UCelestialMaths

Units Conventions Distances: Distances are expressed in Astronomical units - Specified by the "AU" mention in the function name

API > API/Plugins > API/Plugins/CelestialVault

Units Conventions Distances: Distances are expressed in Astronomical units - Specified by the "AU" mention in the function name

Time: Local/UTC Time: All function parameters contains either the "Local" or "UTC" prefix in their name to specify if they expect a Local or UTC Time.

Most Celestial functions are expecting an absolute time expressed using a Julian Date. When the name "JulianDay" is used, it means the Julian Date when t=0 (midnight, beginning of the day) By definition, a Julian Date is finishing by 0.5 at Midnight.

Angles: GMST and GAST angle are expressed in Degrees Some Celestial data involve ArcSeconds (1 Degree = 3600 Arcseconds) - Conversion functions are provided

   
Name UCelestialMaths
Type class
Header File /Engine/Plugins/Runtime/CelestialVault/Source/CelestialVault/Public/CelestialMaths.h
Include Path #include "CelestialMaths.h"

Syntax

UCLASS ()  
class UCelestialMaths : public UBlueprintFunctionLibrary

Inheritance Hierarchy

Classes

Name Remarks
WGS84  

Constants

Name Type Remarks Include Path
AstronomicalUnitsMeters const double   CelestialMaths.h
NewMoonReferenceJulianDate const double   CelestialMaths.h
ParsecAstronomicalUnits const double   CelestialMaths.h
SpeedOfLightMetersPerSeconds const double   CelestialMaths.h
SynodicMonthAverage const double Static const Members. CelestialMaths.h
VSOPEclipticToFK5Equatorial const FMatrix   CelestialMaths.h

Functions

Static

Name Remarks Include Path Unreal Specifiers

static double ArcsecondsToDegrees ( double Arcseconds
)

 Convert Arcseconds to Degrees1 Degree = 3600 Arcseconds CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Angles"

static double ArcsecondsToRadians ( double Arcseconds
)

 Convert Arcseconds to Radians2 PI Rad = 360 Degrees = 360 * 3600 Arcseconds CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Angles"

static double AstronomicalUnitsToMeters ( double AU
)

 Convert Astronomical Unit (UA) to meters1 AU = 149 597 870 700 m CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Utilities"

static double AstronomicalUnitsToParsec ( double AU
)

 Convert Astronomical Unit (UA) to Parsecs1 Parsec = 206 264.806 AU CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Utilities"

static FLinearColor BVtoLinearColor ( float BV
)

 Returns the RGB normalized components [0..1] from the Color Index (B-V) Value CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Color"

static FVector ComputeAberration ( const FVector& TopocentricTargetLocationAU,
const FVector& EarthVelocity
)

 Compute the Aberration of an object located far from the Earth. CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Earth"

static FString Conv_CelestialBodyToString ( const FCelestialBody& CelestialBody
)

 Celestial Body String Builder CelestialMaths.h
  • BlueprintPure
  • Meta=(DisplayName="To String (CelestialBody)", CompactNodeTitle="->", BlueprintAutocast)
  • Category="Celestial|Utilities"

static FString Conv_DeclinationToString ( const double& DecDegrees
)

 Declination String Builder CelestialMaths.h
  • BlueprintPure
  • Meta=(DisplayName="To String (Declination in Degrees)")
  • Category="Celestial|Utilities"

static FString Conv_DegreesToDMSString ( double Degrees
)

 DMS String Builder CelestialMaths.h
  • BlueprintPure
  • Meta=(DisplayName="To DMS String (Angle in Degrees)")
  • Category="Celestial|Utilities"

static FString Conv_DegreesToHMSString ( double Degrees
)

 HMS String Builder CelestialMaths.h
  • BlueprintPure
  • Meta=(DisplayName="To HMS String (Angle in Degrees)")
  • Category="Celestial|Utilities"

static FString Conv_DMSToString ( bool Sign,
int32 Degrees,
int32 Minutes,
double Seconds
)

 DMS String Builder CelestialMaths.h
  • BlueprintPure
  • Meta=(DisplayName="To String (Signed Angle in Degrees, Minutes, Seconds )")
  • Category="Celestial|Utilities"

static FString Conv_HMSToString ( int32 Hours,
int32 Minutes,
double Seconds
)

 HMS String Builder CelestialMaths.h
  • BlueprintPure
  • Meta=(DisplayName="To String (Angle in Hours Minutes Seconds)")
  • Category="Celestial|Utilities"

static FString Conv_PlanetaryBodyToString ( const FPlanetaryBody& PlanetaryBody
)

 Planetary Body String Builder CelestialMaths.h
  • BlueprintPure
  • Meta=(DisplayName="To String (PlanetaryBody)", CompactNodeTitle="->", BlueprintAutocast)
  • Category="Celestial|Utilities"

static FString Conv_RightAscensionToString ( const double& RightAscensionHours
)

 Right Ascension String Builder CelestialMaths.h
  • BlueprintPure
  • Meta=(DisplayName="To String (Right Ascension in hours)")
  • Category="Celestial|Utilities"

static FString Conv_StellarBodyToString ( const FStellarBody& StellarBody
)

 Stellar Body ToString String Builder CelestialMaths.h
  • BlueprintPure
  • Meta=(DisplayName="To String (StellarBody)", CompactNodeTitle="->", BlueprintAutocast)
  • Category="Celestial|Utilities"

static double DateTimeToGreenwichMeanSiderealTime ( FDateTime UTCDateTime
)

 Return the Greenwich Mean Sidereal Time (GMST) for a specific DateTime, in Degrees CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"
Return the Greenwich Mean Sidereal Time (GMST) for a specific DateTime, in Degrees, without doing any ModPositive, so unwrapped CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static double DaysToSeconds ( double Days
)

 Converts decimal Days to Seconds CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static double DegreesToArcseconds ( double Degrees
)

 Convert Degrees to Arcseconds1 Degree = 3600 Arcseconds CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Angles"

static void DegreesToDMS ( double DecimalDegrees,
bool& Sign,
int32& Degrees,
int32& Minutes,
double& Seconds
)

 Convert decimal degrees to Degrees, Minutes, Seconds, with the appropriate Sign (True if Positive) CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static void DegreesToHMS ( double DecimalDegrees,
int32& Hours,
int32& Minutes,
double& Seconds
)

 Convert Decimal degrees to Hours, Minutes, Seconds ( One Hour equals 15 degrees) CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static void ECEFXYZAUToGeodeticLatLon ( FVector ECEFLocationAU,
double& Latitude,
double& Longitude,
double& AltitudeMeters
)

 Converts a ECEF Location for the WGS84 Ellipsoid into Geodetic Latitude and Longitude. CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Earth"

static double EquationOfTheEquinoxes ( double JulianDate
)

 Return the nutation in right ascension ( aka the equation of the equinoxes) in Degrees CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Earth"

static int32 FloorForJulianDate ( double JulianDate
)

 Because the Dates are expressed around Jan 1, 4713 BC, we need a special Floor function to have the right years continuity CelestialMaths.h  

static FVector GeodeticLatLonToECEFXYZAU ( double Latitude,
double Longitude,
double Altitude
)

 Convert Geodetic Lat Lon to Geocentric XYZ position vector in ECEF coordinates, for the WGS84 Ellipsoid. CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Earth"

static void GetBodyCelestialCoordinatesAU ( double JulianDate,
EVSOP87BodyType VSOP87BodyType,
double ObserverLatitude,
double ObserverLongitude,
bool bGeoCentricObserver,
bool bIgnoreRelativisticEffect,
double& RAJ2000Hours,
double& DECJ2000Degrees,
double& RAHours,
double& DECDegrees,
double& RAGeocentricHours,
double& DECGeocentricDegrees,
double& DistanceBodyToEarthAU,
double& DistanceBodyToSunAU,
double& DistanceEarthToSunAU
)

 Return the location of a Planetary Body relative to the Earth, expressed in Celestial Coordinates (RA, DEC, Distance) It requires the Observer location on Earth for more precise computations This function also returns the distance between bodies, as it can help for Magnitude computations CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Planetary bodies"

static void GetBodyCelestialCoordinatesAU_UsingKnownState ( double JulianDate,
EVSOP87BodyType VSOP87BodyType,
const FPlanetaryBodyKinematicState& EarthKinematicState,
double ObserverLatitude,
double ObserverLongitude,
bool bGeoCentricObserver,
bool bIgnoreRelativisticEffect,
double& RAJ2000Hours,
double& DECJ2000Degrees,
double& RAHours,
double& DECDegrees,
double& RAGeocentricHours,
double& DECGeocentricDegrees,
double& DistanceBodyToEarthAU,
double& DistanceBodyToSunAU,
double& DistanceEarthToSunAU
)

 Return the location of a Planetary Body relative to the Earth, expressed in Celestial Coordinates (RA, DEC, Distance) It requires the Observer location on Earth for more precise computations This function also returns the distance between bodies, as it can help for Magnitude computations CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Planetary bodies"

static FTransform GetEarthCenterTransformECEF ( double Latitude,
double Longitude,
double Altitude
)

 Return the Transformation to apply to a WGS84 Ellipsoid model so that its location in Lat,long,Altitude is tangent to the Origin The Transform is expressed in the ECEF Frame (Location units are meters, right-handed ECEF Frame) CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Earth"

static FTransform GetEarthCenterTransformUEFrame ( double Latitude,
double Longitude,
double Altitude,
bool Geocentric
)

 Return the Transformation to apply to a WGS84 Ellipsoid model so that its location in Lat,long,Altitude is tangent to the Origin It's used to locate the Rotating Celestial Vault for a specific UE Origin The Transform is expressed in the UE Frame (Location units are UE Units, left-handed Unreal Frame) CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Earth"

static double GetEarthRotationAngle ( double JulianDate
)

 Retrurn the Earth Rotation Angle (In Degrees) as measured by GMST (Greenwich Mean Sidereal Time) CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Earth"

static double GetIlluminationPercentage ( double NormalizedAge
)

 Return the illumination factor (0..1) of a Body, considering his normalized age and the crescent effects CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Color"

static double GetLeapSeconds ( double JulianDate
)

 Returns the Leap Seconds for a specific Julian Date CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static double GetMoonNormalizedAgeSimple ( double JulianDate
)

 Returns the Moon Phase for a specific Date CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Planetary bodies"

static FMatrix GetNutationMatrix ( double JulianDate
)

 Return the Nutation Matrix The Nutation matrix accounts for Nutation, the small, periodic wobble of Earth’s rotation axis – when transforming between “mean” and “true” celestial coordinate frames. CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Earth"

static FVector GetObserverGeocentricLocationAU ( double Latitude,
double Longitude,
double Altitude,
double JulianDate
)

 Return the Geocentric position of an observer located at the Earth surface, considering the rotation at this specific JulianDate, using the Greenwich Apparent Didereal Time. CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Earth"
Returns the Body location and velocity in the VSOP87 and FK5J2000 frames CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|VSOP87"

static double GetPlanetaryBodyMagnitude ( EVSOP87BodyType VSOP87BodyType,
double DistanceToSunAU,
double DistanceToEarthAU,
double DistanceEarthToSunAU,
double& PhaseAngle
)

 Return the Magnitude of a Planetary Body as seen from the Earth CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Planetary bodies"

static FMatrix GetPrecessionMatrix ( double JulianDate
)

 Return the Precession Matrix The Precession matrix transforms coordinates from one equatorial reference epoch to another by accounting for Earth’s long-term, secular drift of its rotation axis (precession of the equinox). CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Earth"

static FString GetPreciseVectorString ( FVector Vector,
int32 MinimumFractionalDigits
)

 Returns a String displaying a vector with a large number of digits CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Utilities"

static FMatrix GetRotationXMatrix ( double AngleRadians
)

 Return a Rotation Matrix around X, for Precession/Nutation computations CelestialMaths.h  

static FMatrix GetRotationYMatrix ( double AngleRadians
)

 Return a Rotation Matrix around Y, for Precession/Nutation computations CelestialMaths.h  

static FMatrix GetRotationZMatrix ( double AngleRadians
)

 Return a Rotation Matrix around Z, for Precession/Nutation computations CelestialMaths.h  

static FVector GetSolarSystemBodyLocation_VSOP87_Relativistic ( FVector ReferenceBodyLocation_Heliocentric_AU,
EVSOP87BodyType VSOP87BodyType,
double JulianDate
)

 Returns the location of a specific Solar System Body, in the VSOP Coordinate system CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|VSOP87"

static void GetSolarSystemBodyLocationVelocity_VSOP87_AU ( EVSOP87BodyType VSOP87BodyType,
double JulianDate,
FVector& LocationAU,
FVector& Velocity
)

 Returns the location of a specific Solar System body, in the VSOP Coordinate system CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|VSOP87"

static double GetSpeedOfLight()

 Returns the Speed of Light 299 792 458 (m/s) CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Utilities"

static FStellarBody GetSunInformation ( double JulianDate,
double ObserverLatitude,
double ObserverLongitude,
bool bGeoCentric
)

 Compute all Sun Properties for a specific JulianDate CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Sun"

static FStellarBody GetSunInformation_UsingKnownState ( double JulianDate,
const FPlanetaryBodyKinematicState& EarthKinematicState,
double ObserverLatitude,
double ObserverLongitude,
bool bGeoCentric
)

 Compute all Sun Properties for a specific JulianDate CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Sun"

static double InternationalAtomicTimeToTerrestrialTime ( double TAI
)

 Returns the Terrestrial Time in SI secondsTT = TAI + 32.184 seconds; CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static double JulianDateToGreenwichApparentSiderealTime ( double JulianDate
)

 Return the Greenwich Apparent Sidereal Time (GAST) for a specific UTC DateTime, in Degrees. CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static double JulianDateToGreenwichMeanSiderealTime ( double JulianDate
)

 Return the Greenwich Mean Sidereal Time (GMST) for a specific Julian Date, In Degrees CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static double JulianDateToInternationalAtomicTime ( double JulianDate
)

 Returns the International Atomic Time in SI seconds CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static double JulianDateToJulianCenturies ( double JulianDate
)

 Returns the Julien CenturiesJulian Centuries = (JulianDate - 2451545.0) / 36525.0 CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static FDateTime JulianDateToUTCDateTime ( double JulianDate
)

 Return the UTC Time for a specific Julian Date CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static double JulianDateToVSOP87Time ( double JulianDate
)

 Converts a Julian Date to a proper VSOP87Time, suitable for the VSOP87 computations CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static double LocalSideralTime ( double LongitudeDegrees,
double GreenwichMeanSideralTime
)

 Return the Sidereal Time for a specific Longitude and GMST CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static FDateTime LocalTimeToUTCTime ( FDateTime LocalTime,
double TimeZoneOffset,
bool IsDst
)

 Return the UTC for a specific Local Time, using the TimeZone and Daylight Saving Information CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static double MetersToAstronomicalUnits ( double Meters
)

 Convert meters to Astronomical Unit (UA)1 AU = 149 597 870 700 m CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Utilities"

static double ModPositive ( double Value,
double Modulo
)

 Special Mod function that makes sure to always return positive values CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Angles"

static void Nutation2000BTruncated ( double JulianDate,
double& DeltaPsiDegrees,
double& DeltaEpsilonDegrees
)

 Approximation of the IAU2000A/B nutation model used in the Equation Of The Equinoxes, accurate enough for VSOP87 computations CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Earth"

static double ParsecsToAstronomicalUnits ( double Parsecs
)

 Convert Parsecs to Astronomical Unit (UA)1 Parsec = 206 264.806 AU CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Utilities"

static FVector RADECToXYZ_RH ( double RADegrees,
double DECDegrees,
double Radius
)

 Convert Polar Coordinates to Cartesian Coordinates, using a Righ-Handed Frame CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Utilities"

static double SecondsToDay ( double Seconds
)

 Converts Seconds to Decimal Days CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static double UTCDateTimeToJulianDate ( FDateTime UTCDateTime
)

 Return the Julian Date for a specific UTC Time CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static FDateTime UTCTimeToLocalTime ( FDateTime UTCTime,
double TimeZoneOffset,
bool IsDst
)

 Return the Local Time for a specific UTC Time, using the TimeZone and Daylight Saving Information CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Time"

static double WGS84GeocentricRadius ( double Latitude
)

 Return the WGS84 Radius (in Meters) for a specific Latitude CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Earth"

static void XYZToRADEC_RH ( FVector XYZ,
double& RADegrees,
double& DECDegrees,
double& Radius
)

 Convert Cartesian Coordinates to Polar Coordinates, using a Righ-Handed Frame CelestialMaths.h
  • BlueprintCallable
  • Category="Celestial Vault|Utilities"

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