PCL
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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 |
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constexpr T | pcl::Angle (int d, int m, T s) noexcept |
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constexpr T | pcl::Angle (int d, T m) noexcept |
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constexpr T | pcl::ArcCos (T x) noexcept |
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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 |
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constexpr T | pcl::ArcSinh (T x) noexcept |
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constexpr T | pcl::ArcTan (T x) noexcept |
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constexpr T | pcl::ArcTan (T y, T x) noexcept |
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T | pcl::ArcTan2Pi (T y, T x) noexcept |
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constexpr T | pcl::ArcTanh (T x) noexcept |
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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 |
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constexpr T | pcl::Ceil (T x) noexcept |
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constexpr T | pcl::Cos (T x) noexcept |
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constexpr T | pcl::Cosh (T x) noexcept |
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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 |
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constexpr T | pcl::Deg (T x) noexcept |
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constexpr T | pcl::Erf (T x) noexcept |
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constexpr T | pcl::ErfInv (T x) noexcept |
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constexpr T | pcl::Exp (T x) noexcept |
double | pcl::Factorial (int n) noexcept |
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constexpr T | pcl::Floor (T x) noexcept |
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constexpr T | pcl::Frac (T x) noexcept |
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void | pcl::Frexp (T x, T &m, int &p) noexcept |
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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 |
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T | pcl::L1Norm (const T *i, const T *j) noexcept |
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T | pcl::L2Norm (const T *i, const T *j) noexcept |
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constexpr T | pcl::Ldexp (T m, int p) noexcept |
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constexpr T | pcl::Ln (T x) noexcept |
constexpr long double | pcl::Ln2 () noexcept |
double | pcl::LnFactorial (int n) noexcept |
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constexpr T | pcl::Log (T x) noexcept |
constexpr long double | pcl::Log2 () noexcept |
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constexpr T | pcl::Log2 (T x) noexcept |
constexpr long double | pcl::Log2e () noexcept |
constexpr long double | pcl::Log2T () noexcept |
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constexpr T | pcl::LogN (T n, T x) noexcept |
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constexpr T | pcl::MasRad (T x) noexcept |
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constexpr T | pcl::MinRad (T x) noexcept |
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constexpr T | pcl::Mod (T x, T y) noexcept |
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constexpr T | pcl::Mod2Pi (T x) noexcept |
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constexpr T | pcl::ModPi (T x) noexcept |
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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 |
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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 |
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T | pcl::Poly (T x, std::initializer_list< T > c) noexcept |
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constexpr T | pcl::Pow (T x, T y) noexcept |
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T | pcl::Pow10 (T x) noexcept |
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constexpr T | pcl::Pow2 (T x) noexcept |
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T | pcl::PowI (T x, int n) noexcept |
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T | pcl::PowI10 (T x) noexcept |
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T | pcl::PowI12 (T x) noexcept |
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T | pcl::PowI4 (T x) noexcept |
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T | pcl::PowI6 (T x) noexcept |
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T | pcl::PowI8 (T x) noexcept |
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constexpr T | pcl::Rad (T x) noexcept |
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constexpr T | pcl::RadMin (T x) noexcept |
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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 |
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T | pcl::RotL (T x, uint32 n) noexcept |
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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 |
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T | pcl::Round (T x, int n) noexcept |
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int | pcl::RoundI (T x) noexcept |
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int | pcl::RoundInt (T x) noexcept |
int64 | pcl::RoundInt64 (double x) noexcept |
int64 | pcl::RoundInt64Arithmetic (double x) noexcept |
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int | pcl::RoundIntArithmetic (T x) noexcept |
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int | pcl::RoundIntBanker (T x) noexcept |
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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 |
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constexpr int | pcl::Sign (T x) noexcept |
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constexpr char | pcl::SignChar (T x) noexcept |
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constexpr T | pcl::Sin (T x) noexcept |
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void | pcl::SinCos (T x, T &sx, T &cx) noexcept |
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constexpr T | pcl::Sinh (T x) noexcept |
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void | pcl::Split (T x, T &i, T &f) noexcept |
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constexpr T | pcl::Sqrt (T x) noexcept |
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constexpr T | pcl::Tan (T x) noexcept |
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constexpr T | pcl::Tanh (T x) noexcept |
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T | pcl::Trunc (T x) noexcept |
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int | pcl::TruncI (T x) noexcept |
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int64 | pcl::TruncI64 (T x) noexcept |
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int | pcl::TruncInt (T x) noexcept |
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int64 | pcl::TruncInt64 (T x) noexcept |
constexpr long double | pcl::TwoPi () noexcept |
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constexpr T | pcl::UasRad (T x) noexcept |
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Inverse cosine function (arccosine).
Definition at line 573 of file Math.h.
Referenced by pcl::ProjectionBase::DistanceFast().
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Inverse sine function (arcsine).
Definition at line 585 of file Math.h.
Referenced by pcl::Position::EquatorialToHorizontal().
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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().
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Conversion from arcseconds to radians (a synonym for SecRad()).
Definition at line 1978 of file Math.h.
Referenced by pcl::Position::EpsA().
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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.
[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().
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Computes the Julian date (JD) corresponding to a time point expressed as a date and a day fraction.
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().
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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().
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The inverse error function: erf^-1( x ).
Code adapted from erfinv implementation by Lakshay Garg:
https://github.com/lakshayg/erfinv
Copyright (c) 2017-2019 Lakshay Garg Licensed under MIT license.
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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().
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Computes the date and day fraction corresponding to a time point expressed as a Julian date (JD).
[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().
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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.
[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().
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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().
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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().
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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().
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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).
Definition at line 2166 of file Math.h.
Referenced by pcl::GenericVector< T >::Norm().
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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().
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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().
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General power function: x raised to y.
When you know some of the arguments in advance, faster alternatives are:
Pow10I<T>()( y )
when x == 10 and y is an integer PowI( x, y )
when x != 10 and y is an integer Pow10( y )
when x == 10 and y is not an integerOtherwise, you can also use: Pow2( y*Log2( x ) )
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The exponential function 2**x.
Definition at line 1748 of file Math.h.
Referenced by pcl::PSFData::FWHM(), and pcl::MoffatFilter::FWHMx().
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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().
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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().
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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().
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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().
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Rotates a point on the plane.
[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.
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Rotates a point on the plane.
[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().
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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().
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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().
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Round function: x rounded to the nearest integer (double precision version).
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Round function: x rounded to the nearest integer (single precision version).
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RoundI function: Rounds x to the nearest integer and converts the result to a 32-bit signed integer.
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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.
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().
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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.
Definition at line 1651 of file Math.h.
References pcl::Round().
Referenced by pcl::Rotate(), and pcl::RoundI64().
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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.
Definition at line 1714 of file Math.h.
References pcl::TruncInt64().
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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.
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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().
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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().
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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().
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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().
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TruncI function: Truncated integer part of x as a 32-bit signed integer. to a 32-bit signed integer.
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TruncI64 function: Truncated integer part of x as a 64-bit signed integer.
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TruncInt function: Truncated integer part of x as a 32-bit signed integer.
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().
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TruncInt64 function: Truncated integer part of x as a 64-bit signed integer.
Definition at line 1260 of file Math.h.
Referenced by pcl::RoundInt64Arithmetic().
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Twice the pi constant: 0.6283185...
Definition at line 540 of file Math.h.
Referenced by pcl::GenericVector< T >::ToSpherical2Pi().