (T x) noexcept

template<typename T >
void	pcl::SinCos (T x, T &sx, T &cx) noexcept

template<typename T >
constexpr T	pcl::Sinh (T x) noexcept

template<typename T >
void	pcl::Split (T x, T &i, T &f) noexcept

template<typename T >
constexpr T	pcl::Sqrt (T x) noexcept

template<typename T >
constexpr T	pcl::Tan (T x) noexcept

template<typename T >
constexpr T	pcl::Tanh (T x) noexcept

template<typename T >
T	pcl::Trunc (T x) noexcept

template<typename T >
int	pcl::TruncI (T x) noexcept

template<typename T >
int64	pcl::TruncI64 (T x) noexcept

template<typename T >
int	pcl::TruncInt (T x) noexcept

template<typename T >
int64	pcl::TruncInt64 (T x) noexcept

constexpr long double	pcl::TwoPi () noexcept

template<typename T >
constexpr T	pcl::UasRad (T x) noexcept

Detailed Description

Function Documentation

◆ Abs()

float pcl::Abs ( float x )

inlinenoexcept

Absolute value of x.

Definition at line 390 of file Math.h.

◆ Angle() [1/2]

template<typename T >

constexpr T pcl::Angle	(	int	d,
		int	m,
		T	s
	)

inlineconstexprnoexcept

Merges a compound angle given by degrees, arcminutes and arcseconds into a single scalar in degrees.

Definition at line 562 of file Math.h.

◆ Angle() [2/2]

template<typename T >

constexpr T pcl::Angle	(	int	d,
		T	m
	)

inlineconstexprnoexcept

Merges a compound angle given by degrees and arcminutes into a single scalar in degrees.

Definition at line 552 of file Math.h.

◆ ArcCos()

template<typename T >

constexpr T pcl::ArcCos ( T x )

inlineconstexprnoexcept

Inverse cosine function (arccosine).

Definition at line 573 of file Math.h.

Referenced by pcl::ProjectionBase::DistanceFast().

◆ ArcCosh()

template<typename T >

constexpr T pcl::ArcCosh ( T x )

inlineconstexprnoexcept

Inverse hyperbolic cosine function.

ArcCosh( x ) = 2*Ln( Sqrt( (x + 1)/2 ) + Sqrt( (x - 1)/2 ) )

Definition at line 1876 of file Math.h.

◆ ArcHav()

template<typename T >

constexpr T pcl::ArcHav ( T x )

inlineconstexprnoexcept

Inverse haversine (archaversine) function:

ArcHav( x ) = 2*ArcSin( Sqrt( x ) )

The haversine is useful to work with tiny angles.

Definition at line 1914 of file Math.h.

◆ ArcSin()

template<typename T >

constexpr T pcl::ArcSin ( T x )

inlineconstexprnoexcept

Inverse sine function (arcsine).

Definition at line 585 of file Math.h.

Referenced by pcl::Position::EquatorialToHorizontal().

◆ ArcSinh()

template<typename T >

constexpr T pcl::ArcSinh ( T x )

inlineconstexprnoexcept

Inverse hyperbolic sine function.

ArcSinh( x ) = Ln( x + Sqrt( 1 + x**2 ) )

Definition at line 1858 of file Math.h.

◆ ArcTan() [1/2]

template<typename T >

constexpr T pcl::ArcTan ( T x )

inlineconstexprnoexcept

Inverse tangent function (arctangent).

Definition at line 597 of file Math.h.

Referenced by pcl::GenericVector< T >::Angle3D(), pcl::Position::EquatorialToHorizontal(), and pcl::ZenithalProjectionBase::Unproject().

◆ ArcTan() [2/2]

template<typename T >

constexpr T pcl::ArcTan	(	T	y,
		T	x
	)

inlineconstexprnoexcept

Arctangent of y/x, result in the proper quadrant.

Definition at line 608 of file Math.h.

◆ ArcTan2Pi()

template<typename T >

T pcl::ArcTan2Pi	(	T	y,
		T	x
	)

inlinenoexcept

Arctangent of y/x, proper quadrant, result in the interval [0,2pi).

Definition at line 619 of file Math.h.

◆ ArcTanh()

template<typename T >

constexpr T pcl::ArcTanh ( T x )

inlineconstexprnoexcept

Inverse hyperbolic tangent function.

ArcTanh( x ) = (Ln( 1 + x ) - Ln( 1 - x ))/2

Definition at line 1894 of file Math.h.

◆ AsRad()

template<typename T >

constexpr T pcl::AsRad ( T x )

inlineconstexprnoexcept

Conversion from arcseconds to radians (a synonym for SecRad()).

Definition at line 1978 of file Math.h.

Referenced by pcl::Position::EpsA().

◆ CalendarTimeToJD() [1/2]

void PCL_FUNC pcl::CalendarTimeToJD	(	int &	jdi,
		double &	jdf,
		int	year,
		int	month,
		int	day,
		double	dayf = `0`
	)

noexcept

Computes the Julian date (JD) corresponding to a time point expressed as a date and a day fraction, providing the result by its separate integer and fractional parts.

Parameters

[out]	jdi	On output, the integer part of the resulting JD.
[out]	jdf	On output, the fractional part of the resulting JD.
	year	The year of the date. Positive and negative years are supported. Years are counted arithmetically: the year zero is the year before the year +1, that is, what historians call the year 1 B.C.
	month	The month of the date. Usually in the [1,12] range but can be any integer number.
	day	The day of the date. Usually in the [1,31] range but can be any integer number.
	dayf	The day fraction. The default value is zero, which computes the JD at zero hours. Usually in the [0,1) range but can be any real number.

This routine, as well as JDToCalendarTime(), implement modified versions of the original algorithms due to Jean Meeus. Our modifications allow for negative Julian dates, which extends the range of allowed dates to the past considerably. We developed these modifications in the context of large-scale solar system ephemeris calculations.

The computed value is the JD corresponding to the specified date and day fraction, which is equal to the sum of the jdi and jdf variables.

References

Meeus, Jean (1991), Astronomical Algorithms, Willmann-Bell, Inc., chapter 7.

Referenced by pcl::TimePoint::TimePoint(), and pcl::CalendarTimeToJD().

◆ CalendarTimeToJD() [2/2]

double pcl::CalendarTimeToJD	(	int	year,
		int	month,
		int	day,
		double	dayf = `0`
	)

inlinenoexcept

Computes the Julian date (JD) corresponding to a time point expressed as a date and a day fraction.

Parameters

year	The year of the date. Positive and negative years are supported. Years are counted arithmetically: the year zero is the year before the year +1, that is, what historians call the year 1 B.C.
month	The month of the date. Usually in the [1,12] range but can be any integer number.
day	The day of the date. Usually in the [1,31] range but can be any integer number.
dayf	The day fraction. The default value is zero, which computes the JD at zero hours. Usually in the [0,1) range but can be any real number.

This routine, as well as JDToCalendarTime(), implement modified versions of the original algorithms due to Jean Meeus. Our modifications allow for negative Julian dates, which extends the range of allowed dates to the past considerably. We developed these modifications in the context of large-scale solar system ephemeris calculations.

The returned value is the JD corresponding to the specified date and day fraction.

Because of the numerical precision of the double type (IEEE 64-bit floating point), this routine can return JD values accurate only to within one millisecond.

References

Meeus, Jean (1991), Astronomical Algorithms, Willmann-Bell, Inc., chapter 7.

Definition at line 2459 of file Math.h.

References pcl::CalendarTimeToJD().

◆ Ceil()

template<typename T >

constexpr T pcl::Ceil ( T x )

inlineconstexprnoexcept

The ceil function: lowest integer >= x.

Definition at line 633 of file Math.h.

◆ Cos()

template<typename T >

constexpr T pcl::Cos ( T x )

inlineconstexprnoexcept

Cosine function.

Definition at line 644 of file Math.h.

◆ Cosh()

template<typename T >

constexpr T pcl::Cosh ( T x )

inlineconstexprnoexcept

Hyperbolic Cosine function.

Definition at line 655 of file Math.h.

◆ Cotan()

template<typename T >

constexpr T pcl::Cotan ( T x )

inlineconstexprnoexcept

Cotangent of x, equal to Cos(x)/Sin(x) or 1/Tan(x).

Definition at line 666 of file Math.h.

◆ DecimalToSexagesimal()

template<typename S1 , typename S2 , typename S3 , typename D >

void pcl::DecimalToSexagesimal	(	int &	sign,
		S1 &	s1,
		S2 &	s2,
		S3 &	s3,
		const D &	d
	)

inlinenoexcept

Conversion of a decimal scalar d to the equivalent sexagesimal decimal components sign, s1, s2 and s3, such that:

d = sign * (s1 + (s2 + s3/60)/60)

with the following constraints:

sign = -1 iff d < 0
sign = +1 iff d ≥ 0
0 ≤ s1
0 ≤ s2 < 60
0 ≤ s3 < 60

Definition at line 2556 of file Math.h.

◆ Deg()

template<typename T >

constexpr T pcl::Deg ( T x )

inlineconstexprnoexcept

Conversion from radians to degrees.

Definition at line 677 of file Math.h.

Referenced by pcl::ProjectionBase::CelestialPoleNativeCoordinates(), pcl::GenericPoint< T >::Deg(), pcl::ProjectionBase::DistanceFast(), pcl::ProjectionBase::ProjectionOrigin(), pcl::ProjectionBase::ReferenceCelestialCoordinates(), pcl::GenericPoint< T >::ToDeg(), and pcl::ZenithalProjectionBase::Unproject().

◆ Erf()

template<typename T >

constexpr T pcl::Erf ( T x )

inlineconstexprnoexcept

The error function: erf( x ).

Definition at line 4679 of file Math.h.

◆ ErfInv()

template<typename T >

constexpr T pcl::ErfInv ( T x )

inlineconstexprnoexcept

The inverse error function: erf^-1( x ).

Code adapted from erfinv implementation by Lakshay Garg:

https://github.com/lakshayg/erfinv

Definition at line 4696 of file Math.h.

◆ Exp()

template<typename T >

constexpr T pcl::Exp ( T x )

inlineconstexprnoexcept

The exponential function e**x.

Definition at line 688 of file Math.h.

◆ Factorial()

double pcl::Factorial ( int n )

inlinenoexcept

The factorial of n ≥ 0.

A static lookup table is used to speed up for n <= 127.

Definition at line 783 of file Math.h.

◆ Floor()

template<typename T >

constexpr T pcl::Floor ( T x )

inlineconstexprnoexcept

The floor function: highest integer <= x.

Definition at line 699 of file Math.h.

◆ Frac()

template<typename T >

constexpr T pcl::Frac ( T x )

inlineconstexprnoexcept

Fractional part of x. The returned value is within (-1,+1), and has the same sign as x.

Definition at line 711 of file Math.h.

Referenced by pcl::TimePoint::TimePoint(), pcl::TimePoint::GetCalendarTime(), and pcl::JDToCalendarTime().

◆ Frexp()

template<typename T >

void pcl::Frexp	(	T	x,
		T &	m,
		int &	p
	)

inlinenoexcept

Calculates base-2 mantissa and exponent. The arguments m and p receive the values of the base-2 mantissa and exponent, respectively, such that: 0.5 <= m < 1.0, x = m * 2**p

Definition at line 724 of file Math.h.

◆ Hav()

template<typename T >

constexpr T pcl::Hav ( T x )

inlineconstexprnoexcept

Haversine function:

Hav( x ) = (1 - Cos( x ))/2

The haversine is useful to work with tiny angles.

Definition at line 740 of file Math.h.

◆ JDToCalendarTime() [1/2]

void pcl::JDToCalendarTime	(	int &	year,
		int &	month,
		int &	day,
		double &	dayf,
		double	jd
	)

inlinenoexcept

Computes the date and day fraction corresponding to a time point expressed as a Julian date (JD).

Parameters

[out]	year	On output, this variable receives the year of the resulting date.
[out]	month	On output, this variable receives the month of the resulting date in the range [1,12].
[out]	day	On output, this variable receives the day of the resulting date in the range [1,31]. Different month day counts and leap years are taken into account, so the returned day corresponds to an existing calendar date.
[out]	dayf	On output, this variable receives the day fraction for the specified time point, in the [0,1) range.
	jd	The input time point as a Julian date.

Because of the numerical precision of the double type (IEEE 64-bit floating point), this routine can handle JD values accurate only to within one millisecond.

For more information about the implemented algorithms and references, see the documentation for CalendarTimeToJD().

Definition at line 2528 of file Math.h.

References pcl::Frac(), pcl::JDToCalendarTime(), and pcl::TruncInt().

◆ JDToCalendarTime() [2/2]

void PCL_FUNC pcl::JDToCalendarTime	(	int &	year,
		int &	month,
		int &	day,
		double &	dayf,
		int	jdi,
		double	jdf
	)

noexcept

Computes the date and day fraction corresponding to a time point expressed as a Julian date (JD), specified by its separate integer and fractional parts.

Parameters

[out]	year	On output, this variable receives the year of the resulting date.
[out]	month	On output, this variable receives the month of the resulting date in the range [1,12].
[out]	day	On output, this variable receives the day of the resulting date in the range [1,31]. Different month day counts and leap years are taken into account, so the returned day corresponds to an existing calendar date.
[out]	dayf	On output, this variable receives the day fraction for the specified time point, in the [0,1) range.
	jdi	The integer part of the input Julian date.
	jdf	The fractional part of the input Julian date.

The input time point must be equal to the sum of jdi and jdf.

For more information about the implemented algorithms and references, see the documentation for CalendarTimeToJD().

Referenced by pcl::TimePoint::Day(), pcl::TimePoint::DayFraction(), pcl::TimePoint::GetCalendarTime(), pcl::JDToCalendarTime(), pcl::TimePoint::Month(), and pcl::TimePoint::Year().

◆ L1Norm()

template<typename T >

T pcl::L1Norm	(	const T *	i,
		const T *	j
	)

inlinenoexcept

Computes the L1 norm (or Manhattan norm) of the elements in the sequence [i,j). The L1 norm is the sum of the absolute values of the elements.

Definition at line 2225 of file Math.h.

Referenced by pcl::GenericVector< T >::L1Norm().

◆ L2Norm()

template<typename T >

T pcl::L2Norm	(	const T *	i,
		const T *	j
	)

inlinenoexcept

Computes the L2 norm (or Euclidean norm) of the elements in the sequence [i,j). The L2 norm is the square root of the sum of squared elements.

Definition at line 2284 of file Math.h.

Referenced by pcl::GenericVector< T >::L2Norm(), and pcl::GenericVector< T >::Norm().

◆ Ldexp()

template<typename T >

constexpr T pcl::Ldexp	(	T	m,
		int	p
	)

inlineconstexprnoexcept

Calculates m * 2**p.

Definition at line 751 of file Math.h.

◆ Ln()

template<typename T >

constexpr T pcl::Ln ( T x )

inlineconstexprnoexcept

Natural (base e) logarithm of x.

Definition at line 762 of file Math.h.

◆ Ln2()

constexpr long double pcl::Ln2 ( )

inlineconstexprnoexcept

Natural (base e) logarithm of two.

Definition at line 870 of file Math.h.

◆ LnFactorial()

double pcl::LnFactorial ( int n )

inlinenoexcept

The natural logarithm of the factorial of n ≥ 0.

For n <= 127 computes the natural logarithm of the factorial function directly. For n > 127 computes a series approximation, so that the function won't overflow even for very large arguments.

Definition at line 803 of file Math.h.

References pcl::Ln().

◆ Log()

template<typename T >

constexpr T pcl::Log ( T x )

inlineconstexprnoexcept

Base 10 Logarithm of x.

Definition at line 881 of file Math.h.

◆ Log2() [1/2]

constexpr long double pcl::Log2 ( )

inlineconstexprnoexcept

Base 10 Logarithm of two.

Definition at line 893 of file Math.h.

◆ Log2() [2/2]

template<typename T >

constexpr T pcl::Log2 ( T x )

inlineconstexprnoexcept

Base 2 Logarithm of x.

Definition at line 906 of file Math.h.

◆ Log2e()

constexpr long double pcl::Log2e ( )

inlineconstexprnoexcept

Base 2 Logarithm of e.

Definition at line 920 of file Math.h.

◆ Log2T()

constexpr long double pcl::Log2T ( )

inlineconstexprnoexcept

Base 2 Logarithm of ten.

Definition at line 933 of file Math.h.

◆ LogN()

template<typename T >

constexpr T pcl::LogN	(	T	n,
		T	x
	)

inlineconstexprnoexcept

Base n logarithm of x.

Definition at line 946 of file Math.h.

◆ MasRad()

template<typename T >

constexpr T pcl::MasRad ( T x )

inlineconstexprnoexcept

Conversion from milliarcseconds (mas) to radians.

Definition at line 1989 of file Math.h.

◆ MinRad()

template<typename T >

constexpr T pcl::MinRad ( T x )

inlineconstexprnoexcept

Conversion from arcminutes to radians.

Definition at line 1958 of file Math.h.

◆ Mod()

template<typename T >

constexpr T pcl::Mod	(	T	x,
		T	y
	)

inlineconstexprnoexcept

Remainder of x/y.

Definition at line 958 of file Math.h.

◆ Mod2Pi()

template<typename T >

constexpr T pcl::Mod2Pi ( T x )

inlineconstexprnoexcept

An angle in radians reduced to the (-2pi,+2pi) range, that is, the remainder of x/(2*pi).

Definition at line 2024 of file Math.h.

◆ ModPi()

template<typename T >

constexpr T pcl::ModPi ( T x )

inlineconstexprnoexcept

An angle in radians reduced to the [-pi,+pi] range.

Definition at line 2011 of file Math.h.

◆ Norm() [1/2]

template<typename T >

T pcl::Norm	(	const T *	i,
		const T *	j
	)

inlinenoexcept

Computes the L2 norm (or Euclidean norm) of the elements in the sequence [i,j). This function is a synonym for L2Norm().

Definition at line 2334 of file Math.h.

◆ Norm() [2/2]

template<typename T , typename P >

T pcl::Norm	(	const T *	i,
		const T *	j,
		const P &	p
	)

inlinenoexcept

Computes the norm of the elements in the sequence [i,j). For any real p > 0, the norm N is given by:

N = sum( abs( x )^p )^(1/p)

for all x in [i,j).

See also: L1Norm(), L2Norm()

Definition at line 2166 of file Math.h.

Referenced by pcl::GenericVector< T >::Norm().

◆ Norm2Pi()

template<typename T >

constexpr T pcl::Norm2Pi ( T x )

inlineconstexprnoexcept

An angle in radians normalized to the [0,2pi) range.

Definition at line 2035 of file Math.h.

Referenced by pcl::Position::EquatorialToHorizontal(), and pcl::OsculatingElements::MeanAnomalyFromTimeOfPerifocalPassage().

◆ Pi()

constexpr long double pcl::Pi ( )

inlineconstexprnoexcept

The pi constant: 3.141592...

Definition at line 531 of file Math.h.

◆ Poly() [1/2]

template<typename T , typename C >

T pcl::Poly	(	T	x,
		C	c,
		int	n
	)

inlinenoexcept

Horner's algorithm to evaluate the polynomial function with the specified array c of n + 1 coefficients:

y = c[0] + c[1]*x + c[2]*x**2 + ... + c[n]*x**n

The array c of coefficients must provide contiguous storage for at least n + 1 values of type T. The degree n must be >= 0; otherwise this function invokes undefined behavior.

Definition at line 979 of file Math.h.

Referenced by pcl::Position::EpsA().

◆ Poly() [2/2]

template<typename T >

T pcl::Poly	(	T	x,
		std::initializer_list< T >	c
	)

inlinenoexcept

Horner's algorithm to evaluate the polynomial function:

y = c[0] + c[1]*x + c[2]*x**2 + ... + c[n]*x**n

The specified coefficients initializer list c must not be empty; otherwise this function invokes undefined behavior.

Definition at line 1003 of file Math.h.

◆ Pow()

template<typename T >

constexpr T pcl::Pow	(	T	x,
		T	y
	)

inlineconstexprnoexcept

General power function: x raised to y.

When you know some of the arguments in advance, faster alternatives are:

Use Pow10I<T>()( y ) when x == 10 and y is an integer
Use PowI( x, y ) when x != 10 and y is an integer
Use Pow10( y ) when x == 10 and y is not an integer

Otherwise, you can also use: Pow2( y*Log2( x ) )

Definition at line 1298 of file Math.h.

◆ Pow10()

template<typename T >

T pcl::Pow10 ( T x )

inlinenoexcept

The exponential function 10**x.

Definition at line 1359 of file Math.h.

◆ Pow2()

template<typename T >

constexpr T pcl::Pow2 ( T x )

inlineconstexprnoexcept

The exponential function 2**x.

Definition at line 1748 of file Math.h.

Referenced by pcl::PSFData::FWHM(), and pcl::MoffatFilter::FWHMx().

◆ PowI()

template<typename T >

T pcl::PowI	(	T	x,
		int	n
	)

inlinenoexcept

The exponential function x**n, where n is a signed integer.

Definition at line 1786 of file Math.h.

◆ PowI10()

template<typename T >

T pcl::PowI10 ( T x )

inlinenoexcept

Returns x raised to the 10th power.

Definition at line 1835 of file Math.h.

◆ PowI12()

template<typename T >

T pcl::PowI12 ( T x )

inlinenoexcept

Returns x raised to the 12th power.

Definition at line 1844 of file Math.h.

◆ PowI4()

template<typename T >

T pcl::PowI4 ( T x )

inlinenoexcept

Returns x raised to the 4th power.

Definition at line 1808 of file Math.h.

◆ PowI6()

template<typename T >

T pcl::PowI6 ( T x )

inlinenoexcept

Returns x raised to the 6th power.

Definition at line 1817 of file Math.h.

◆ PowI8()

template<typename T >

T pcl::PowI8 ( T x )

inlinenoexcept

Returns x raised to the 8th power.

Definition at line 1826 of file Math.h.

◆ Rad()

template<typename T >

constexpr T pcl::Rad ( T x )

inlineconstexprnoexcept

Conversion from degrees to radians.

Definition at line 1925 of file Math.h.

Referenced by pcl::GnomonicProjection::GnomonicProjection(), pcl::ProjectionBase::Distance(), pcl::ProjectionBase::DistanceFast(), pcl::Position::EquatorialToHorizontal(), pcl::ZenithalProjectionBase::Project(), and pcl::GenericPoint< T >::ToRad().

◆ RadMin()

template<typename T >

constexpr T pcl::RadMin ( T x )

inlineconstexprnoexcept

Conversion from radians to arcminutes.

Definition at line 1936 of file Math.h.

◆ RadSec()

template<typename T >

constexpr T pcl::RadSec ( T x )

inlineconstexprnoexcept

Conversion from radians to arcseconds.

Definition at line 1947 of file Math.h.

◆ Rotate() [1/5]

template<typename T1 , typename T2 >

void pcl::Rotate	(	int &	x,
		int &	y,
		T1	sa,
		T1	ca,
		T2	xc,
		T2	yc
	)

inlinenoexcept

Rotates a point on the plane.

This is a template instantiation of Rotate( T&, T&, T1, T1, T2, T2 ) for the int type.

Rotated coordinates are rounded to the nearest integers.

Definition at line 2074 of file Math.h.

References pcl::RoundInt().

◆ Rotate() [2/5]

template<typename T1 , typename T2 >

void pcl::Rotate	(	int64 &	x,
		int64 &	y,
		T1	sa,
		T1	ca,
		T2	xc,
		T2	yc
	)

inlinenoexcept

Rotates a point on the plane.

This is a template instantiation of Rotate( T&, T&, T1, T1, T2, T2 ) for the int64 type.

Rotated coordinates are rounded to the nearest integers.

Definition at line 2112 of file Math.h.

References pcl::RoundInt64().

◆ Rotate() [3/5]

template<typename T1 , typename T2 >

void pcl::Rotate	(	long &	x,
		long &	y,
		T1	sa,
		T1	ca,
		T2	xc,
		T2	yc
	)

inlinenoexcept

Rotates a point on the plane.

This is a template instantiation of Rotate( T&, T&, T1, T1, T2, T2 ) for the long type.

Rotated coordinates are rounded to the nearest integers.

Definition at line 2093 of file Math.h.

References pcl::RoundInt().

◆ Rotate() [4/5]

template<typename T , typename T1 , typename T2 >

void pcl::Rotate	(	T &	x,
		T &	y,
		T1	a,
		T2	xc,
		T2	yc
	)

inlinenoexcept

Rotates a point on the plane.

Parameters

[out]	x,y	Point coordinates. On output, these variables will receive the corresponding rotated coordinates.
	a	Rotation angle in radians.
	xc,yc	Coordinates of the center of rotation.

Instantiations for integer types round rotated coordinated to the nearest integers.

Definition at line 2136 of file Math.h.

◆ Rotate() [5/5]

template<typename T , typename T1 , typename T2 >

void pcl::Rotate	(	T &	x,
		T &	y,
		T1	sa,
		T1	ca,
		T2	xc,
		T2	yc
	)

inlinenoexcept

Rotates a point on the plane.

Parameters

[out]	x,y	Point coordinates. On output, these variables will receive the corresponding rotated coordinates.
	sa,ca	Sine and cosine of the rotation angle.
	xc,yc	Coordinates of the center of rotation.

Definition at line 2055 of file Math.h.

Referenced by pcl::Array< T, A >::Rotate(), pcl::Rotate(), pcl::GenericPoint< T >::Rotate(), and pcl::GenericRectangle< T >::Rotate().

◆ RotL()

template<typename T >

T pcl::RotL	(	T	x,
		uint32	n
	)

inlinenoexcept

Bitwise rotate left function: Rotates x to the left by n bits.

The template argument T must be an unsigned arithmetic type (uint8, uint16, uint32 or uint64). The bit count n must be smaller than the number of bits required to store an instance of T; for example, if T is uint32, n must be in the range [0,31].

Definition at line 1377 of file Math.h.

Referenced by pcl::BigToLittleEndian(), pcl::XoShiRo256ss::UI64(), and pcl::XoRoShiRo1024ss::UI64().

◆ RotR()

template<typename T >

T pcl::RotR	(	T	x,
		uint32	n
	)

inlinenoexcept

Bitwise rotate right function: Rotates x to the right by n bits.

The template argument T must be an unsigned arithmetic type (uint8, uint16, uint32 or uint64). The bit count n must be smaller than the number of bits required to store an instance of T; for example, if T is uint32, n must be in the range [0,31].

Definition at line 1398 of file Math.h.

Referenced by pcl::BigToLittleEndian().

◆ Round() [1/4]

double pcl::Round ( double x )

inlinenoexcept

Round function: x rounded to the nearest integer (double precision version).

Note: This is a performance-critical routine. It has been implemented using high-performance, low-level techniques that may include inline assembly code and/or compiler intrinsic functions.

Definition at line 1420 of file Math.h.

◆ Round() [2/4]

float pcl::Round ( float x )

inlinenoexcept

Round function: x rounded to the nearest integer (single precision version).

Note: This is a performance-critical routine. It has been implemented using high-performance, low-level techniques that may include inline assembly code and/or compiler intrinsic functions.

Definition at line 1453 of file Math.h.

◆ Round() [3/4]

long double pcl::Round ( long double x )

inlinenoexcept

Round function: x rounded to the nearest integer (long double version).

Note: This is a performance-critical routine. It has been implemented using high-performance, low-level techniques that may include inline assembly code and/or compiler intrinsic functions.

Definition at line 1486 of file Math.h.

◆ Round() [4/4]

template<typename T >

T pcl::Round	(	T	x,
		int	n
	)

inlinenoexcept

General rounding function: x rounded to n fractional digits.

Definition at line 1736 of file Math.h.

◆ RoundI()

template<typename T >

int pcl::RoundI ( T x )

inlinenoexcept

RoundI function: Rounds x to the nearest integer and converts the result to a 32-bit signed integer.

Deprecated:: Use RoundInt() in newly produced code.

Definition at line 1575 of file Math.h.

◆ RoundInt()

template<typename T >

int pcl::RoundInt ( T x )

inlinenoexcept

RoundInt function: Rounds x to the nearest integer and converts the result to a 32-bit signed integer.

This function follows the Banker's rounding rule: a perfect half is always rounded to the nearest even digit. Some examples:

RoundInt( 0.5 ) -> 0
RoundInt( 1.5 ) -> 2
RoundInt( 2.5 ) -> 2
RoundInt( 3.5 ) -> 4

By contrast, arithmetic rounding rounds a perfect half to the nearest digit, either odd or even. For example:

RoundIntArithmetic( 0.5 ) -> 1
RoundIntArithmetic( 1.5 ) -> 2
RoundIntArithmetic( 2.5 ) -> 3
RoundIntArithmetic( 3.5 ) -> 4

Banker's rounding (also known as Gaussian rounding) is statistically more accurate than the usual arithmetic rounding, but it causes aliasing problems in some specific algorithms that depend critically on uniform rounding, such as nearest neighbor upsampling.

Note: This is a performance-critical routine. It has been implemented using high-performance, low-level techniques that may include inline assembly code and/or compiler intrinsic functions.

See also: RoundIntArithmetic(), RoundIntBanker()

Definition at line 1550 of file Math.h.

Referenced by pcl::Histogram::HistogramLevel(), pcl::Control::LogicalPixelsToPhysical(), pcl::Sizer::LogicalPixelsToPhysical(), pcl::Control::LogicalPixelsToResource(), pcl::Control::PhysicalPixelsToLogical(), pcl::Sizer::PhysicalPixelsToLogical(), pcl::Histogram::Resample(), pcl::Control::ResourcePixelsToLogical(), pcl::Rotate(), pcl::GenericPoint< T >::RoundedToInt(), pcl::GenericRectangle< T >::RoundedToInt(), pcl::Control::ScaledCursorHotSpot(), pcl::UInt24PixelTraits::ToSample(), pcl::UInt20PixelTraits::ToSample(), pcl::UIResourceScalingIndex(), pcl::UIScaled(), and pcl::UIUnscaled().

◆ RoundInt64()

int64 pcl::RoundInt64 ( double x )

inlinenoexcept

RoundInt64 function: Rounds x to the nearest integer and converts the result to a 64-bit signed integer.

Since the default IEEE 754 rounding mode follows Banker's rounding rule, this is what you should expect when calling this function. See the documentation for RoundInt() for more information on rounding modes.

Note: This is a performance-critical routine. It has been implemented using high-performance, low-level techniques that may include inline assembly code and/or compiler intrinsic functions.

Definition at line 1651 of file Math.h.

References pcl::Round().

Referenced by pcl::Rotate(), and pcl::RoundI64().

◆ RoundInt64Arithmetic()

int64 pcl::RoundInt64Arithmetic ( double x )

inlinenoexcept

Rounds x to the nearest integer using the arithmetic rounding rule, and converts the result to a 64-bit signed integer.

Arithmetic rounding rounds a perfect half to the nearest digit, either odd or even. For example:

RoundIntArithmetic( 0.5 ) -> 1
RoundIntArithmetic( 1.5 ) -> 2
RoundIntArithmetic( 2.5 ) -> 3
RoundIntArithmetic( 3.5 ) -> 4

See the RoundInt() function for more information on rounding rules.

Note: This is a performance-critical routine. It has been implemented using high-performance, low-level techniques that may include inline assembly code and/or compiler intrinsic functions.

See also: RoundInt(), RoundIntBanker()

Definition at line 1714 of file Math.h.

References pcl::TruncInt64().

◆ RoundIntArithmetic()

template<typename T >

int pcl::RoundIntArithmetic ( T x )

inlinenoexcept

Rounds x to the nearest integer using the arithmetic rounding rule, and converts the result to a 32-bit signed integer.

Arithmetic rounding rounds a perfect half to the nearest digit, either odd or even. For example:

RoundIntArithmetic( 0.5 ) -> 1
RoundIntArithmetic( 1.5 ) -> 2
RoundIntArithmetic( 2.5 ) -> 3
RoundIntArithmetic( 3.5 ) -> 4

See the RoundInt() function for more information on rounding rules.

Note: This is a performance-critical routine. It has been implemented using high-performance, low-level techniques that may include inline assembly code and/or compiler intrinsic functions.

See also: RoundInt(), RoundIntBanker()

Definition at line 1617 of file Math.h.

◆ RoundIntBanker()

template<typename T >

int pcl::RoundIntBanker ( T x )

inlinenoexcept

Rounds x to the nearest integer using the Banker's rounding rule, and converts the result to a 32-bit signed integer.

This function is a convenience synonym for RoundInt().

Definition at line 1588 of file Math.h.

◆ SecRad()

template<typename T >

constexpr T pcl::SecRad ( T x )

inlineconstexprnoexcept

Conversion from arcseconds to radians.

Definition at line 1969 of file Math.h.

◆ SexagesimalToDecimal()

template<typename S1 , typename S2 , typename S3 >

double pcl::SexagesimalToDecimal	(	int	sign,
		const S1 &	s1,
		const S2 &	s2 = `S2( 0 )`,
		const S3 &	s3 = `S3( 0 )`
	)

inlinenoexcept

Conversion of the sexagesimal decimal components sign, s1, s2 and s3 to their equivalent decimal scalar. The returned value is equal to:

((sign < 0) ? -1 : +1)*(Abs( s1 ) + (s2 + s3/60)/60);

Definition at line 2578 of file Math.h.

References pcl::Abs().

◆ Sign()

template<typename T >

constexpr int pcl::Sign ( T x )

inlineconstexprnoexcept

Sign function:

-1 if x ≤ 0
 0 if x = 0
+1 if x ≥ 0

Definition at line 1022 of file Math.h.

◆ SignChar()

template<typename T >

constexpr char pcl::SignChar ( T x )

inlineconstexprnoexcept

Sign character:

'-' if x ≤ 0
' ' if x = 0
'+' if x ≥ 0

Definition at line 1040 of file Math.h.

◆ Sin()

template<typename T >

constexpr T pcl::Sin ( T x )

inlineconstexprnoexcept

Sine function

Definition at line 1051 of file Math.h.

◆ SinCos()

template<typename T >

void pcl::SinCos	(	T	x,
		T &	sx,
		T &	cx
	)

inlinenoexcept

Sine and cosine of x.

The arguments sx and cx will receive, respectively, the values of the sine and cosine of x.

If supported by the underlying standard math library, this function is roughly twice as fast as calling Sin() and Cos() separately. For code that spend a significant amount of time calculating sines and cosines, this optimization is critical.

Definition at line 1101 of file Math.h.

Referenced by pcl::GnomonicProjection::GnomonicProjection(), pcl::ProjectionBase::Distance(), pcl::ProjectionBase::DistanceFast(), pcl::Position::EclipticToEquatorial(), pcl::Position::EquatorialToEcliptic(), pcl::Position::EquatorialToHorizontal(), pcl::GenericVector< T >::FromSpherical(), pcl::ZenithalProjectionBase::Project(), pcl::GenericRectangle< T >::Rotate(), pcl::GenericMatrix< T >::RotateX(), pcl::GenericMatrix< T >::RotateY(), pcl::GenericMatrix< T >::RotateZ(), pcl::GenericMatrix< T >::RotationX(), pcl::GenericMatrix< T >::RotationY(), and pcl::GenericMatrix< T >::RotationZ().

◆ Sinh()

template<typename T >

constexpr T pcl::Sinh ( T x )

inlineconstexprnoexcept

Hyperbolic Sine function.

Definition at line 1062 of file Math.h.

◆ Split()

template<typename T >

void pcl::Split	(	T	x,
		T &	i,
		T &	f
	)

inlinenoexcept

Integer and fractional parts of x.

The arguments i and f receive, respectively, the integer (truncated) part and the fractional part of x. It holds that x = i + f, i.e. both i and f have the same sign as x.

Definition at line 1122 of file Math.h.

◆ Sqrt()

template<typename T >

constexpr T pcl::Sqrt ( T x )

inlineconstexprnoexcept

Square root function.

Definition at line 1133 of file Math.h.

◆ Tan()

template<typename T >

constexpr T pcl::Tan ( T x )

inlineconstexprnoexcept

Tangent function.

Definition at line 1144 of file Math.h.

◆ Tanh()

template<typename T >

constexpr T pcl::Tanh ( T x )

inlineconstexprnoexcept

Hyperbolic Tangent function.

Definition at line 1155 of file Math.h.

◆ Trunc()

template<typename T >

T pcl::Trunc ( T x )

inlinenoexcept

Truncated integer part of x.

Definition at line 1166 of file Math.h.

Referenced by pcl::GenericPoint< T >::Truncate(), pcl::GenericRectangle< T >::Truncate(), pcl::GenericPoint< T >::Truncated(), and pcl::GenericRectangle< T >::Truncated().

◆ TruncI()

template<typename T >

int pcl::TruncI ( T x )

inlinenoexcept

TruncI function: Truncated integer part of x as a 32-bit signed integer. to a 32-bit signed integer.

Deprecated:: Use TruncInt() in newly produced code.

Definition at line 1221 of file Math.h.

◆ TruncI64()

template<typename T >

int64 pcl::TruncI64 ( T x )

inlinenoexcept

TruncI64 function: Truncated integer part of x as a 64-bit signed integer.

Deprecated:: Use TruncInt64() in newly produced code.

Definition at line 1278 of file Math.h.

◆ TruncInt()

template<typename T >

int pcl::TruncInt ( T x )

inlinenoexcept

TruncInt function: Truncated integer part of x as a 32-bit signed integer.

Note: This is a performance-critical routine. It has been implemented using high-performance, low-level techniques that may include inline assembly code and/or compiler intrinsic functions.

Definition at line 1203 of file Math.h.

Referenced by pcl::TimePoint::TimePoint(), pcl::JPLEphemeris::DENumber(), pcl::TimePoint::GetCalendarTime(), pcl::JDToCalendarTime(), pcl::JPLEphemeris::LENumber(), pcl::Complex< T >::operator int(), pcl::GenericPoint< T >::TruncatedToInt(), and pcl::GenericRectangle< T >::TruncatedToInt().

◆ TruncInt64()

template<typename T >

int64 pcl::TruncInt64 ( T x )

inlinenoexcept

TruncInt64 function: Truncated integer part of x as a 64-bit signed integer.

Note: This is a performance-critical routine. It has been implemented using high-performance, low-level techniques that may include inline assembly code and/or compiler intrinsic functions.

Definition at line 1260 of file Math.h.

Referenced by pcl::RoundInt64Arithmetic().

◆ TwoPi()

constexpr long double pcl::TwoPi ( )

inlineconstexprnoexcept

Twice the pi constant: 0.6283185...

Definition at line 540 of file Math.h.

Referenced by pcl::GenericVector< T >::ToSpherical2Pi().

◆ UasRad()

template<typename T >

constexpr T pcl::UasRad ( T x )

inlineconstexprnoexcept

Conversion from microarcseconds (uas) to radians.

Definition at line 2000 of file Math.h.

Classes

Functions

Detailed Description

Function Documentation

◆ Abs()

◆ Angle() [1/2]

◆ Angle() [2/2]

◆ ArcCos()

◆ ArcCosh()

◆ ArcHav()

◆ ArcSin()

◆ ArcSinh()

◆ ArcTan() [1/2]

◆ ArcTan() [2/2]

◆ ArcTan2Pi()

◆ ArcTanh()

◆ AsRad()

◆ CalendarTimeToJD() [1/2]

◆ CalendarTimeToJD() [2/2]

◆ Ceil()

◆ Cos()

◆ Cosh()

◆ Cotan()

◆ DecimalToSexagesimal()

◆ Deg()

◆ Erf()

◆ ErfInv()

◆ Exp()

◆ Factorial()

◆ Floor()

◆ Frac()

◆ Frexp()

◆ Hav()

◆ JDToCalendarTime() [1/2]

◆ JDToCalendarTime() [2/2]

◆ L1Norm()

◆ L2Norm()

◆ Ldexp()

◆ Ln()

◆ Ln2()

◆ LnFactorial()

◆ Log()

◆ Log2() [1/2]

◆ Log2() [2/2]

◆ Log2e()

◆ Log2T()

◆ LogN()

◆ MasRad()

◆ MinRad()

◆ Mod()

◆ Mod2Pi()

◆ ModPi()

◆ Norm() [1/2]

◆ Norm() [2/2]

◆ Norm2Pi()

◆ Pi()

◆ Poly() [1/2]

◆ Poly() [2/2]

◆ Pow()

◆ Pow10()

◆ Pow2()

◆ PowI()

◆ PowI10()

◆ PowI12()

◆ PowI4()

◆ PowI6()

◆ PowI8()

◆ Rad()

◆ RadMin()

◆ RadSec()

◆ Rotate() [1/5]

◆ Rotate() [2/5]

◆ Rotate() [3/5]

◆ Rotate() [4/5]

◆ Rotate() [5/5]

◆ RotL()

◆ RotR()

◆ Round() [1/4]

◆ Round() [2/4]

◆ Round() [3/4]