Package pygeodesy :: Module latlonBase :: Class LatLonBase

Class LatLonBase

   object --+        
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 named._Named --+    
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 named._NamedBase --+
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       object --+   |
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named._NamedLocal --+
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                   LatLonBase

Known Subclasses:

(INTERNAL) Base class for ellipsoidal and spherical LatLons.

Instance Methods

PointsIter(self, points, loop=0, dedup=False, wrap=False)
Return a PointsIter iterator.

__eq__(self, other)

__init__(self, lat_llh, lon=None, height=0, datum=None, **wrap_name)
New LatLon.

__ne__(self, other)

__str__(self)
Default str(self).

antipode(self, height=None)
Return the antipode, the point diametrically opposite to this point.

bounds(self, wide, tall, radius=6371008.771415)
DEPRECATED, use method boundsOf.

boundsOf(self, wide, tall, radius=6371008.771415, height=None, **name)
Return the SW and NE lat-/longitude of a great circle bounding box centered at this location.

chordTo(self, other, height=None, wrap=False)
Compute the length of the chord through the earth between this and an other point.

circin6(self, point2, point3, eps=8.881784197001252e-16, **wrap_name)
Return the radius and center of the inscribed aka In-circle of the (planar) triangle formed by this and two other points.

circum3(self, point2, point3, circum=True, eps=8.881784197001252e-16, **wrap_name)
Return the radius and center of the smallest circle through or containing this and two other points.

circum4_(self, *points, **wrap_name)
Best-fit a sphere through this and two or more other points.

compassAngle(self, other, **adjust_wrap)
DEPRECATED, use method compassAngleTo.

compassAngleTo(self, other, **adjust_wrap)
Return the angle from North for the direction vector between this and an other point.

cosineAndoyerLambertTo(self, other, **wrap)
DEPRECATED on 2024.12.31, use method cosineLawTo with corr=1.

cosineForsytheAndoyerLambertTo(self, other, **wrap)
DEPRECATED on 2024.12.31, use method cosineLawTo with corr=2.

cosineLawTo(self, other, **radius__corr_wrap)
Compute the distance between this and an other point using the Law of Cosines formula, optionally corrected.

destinationXyz(self, delta, LatLon=None, **LatLon_kwds)
Calculate the destination using a local delta from this point.

equals(self, other, eps=None)
DEPRECATED, use method isequalTo.

equals3(self, other, eps=None)
DEPRECATED, use method isequalTo3.

equirectangularTo(self, other, **radius_adjust_limit_wrap)
Compute the distance between this and an other point using the Equirectangular Approximation / Projection.

euclideanTo(self, other, **radius_adjust_wrap)
Approximate the Euclidian distance between this and an other point.

flatLocalTo(self, other, radius=None, **wrap)
Compute the distance between this and an other point using the ellipsoidal Earth to plane projection aka Hubeny formula.

flatPolarTo(self, other, **radius_wrap)
Compute the distance between this and an other point using the polar coordinate flat-Earth formula.

hartzell(self, los=False, earth=None)
Compute the intersection of a Line-Of-Sight from this (geodetic) Point-Of-View (pov) with this point's ellipsoid surface.

haversineTo(self, other, **radius_wrap)
Compute the distance between this and an other point using the Haversine formula.

height4(self, earth=None, normal=True, LatLon=None, **LatLon_kwds)
Compute the projection of this point on and the height above or below this datum's ellipsoid surface.

heightStr(self, prec=-2, m='m')
Return this point's height as string.

hubenyTo(self, other, radius=None, **wrap)
Compute the distance between this and an other point using the ellipsoidal Earth to plane projection aka Hubeny formula.

intersecant2(self, *args, **kwds)
Not implemented, throws a NotImplementedError always.

isantipode(self, other, eps=2.220446049250313e-16)
DEPRECATED, use method isantipodeTo.

isantipodeTo(self, other, eps=2.220446049250313e-16)
Check whether this and an other point are antipodal, on diametrically opposite sides of the earth.

isequalTo(self, other, eps=None)
Compare this point with an other point, ignoring height.

isequalTo3(self, other, eps=None)
Compare this point with an other point, including height.

latlon2(self, ndigits=0)
Return this point's lat- and longitude in degrees, rounded.

latlon2round(self, ndigits=0)
DEPRECATED, use method latlon2.

latlon_(self, ndigits=0)
DEPRECATED, use method latlon2.

nearestOn6(self, points, closed=False, height=None, wrap=False)
Locate the point on a path or polygon closest to this point.

nearestTo(self, *args, **kwds)
Not implemented, throws a NotImplementedError always.

normal(self)
Normalize this point in-place to abs(lat) <= 90 and abs(lon) <= 180.

philam2(self, ndigits=0)
Return this point's lat- and longitude in radians, rounded.

points(self, points, **closed)
DEPRECATED, use method points2.

points2(self, points, closed=True)
Check a path or polygon represented by points.

radii11(self, point2, point3, wrap=False)
Return the radii of the Circum-, In-, Soddy and Tangent circles of a (planar) triangle formed by this and two other points.

rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False, b360=False)
Return the azimuth (bearing) of a rhumb line (loxodrome) between this and an other (ellipsoidal) point.

rhumbDestination(self, distance, azimuth, radius=None, height=None, exact=False, **name)
Return the destination point having travelled the given distance from this point along a rhumb line (loxodrome) of the given azimuth.

rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False)
Return the distance from this to an other point along a rhumb line (loxodrome).

rhumbIntersecant2(self, circle, point, other, height=None, **exact_radius_wrap_eps_tol)
Compute the intersections of a circle and a rhumb line given as two points or as a point and azimuth.

rhumbLine(self, other, exact=False, radius=None, wrap=False, **name_caps)
Get a rhumb line through this point at a given azimuth or through this and an other point.

rhumbMidpointTo(self, other, exact=False, radius=None, height=None, fraction=0.5, **wrap_name)
Return the (loxodromic) midpoint on the rhumb line between this and an other point.

thomasTo(self, other, **wrap)
Compute the distance between this and an other point using Thomas' formula.

to2ab(self)
DEPRECATED, use property philam.

to3llh(self, height=None)
DEPRECATED, use property latlonheight or latlon.to3Tuple(height).

to3xyz(self)
DEPRECATED, use property xyz or method toNvector, toVector, toVector3d or perhaps (geocentric) toEcef.

toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds)
Convert this point to cartesian, geocentric coordinates, also known as Earth-Centered, Earth-Fixed (ECEF).

toDatum(self, datum2, height=None, **name)
Must be overloaded.

toEcef(self, height=None, M=False)
Convert this point to geocentric coordinates, also known as Earth-Centered, Earth-Fixed (ECEF).

toNormal(self, deep=False, **name)
Get this point normalized to abs(lat) <= 90 and abs(lon) <= 180.

toNvector(self, h=None, Nvector=None, **name_Nvector_kwds)
Convert this point to n-vector (normal to the earth's surface) components, including height.

toStr(self, form='dms', joined=', ', m='m', **prec_sep_s_D_M_S)
Convert this point to a "lat, lon[, +/-height]" string, formatted in the given format.

toVector(self, Vector=None, **Vector_kwds)
Convert this point to a Vector with the geocentric (x, y, z) (ECEF) coordinates, ignoring height.

toVector3d(self, norm=True, **Vector3d_kwds)
Convert this point to a Vector3d with the geocentric (x, y, z) (ECEF) coordinates, ignoring height.

toWm(self, **toWm_kwds)
Convert this point to a WM coordinate.

vincentysTo(self, other, **radius_wrap)
Compute the distance between this and an other point using Vincenty's spherical formula.

Inherited from named._NamedBase: __repr__, others, toRepr

Inherited from named._Named: __format__, __imatmul__, __matmul__, __rmatmul__, attrs, classof, copy, dup, methodname, rename, renamed, toStr2

Inherited from named._NamedLocal: toAer, toEnu, toLocal, toLtp, toNed, toXyz

Inherited from object: __delattr__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __setattr__, __sizeof__, __subclasshook__

Properties
	clipid Get the (polygonal) clip (`int`).
	datum Must be overloaded.
	ellipsoidalLatLon Get the `LatLon type` iff ellipsoidal, overloaded in LatLonEllipsoidalBase.
	height Get the height (`meter`).
	isEllipsoidal Check whether this point is ellipsoidal (`bool` or `None` if unknown).
	isSpherical Check whether this point is spherical (`bool` or `None` if unknown).
	isnormal Return `True` if this point is normal (`bool`), meaning `abs(lat) <= 90` and `abs(lon) <= 180`.
	lam Get the longitude (`radians`).
	lat Get the latitude (`degrees90`).
	latlon Get the lat- and longitude (LatLon2Tuple`(lat, lon)`).
	latlonheight Get the lat-, longitude and height (LatLon3Tuple`(lat, lon, height)`).
	lon Get the longitude (`degrees180`).
	phi Get the latitude (`radians`).
	philam Get the lat- and longitude (PhiLam2Tuple`(phi, lam)`).
	philamheight Get the lat-, longitude in `radians` and height (PhiLam3Tuple`(phi, lam, height)`).
	sphericalLatLon Get the `LatLon type` iff spherical, overloaded in LatLonSphericalBase.
	xyz Get the geocentric `(x, y, z)` coordinates (Vector3Tuple`(x, y, z)`)
	xyz3 Get the geocentric `(x, y, z)` coordinates as `3-tuple`.
	xyzh Get the geocentric `(x, y, z)` coordinates and height (Vector4Tuple`(x, y, z, h)`)
Inherited from `named._Named`: `classname`, `classnaming`, `iteration`, `name`, `named`, `named2`, `named3`, `named4`, `sizeof` Inherited from `named._NamedLocal`: `Ecef` Inherited from `object`: `__class__`

Method Details

PointsIter (self, points, loop=0, dedup=False, wrap=False)

Return a PointsIter iterator.

Arguments:

points - The path or polygon points (LatLon[])
loop - Number of loop-back points (non-negative int).
dedup - If True, skip duplicate points (bool).
wrap - If True, wrap or normalize the enum-/iterated points (bool).

Returns:

A new PointsIter iterator.

Raises:

PointsError - Insufficient number of points.

init (self, lat_llh, lon=None, height=0, datum=None, **wrap_name)
(Constructor)

New LatLon.

Arguments:

lat_llh - Latitude (degrees or DMS str with N or S suffix) or a previous LatLon instance provided lon=None.
lon - Longitude (degrees or DMS str with E or W suffix), required if lat_llh is degrees or str.
height - Optional height above (or below) the earth surface (meter, conventionally).
datum - Optional datum (Datum, Ellipsoid, Ellipsoid2, a_f2Tuple or scalar radius) or None.
wrap_name - Optional name=NN (str) and optional keyword argument wrap=False, if True, wrap or normalize lat and lon (bool).

Returns:

New instance (LatLon).

Raises:

RangeError - A lon or lat value outside the valid range and rangerrors set to True.
TypeError - If lat_llh is not a LatLon.
UnitError - Invalid lat, lon or height.

Overrides: object.__init__

str (self)
(Informal representation operator)

Default str(self).

Overrides: object.__str__: (inherited documentation)

antipode (self, height=None)

Return the antipode, the point diametrically opposite to this point.

Arguments:

height - Optional height of the antipode (meter), this point's height otherwise.

Returns:

The antipodal point (LatLon).

bounds (self, wide, tall, radius=6371008.771415)

DEPRECATED, use method boundsOf.

Decorators:

@deprecated_method

boundsOf (self, wide, tall, radius=6371008.771415, height=None, **name)

Return the SW and NE lat-/longitude of a great circle bounding box centered at this location.

Arguments:

wide - Longitudinal box width (meter, same units as radius or degrees if radius is None).
tall - Latitudinal box size (meter, same units as radius or degrees if radius is None).
radius - Mean earth radius (meter) or None if both wide and tall are in degrees.
height - Height for latlonSW and latlonNE (meter), overriding the point's height.
name - Optional name=NN (str).

Returns:

A Bounds2Tuple(latlonSW, latlonNE), the lower-left and upper-right corner (LatLon).

chordTo (self, other, height=None, wrap=False)

Compute the length of the chord through the earth between this and an other point.

Arguments:

other - The other point (LatLon).
height - Overriding height for both points (meter), or if None, use each point's height.
wrap - If True, wrap or normalize the other point (bool).

Returns:

The chord length (conventionally meter).

Raises:

TypeError - The other point is not LatLon.

circin6 (self, point2, point3, eps=8.881784197001252e-16, **wrap_name)

Return the radius and center of the inscribed aka In-circle of the (planar) triangle formed by this and two other points.

Arguments:

point2 - Second point (LatLon).
point3 - Third point (LatLon).
eps - Tolerance for function pygeodesy.trilaterate3d2.
wrap_name - Optional name=NN (str) and optional keyword argument wrap=False, if True, wrap or normalize the points (bool).

Returns:

A Circin6Tuple

(radius, center, deltas, cA, 
          cB, cC)

. The center and contact points cA, cB and cC, each an instance of this (sub-)class, are co-planar with this and the two given points, see the Note below.

Raises:

ImportError - Package numpy not found, not installed or older than version 1.10.
IntersectionError - Near-coincident or -colinear points or a trilateration or numpy issue.
TypeError - Invalid point2 or point3.

Note: The center is trilaterated in cartesian (ECEF) space and converted back to geodetic lat-, longitude and height. The latter, conventionally in meter indicates whether the center is above, below or on the surface of the earth model. If deltas is None, the center is unambigous. Otherwise deltas is a LatLon3Tuple(lat, lon, height) representing the differences between both results from pygeodesy.trilaterate3d2 and center is the mean thereof.

See Also: Function pygeodesy.circin6, method circum3, Incircle and Contact Triangle.

circum3 (self, point2, point3, circum=True, eps=8.881784197001252e-16, **wrap_name)

Return the radius and center of the smallest circle through or containing this and two other points.

Arguments:

point2 - Second point (LatLon).
point3 - Third point (LatLon).
circum - If True, return the circumradius and circumcenter, always, ignoring the Meeus' Type I case (bool).
eps - Tolerance for function pygeodesy.trilaterate3d2.
wrap_name - Optional name=NN (str) and optional keyword argument wrap=False, if True, wrap or normalize the points (bool).

Returns:

A Circum3Tuple

(radius, center, 
          deltas)

. The center, an instance of this (sub-)class, is co-planar with this and the two given points. If deltas is None, the center is unambigous. Otherwise deltas is a LatLon3Tuple(lat, lon, height) representing the difference between both results from pygeodesy.trilaterate3d2 and center is the mean thereof.

Raises:

ImportError - Package numpy not found, not installed or older than version 1.10.
IntersectionError - Near-concentric, -coincident or -colinear points, incompatible Ecef classes or a trilateration or numpy issue.
TypeError - Invalid point2 or point3.

Note: The center is trilaterated in cartesian (ECEF) space and converted back to geodetic lat-, longitude and height. The latter, conventionally in meter indicates whether the center is above, below or on the surface of the earth model. If deltas is None, the center is unambigous. Otherwise deltas is a LatLon3Tuple(lat, lon, height) representing the difference between both results from pygeodesy.trilaterate3d2 and center is the mean thereof.

See Also: Function pygeodesy.circum3 and methods circin6 and circum4_.

circum4_ (self, *points, **wrap_name)

Best-fit a sphere through this and two or more other points.

Arguments:

points - The other points (each a LatLon).
wrap_name - Optional name=NN (str) and optional keyword argument wrap=False, if True, wrap or normalize the points (bool).

Returns:

A Circum4Tuple

(radius, center, rank, 
          residuals)

with center an instance of this (sub-)class.

Raises:

ImportError - Package numpy not found, not installed or older than version 1.10.
NumPyError - Some numpy issue.
TypeError - One of the points invalid.
ValueError - Too few points.

See Also: Function pygeodesy.circum4_ and circum3.

compassAngle (self, other, **adjust_wrap)

DEPRECATED, use method compassAngleTo.

Decorators:

@deprecated_method

compassAngleTo (self, other, **adjust_wrap)

Return the angle from North for the direction vector between this and an other point.

Suitable only for short, non-near-polar vectors up to a few hundred Km or Miles. Use method initialBearingTo for larger distances.

Arguments:

other - The other point (LatLon).
adjust_wrap - Optional keyword arguments for function pygeodesy.compassAngle.

Returns:

Compass angle from North (degrees360).

Raises:

TypeError - The other point is not LatLon.

Note: Courtesy of Martin Schultz.

See Also: Local, flat earth approximation.

cosineAndoyerLambertTo (self, other, **wrap)

DEPRECATED on 2024.12.31, use method cosineLawTo with corr=1.

Decorators:

@deprecated_method

cosineForsytheAndoyerLambertTo (self, other, **wrap)

DEPRECATED on 2024.12.31, use method cosineLawTo with corr=2.

Decorators:

@deprecated_method

cosineLawTo (self, other, **radius__corr_wrap)

Compute the distance between this and an other point using the Law of Cosines formula, optionally corrected.

Arguments:

other - The other point (LatLon).
radius__corr_wrap - Optional earth radius=None (meter), overriding the equatorial or mean radius of this point's datum's ellipsoid and keyword arguments for function pygeodesy.cosineLaw.

Returns:

Distance (meter, same units as radius).

Raises:

TypeError - The other point is not LatLon.

See Also: Function pygeodesy.cosineLaw and methods distanceTo*, equirectangularTo, euclideanTo, flatLocalTo / hubenyTo, flatPolarTo, haversineTo, thomasTo and vincentysTo.

destinationXyz (self, delta, LatLon=None, **LatLon_kwds)

Calculate the destination using a local delta from this point.

Arguments:

delta - Local delta to the destination (XyzLocal, Aer, Enu, Ned or Local9Tuple).
LatLon - Optional (geodetic) class to return the destination or None.
LatLon_kwds - Optionally, additional LatLon keyword arguments, ignored if LatLon is None.

Returns:

An LatLon instance or if

LatLon 
          is None

, a LatLon4Tuple

(lat, lon, height, 
          datum)

or LatLon3Tuple(lat, lon, height) if a datum keyword is specified or not.

Raises:

TypeError - Invalid delta, LatLon or LatLon_kwds item.

equals (self, other, eps=None)

DEPRECATED, use method isequalTo.

Decorators:

@deprecated_method

equals3 (self, other, eps=None)

DEPRECATED, use method isequalTo3.

Decorators:

@deprecated_method

equirectangularTo (self, other, **radius_adjust_limit_wrap)

Compute the distance between this and an other point using the Equirectangular Approximation / Projection.

Suitable only for short, non-near-polar distances up to a few hundred Km or Miles. Use method haversineTo or distanceTo* for more accurate and/or larger distances.

Arguments:

other - The other point (LatLon).
radius_adjust_limit_wrap - Optional keyword arguments for function pygeodesy.equirectangular, overriding the default mean radius of this point's datum ellipsoid.

Returns:

Distance (meter, same units as radius).

Raises:

TypeError - The other point is not LatLon.

See Also: Function pygeodesy.equirectangular and methods cosineLawTo, distanceTo*, euclideanTo, flatLocalTo / hubenyTo, flatPolarTo, haversineTo, thomasTo and vincentysTo.

euclideanTo (self, other, **radius_adjust_wrap)

Approximate the Euclidian distance between this and an other point.

See function pygeodesy.euclidean for the available options.

Arguments:

other - The other point (LatLon).
radius_adjust_wrap - Optional keyword arguments for function pygeodesy.euclidean, overriding the default mean radius of this point's datum ellipsoid.

Returns:

Distance (meter, same units as radius).

Raises:

TypeError - The other point is not LatLon.

See Also: Function pygeodesy.euclidean and methods cosineLawTo, distanceTo*, equirectangularTo, flatLocalTo / hubenyTo, flatPolarTo, haversineTo, thomasTo and vincentysTo.

flatLocalTo (self, other, radius=None, **wrap)

Compute the distance between this and an other point using the ellipsoidal Earth to plane projection aka Hubeny formula.

Arguments:

other - The other point (LatLon).
radius - Mean earth radius (meter) or None for the equatorial radius of this point's datum ellipsoid.
wrap - Optional keyword argument wrap=False, if True, wrap or normalize and unroll the other point (bool).

Returns:

Distance (meter, same units as radius).

Raises:

TypeError - The other point is not LatLon.
ValueError - Invalid radius.

See Also: Function pygeodesy.flatLocal/pygeodesy.hubeny, methods cosineLawTo, distanceTo*, equirectangularTo, euclideanTo, flatPolarTo, haversineTo, thomasTo and vincentysTo and local, flat Earth approximation.

flatPolarTo (self, other, **radius_wrap)

Compute the distance between this and an other point using the polar coordinate flat-Earth formula.

Arguments:

other - The other point (LatLon).
radius_wrap - Optional radius=R_M and wrap=False for function pygeodesy.flatPolar, overriding the default mean radius of this point's datum ellipsoid.

Returns:

Distance (meter, same units as radius).

Raises:

TypeError - The other point is not LatLon.

See Also: Function pygeodesy.flatPolar and methods cosineLawTo, distanceTo*, equirectangularTo, euclideanTo, flatLocalTo / hubenyTo, haversineTo, thomasTo and vincentysTo.

hartzell (self, los=False, earth=None)

Compute the intersection of a Line-Of-Sight from this (geodetic) Point-Of-View (pov) with this point's ellipsoid surface.

Arguments:

los - Line-Of-Sight, direction to the ellipsoid (Los, Vector3d), True for the normal, plumb onto the surface or False or None to point to the center of the ellipsoid.
earth - The earth model (Datum, Ellipsoid, Ellipsoid2, a_f2Tuple or scalar radius in meter), overriding this point's datum ellipsoid.

Returns:

The intersection (LatLon) with attribute .height set to the distance to this pov.

Raises:

IntersectionError - Null or bad pov or los, this pov is inside the ellipsoid or los points outside or away from the ellipsoid.
TypeError - Invalid los or invalid or undefined earth or datum.

See Also: Function hartzell for further details.

haversineTo (self, other, **radius_wrap)

Compute the distance between this and an other point using the Haversine formula.

Arguments:

other - The other point (LatLon).
radius_wrap - Optional radius=R_M and wrap=False for function pygeodesy.haversine, overriding the default mean radius of this point's datum ellipsoid.

Returns:

Distance (meter, same units as radius).

Raises:

TypeError - The other point is not LatLon.

See Also: Function pygeodesy.haversine and methods cosineLawTo, distanceTo*, equirectangularTo, euclideanTo, flatLocalTo / hubenyTo, flatPolarTo, thomasTo and vincentysTo.

height4 (self, earth=None, normal=True, LatLon=None, **LatLon_kwds)

Compute the projection of this point on and the height above or below this datum's ellipsoid surface.

Arguments:

earth - A datum, ellipsoid, triaxial ellipsoid or earth radius, overriding this datum (Datum, Ellipsoid, Ellipsoid2, a_f2Tuple, Triaxial, Triaxial_, JacobiConformal or meter, conventionally).
normal - If True, the projection is the normal to this ellipsoid's surface, otherwise the intersection of the radial line to this ellipsoid's center (bool).
LatLon - Optional class to return the projection, height and datum (LatLon) or None.
LatLon_kwds - Optionally, additional LatLon keyword arguments, ignored if LatLon is None.

Returns:

A LatLon instance or if

LatLon 
          is None

, a Vector4Tuple(x, y, z, h) with the projection x, y and z coordinates and height h in meter, conventionally.

Raises:

TriaxialError - No convergence in triaxial root finding.
TypeError - Invalid LatLon, LatLon_kwds item, earth or triaxial earth couldn't be converted to biaxial LatLon datum.

Note: Use keyword argument height=0 to override LatLon.height to {0} or any other scalar, conventionally in meter.

See Also: Methods Ellipsoid.height4 and Triaxial_.height4 for more information.

heightStr (self, prec=-2, m=`'m'`)

Return this point's height as string.

Arguments:

prec - Number of (decimal) digits, unstripped (int).
m - Optional unit of the height (str).

See Also: Function pygeodesy.hstr.

hubenyTo (self, other, radius=None, **wrap)

Compute the distance between this and an other point using the ellipsoidal Earth to plane projection aka Hubeny formula.

Arguments:

other - The other point (LatLon).
radius - Mean earth radius (meter) or None for the equatorial radius of this point's datum ellipsoid.
wrap - Optional keyword argument wrap=False, if True, wrap or normalize and unroll the other point (bool).

Returns:

Distance (meter, same units as radius).

Raises:

TypeError - The other point is not LatLon.
ValueError - Invalid radius.

isantipode (self, other, eps=2.220446049250313e-16)

DEPRECATED, use method isantipodeTo.

Decorators:

@deprecated_method

isantipodeTo (self, other, eps=2.220446049250313e-16)

Check whether this and an other point are antipodal, on diametrically opposite sides of the earth.

Arguments:

other - The other point (LatLon).
eps - Tolerance for near-equality (degrees).

Returns:

True if points are antipodal within the given tolerance, False otherwise.

isequalTo (self, other, eps=None)

Compare this point with an other point, ignoring height.

Arguments:

other - The other point (LatLon).
eps - Tolerance for equality (degrees).

Returns:

True if both points are identical, ignoring height, False otherwise.

Raises:

TypeError - The other point is not LatLon or mismatch of the other and this class or type.
UnitError - Invalid eps.

See Also: Method isequalTo3.

isequalTo3 (self, other, eps=None)

Compare this point with an other point, including height.

Arguments:

other - The other point (LatLon).
eps - Tolerance for equality (degrees).

Returns:

True if both points are identical including height, False otherwise.

Raises:

TypeError - The other point is not LatLon or mismatch of the other and this class or type.

See Also: Method isequalTo.

latlon2 (self, ndigits=0)

Return this point's lat- and longitude in degrees, rounded.

Arguments:

ndigits - Number of (decimal) digits (int).

Returns:

A LatLon2Tuple(lat, lon), both float and rounded away from zero.

Note: The rounded values are always float, also if ndigits is omitted.

latlon2round (self, ndigits=0)

DEPRECATED, use method latlon2.

Decorators:

@deprecated_method

latlon_ (self, ndigits=0)

DEPRECATED, use method latlon2.

Decorators:

@deprecated_method

nearestOn6 (self, points, closed=False, height=None, wrap=False)

Locate the point on a path or polygon closest to this point.

Points are converted to and distances are computed in geocentric, cartesian space.

Arguments:

points - The path or polygon points (LatLon[]).
closed - Optionally, close the polygon (bool).
height - Optional height, overriding the height of this and all other points (meter). If None, take the height of points into account for distances.
wrap - If True, wrap or normalize and unroll the points (bool).

Returns:

A NearestOn6Tuple

(closest, distance, fi, j, 
          start, end)

with the closest, the start and the end point each an instance of this LatLon and distance in meter, same units as the cartesian axes.

Raises:

PointsError - Insufficient number of points.
TypeError - Some points or some points' Ecef invalid.
ValueError - Some points' Ecef is incompatible.

See Also: Function nearestOn6.

normal (self)

Normalize this point in-place to abs(lat) <= 90 and abs(lon) <= 180.

Returns:: True if this point was normal, False if it wasn't (but is now).

See Also: Property isnormal and method toNormal.

philam2 (self, ndigits=0)

Return this point's lat- and longitude in radians, rounded.

Arguments:

ndigits - Number of (decimal) digits (int).

Returns:

A PhiLam2Tuple(phi, lam), both float and rounded away from zero.

Note: The rounded values are float, always.

points (self, points, **closed)

DEPRECATED, use method points2.

Decorators:

@deprecated_method

points2 (self, points, closed=True)

Check a path or polygon represented by points.

Arguments:

points - The path or polygon points (LatLon[])
closed - Optionally, consider the polygon closed, ignoring any duplicate or closing final points (bool).

Returns:

A Points2Tuple(number, points), an int and a list or tuple.

Raises:

PointsError - Insufficient number of points.
TypeError - Some points are not LatLon.

radii11 (self, point2, point3, wrap=False)

Return the radii of the Circum-, In-, Soddy and Tangent circles of a (planar) triangle formed by this and two other points.

Arguments:

point2 - Second point (LatLon).
point3 - Third point (LatLon).
wrap - If True, wrap or normalize point2 and point3 (bool).

Returns:

Radii11Tuple

(rA, rB, rC, cR, rIn, riS, 
          roS, a, b, c, s)

Raises:

IntersectionError - Near-coincident or -colinear points.
TypeError - Invalid point2 or point3.

See Also: Function pygeodesy.radii11, Incircle, Soddy Circles and Tangent Circles.

rhumbAzimuthTo (self, other, exact=False, radius=None, wrap=False, b360=False)

Return the azimuth (bearing) of a rhumb line (loxodrome) between this and an other (ellipsoidal) point.

Arguments:

other - The other point (LatLon).
exact - Exact Rhumb... to use (bool or Rhumb...), see method Ellipsoid.rhumb_.
radius - Optional earth radius (meter) or earth model (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple), overriding this point's datum.
wrap - If True, wrap or normalize and unroll the other point (bool).
b360 - If True, return the azimuth as bearing in compass degrees (bool).

Returns:

Rhumb azimuth (degrees180 or compass degrees360).

Raises:

TypeError - The other point is incompatible or radius is invalid.

rhumbDestination (self, distance, azimuth, radius=None, height=None, exact=False, **name)

Return the destination point having travelled the given distance from this point along a rhumb line (loxodrome) of the given azimuth.

Arguments:

distance - Distance travelled (meter, same units as this point's datum (ellipsoid) axes or radius, may be negative.
azimuth - Azimuth (bearing) of the rhumb line (compass degrees).
radius - Optional earth radius (meter) or earth model (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple), overriding this point's datum.
height - Optional height, overriding the default height (meter).
exact - Exact Rhumb... to use (bool or Rhumb...), see method Ellipsoid.rhumb_.
name - Optional name=NN (str).

Returns:

The destination point (ellipsoidal LatLon).

Raises:

TypeError - Invalid radius.
ValueError - Invalid distance, azimuth, radius or height.

rhumbDistanceTo (self, other, exact=False, radius=None, wrap=False)

Return the distance from this to an other point along a rhumb line (loxodrome).

Arguments:

other - The other point (LatLon).
exact - Exact Rhumb... to use (bool or Rhumb...), see method Ellipsoid.rhumb_.
radius - Optional earth radius (meter) or earth model (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple), overriding this point's datum.
wrap - If True, wrap or normalize and unroll the other point (bool).

Returns:

Distance (meter, the same units as this point's datum (ellipsoid) axes or radius.

Raises:

TypeError - The other point is incompatible or radius is invalid.
ValueError - Invalid radius.

rhumbIntersecant2 (self, circle, point, other, height=None, **exact_radius_wrap_eps_tol)

Compute the intersections of a circle and a rhumb line given as two points or as a point and azimuth.

Arguments:

circle - Radius of the circle centered at this location (meter), or a point on the circle (same LatLon class).
point - The start point of the rhumb line (same LatLon class).
other - An other point on (same LatLon class) or the azimuth of (compass degrees) the rhumb line.
height - Optional height for the intersection points (meter, conventionally) or None for interpolated heights.
exact_radius_wrap_eps_tol - Optional keyword arguments, see methods rhumbLine and RhumbLineAux.Intersecant2 or RhumbLine.Intersecant2.

Returns:

2-Tuple of the intersection points (representing a chord), each an instance of this class. Both points are the same instance if the rhumb line is tangent to the circle.

Raises:

IntersectionError - The circle and rhumb line do not intersect.
TypeError - Invalid point, circle or other.
ValueError - Invalid circle, other, height or exact_radius_wrap.

See Also: Methods RhumbLineAux.Intersecant2 and RhumbLine.Intersecant2.

rhumbLine (self, other, exact=False, radius=None, wrap=False, **name_caps)

Get a rhumb line through this point at a given azimuth or through this and an other point.

Arguments:

other - The azimuth of (compass degrees) or an other point on (same LatLon class) the rhumb line.
exact - Exact Rhumb... to use (bool or Rhumb...), see method Ellipsoid.rhumb_.
radius - Optional earth radius (meter) or earth model (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple), overriding this point's datum.
wrap - If True, wrap or normalize and unroll the other point (bool).
name_caps - Optional name=str and caps, see RhumbLine or RhumbLineAux caps.

Returns:

A RhumbLine instance (RhumbLine or RhumbLineAux).

Raises:

TypeError - Invalid radius or other not scalar nor same LatLon class.

See Also: Modules rhumb.aux_ and rhumb.ekx.

rhumbMidpointTo (self, other, exact=False, radius=None, height=None, fraction=0.5, **wrap_name)

Return the (loxodromic) midpoint on the rhumb line between this and an other point.

Arguments:

other - The other point (same LatLon class).
exact - Exact Rhumb... to use (bool or Rhumb...), see method Ellipsoid.rhumb_.
radius - Optional earth radius (meter) or earth model (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple), overriding this point's datum.
height - Optional height, overriding the mean height (meter).
fraction - Midpoint location from this point (scalar), 0 for this, 1 for the other, 0.5 for halfway between this and the other point, may be negative or greater than 1.
wrap_name - Optional name=NN (str) and wrap=False, if True, wrap or normalize and unroll the other point (bool).

Returns:

The midpoint at the given fraction along the rhumb line (same LatLon class).

Raises:

TypeError - The other point is incompatible or radius is invalid.
ValueError - Invalid height or fraction.

thomasTo (self, other, **wrap)

Compute the distance between this and an other point using Thomas' formula.

Arguments:

other - The other point (LatLon).
wrap - Optional keyword argument wrap=False, if True, wrap or normalize and unroll the other point (bool).

Returns:

Distance (meter, same units as the axes of this point's datum ellipsoid).

Raises:

TypeError - The other point is not LatLon.

See Also: Function pygeodesy.thomas and methods cosineLawTo, distanceTo*, equirectangularTo, euclideanTo, flatLocalTo / hubenyTo, flatPolarTo, haversineTo and vincentysTo.

to2ab (self)

DEPRECATED, use property philam.

Decorators:

@deprecated_method

to3llh (self, height=None)

DEPRECATED, use property latlonheight or latlon.to3Tuple(height).

Decorators:

@deprecated_method

to3xyz (self)

DEPRECATED, use property xyz or method toNvector, toVector, toVector3d or perhaps (geocentric) toEcef.

Decorators:

@deprecated_method

toCartesian (self, height=None, Cartesian=None, **Cartesian_kwds)

Convert this point to cartesian, geocentric coordinates, also known as Earth-Centered, Earth-Fixed (ECEF).

Arguments:

height - Optional height, overriding this point's height (meter, conventionally).
Cartesian - Optional class to return the geocentric coordinates (Cartesian) or None.
Cartesian_kwds - Optionally, additional Cartesian keyword arguments, ignored if Cartesian is None.

Returns:

A Cartesian instance or if Cartesian is None, an Ecef9Tuple

(x, y, z, lat, lon, height, C, 
          M, datum)

with C=0 and M if available.

Raises:

TypeError - Invalid Cartesian or Cartesian_kwds item.

See Also: Methods toNvector, toVector and toVector3d.

toEcef (self, height=None, M=False)

Convert this point to geocentric coordinates, also known as Earth-Centered, Earth-Fixed (ECEF).

Arguments:

height - Optional height, overriding this point's height (meter, conventionally).
M - Optionally, include the rotation EcefMatrix (bool).

Returns:

An Ecef9Tuple

(x, y, z, lat, lon, height, C, 
          M, datum)

with C=0 and M if available.

Raises:

EcefError - A .datum or an ECEF issue.

toNormal (self, deep=False, **name)

Get this point normalized to abs(lat) <= 90 and abs(lon) <= 180.

Arguments:

deep - If True, make a deep, otherwise a shallow copy (bool).
name - Optional name=NN (str).

Returns:

A copy of this point, normalized (LatLon), optionally renamed.

See Also: Property isnormal, method normal and function pygeodesy.normal.

toNvector (self, h=None, Nvector=None, **name_Nvector_kwds)

Convert this point to n-vector (normal to the earth's surface) components, including height.

Arguments:

h - Optional height, overriding this point's height (meter).
Nvector - Optional class to return the n-vector components (Nvector) or None.
name_Nvector_kwds - Optional name=NN (str) and optionally, additional Nvector keyword arguments, ignored if Nvector is None.

Returns:

An Nvector instance or a Vector4Tuple(x, y, z, h) if Nvector is None.

Raises:

TypeError - Invalid h, Nvector or name_Nvector_kwds.

See Also: Methods toCartesian, toVector and toVector3d.

toStr (self, form=`'dms'`, joined=', ', m=`'m'`, **prec_sep_s_D_M_S)

Convert this point to a "lat, lon[, +/-height]" string, formatted in the given format.

Arguments:

form - The lat-/longitude format to use (str), see functions pygeodesy.latDMS or pygeodesy.lonDMS.
joined - Separator to join the lat-, longitude and height strings (str or None or NN for non-joined).
m - Optional unit of the height (str), use None to exclude height from the returned string.
prec_sep_s_D_M_S - Optional precision, separator, s_D, s_M, s_S and s_DMS keyword arguments, see function pygeodesy.toDMS for details.

Returns:

This point in the specified format, etc. (str or a 2- or 3-tuple

(lat_str, lon_str[, 
          height_str])

if joined is NN or None).

Overrides: named._Named.toStr

See Also: Function pygeodesy.latDMS or pygeodesy.lonDMS for more details about keyword arguments format, precision, separator, s_D, s_M, s_S and s_DMS.

toVector (self, Vector=None, **Vector_kwds)

Convert this point to a Vector with the geocentric (x, y, z) (ECEF) coordinates, ignoring height.

Arguments:

Vector - Optional class to return the geocentric components (Vector3d) or None.
Vector_kwds - Optionally, additional Vector keyword arguments, ignored if Vector is None.

Returns:

A Vector instance or a Vector3Tuple(x, y, z) if Vector is None.

Raises:

TypeError - Invalid Vector or Vector_kwds.

See Also: Methods toCartesian, toNvector and toVector3d.

toVector3d (self, norm=True, **Vector3d_kwds)

Convert this point to a Vector3d with the geocentric (x, y, z) (ECEF) coordinates, ignoring height.

Arguments:

norm - If False, don't normalize the coordinates (bool).
Vector3d_kwds - Optional Vector3d keyword arguments.

Returns:

Named, unit vector or vector (Vector3d).

Raises:

TypeError - Invalid Vector3d_kwds.

See Also: Methods toCartesian, toNvector and toVector.

toWm (self, **toWm_kwds)

Convert this point to a WM coordinate.

Arguments:

toWm_kwds - Optional pygeodesy.toWm keyword arguments.

Returns:

The WM coordinate (Wm).

See Also: Function pygeodesy.toWm.

vincentysTo (self, other, **radius_wrap)

Compute the distance between this and an other point using Vincenty's spherical formula.

Arguments:

other - The other point (LatLon).
radius_wrap - Optional radius=R_M and wrap=False for function pygeodesy.vincentys, overriding the default mean radius of this point's datum ellipsoid.

Returns:

Distance (meter, same units as radius).

Raises:

TypeError - The other point is not LatLon.

See Also: Function pygeodesy.vincentys and methods cosineLawTo, distanceTo*, equirectangularTo, euclideanTo, flatLocalTo / hubenyTo, flatPolarTo, haversineTo and thomasTo.

Property Details

clipid

Get the (polygonal) clip (int).

Get method:: clipid(self) - Get the (polygonal) clip (int).
Set method:: clipid(self, clipid) - Get the (polygonal) clip (int).

datum

Must be overloaded.

Get method:: datum(self) - Must be overloaded.
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

ellipsoidalLatLon

Get the LatLon type iff ellipsoidal, overloaded in LatLonEllipsoidalBase.

Get method:: ellipsoidalLatLon(self) - Get the LatLon type iff ellipsoidal, overloaded in LatLonEllipsoidalBase.
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

height

Get the height (meter).

Get method:: height(self) - Get the height (meter).
Set method:: height(self, height) - Set the height (meter).
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

isEllipsoidal

Check whether this point is ellipsoidal (bool or None if unknown).

Get method:: isEllipsoidal(self) - Check whether this point is ellipsoidal (bool or None if unknown).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

isSpherical

Check whether this point is spherical (bool or None if unknown).

Get method:: isSpherical(self) - Check whether this point is spherical (bool or None if unknown).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

isnormal

Return True if this point is normal (bool), meaning abs(lat) <= 90 and abs(lon) <= 180.

Get method:: isnormal(self) - Return True if this point is normal (bool), meaning abs(lat) <= 90 and abs(lon) <= 180.
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

See Also: Methods normal, toNormal and functions isnormal and normal.

lam

Get the longitude (radians).

Get method:: lam(self) - Get the longitude (radians).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

lat

Get the latitude (degrees90).

Get method:: lat(self) - Get the latitude (degrees90).
Set method:: lat(self, lat) - Set the latitude (str[N|S] or degrees).
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

latlon

Get the lat- and longitude (LatLon2Tuple(lat, lon)).

Get method:: latlon(self) - Get the lat- and longitude (LatLon2Tuple(lat, lon)).
Set method:: latlon(self, latlonh) - Set the lat- and longitude and optionally the height (2- or 3-tuple or comma- or space-separated str of degrees90, degrees180 and meter).
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

latlonheight

Get the lat-, longitude and height (LatLon3Tuple(lat, lon, height)).

Get method:: latlonheight(self) - Get the lat-, longitude and height (LatLon3Tuple(lat, lon, height)).
Set method:: latlonheight(self, latlonh) - Set the lat- and longitude and optionally the height (2- or 3-tuple or comma- or space-separated str of degrees90, degrees180 and meter).
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

lon

Get the longitude (degrees180).

Get method:: lon(self) - Get the longitude (degrees180).
Set method:: lon(self, lon) - Set the longitude (str[E|W] or degrees).
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

phi

Get the latitude (radians).

Get method:: phi(self) - Get the latitude (radians).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

philam

Get the lat- and longitude (PhiLam2Tuple(phi, lam)).

Get method:: philam(self) - Get the lat- and longitude (PhiLam2Tuple(phi, lam)).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

philamheight

Get the lat-, longitude in radians and height (PhiLam3Tuple(phi, lam, height)).

Get method:: philamheight(self) - Get the lat-, longitude in radians and height (PhiLam3Tuple(phi, lam, height)).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

sphericalLatLon

Get the LatLon type iff spherical, overloaded in LatLonSphericalBase.

Get method:: sphericalLatLon(self) - Get the LatLon type iff spherical, overloaded in LatLonSphericalBase.
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

xyz

Get the geocentric (x, y, z) coordinates (Vector3Tuple(x, y, z))

Get method:: xyz(self) - Get the geocentric (x, y, z) coordinates (Vector3Tuple(x, y, z))
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

xyz3

Get the geocentric (x, y, z) coordinates as 3-tuple.

Get method:: xyz3(self) - Get the geocentric (x, y, z) coordinates as 3-tuple.
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

xyzh

Get the geocentric (x, y, z) coordinates and height (Vector4Tuple(x, y, z, h))

Get method:: xyzh(self) - Get the geocentric (x, y, z) coordinates and height (Vector4Tuple(x, y, z, h))
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

Class LatLonBase

PointsIter (self, points, loop=0, dedup=False, wrap=False)

__init__ (self, lat_llh, lon=None, height=0, datum=None, **wrap_name) (Constructor)

__str__ (self) (Informal representation operator)

antipode (self, height=None)

bounds (self, wide, tall, radius=6371008.771415)

boundsOf (self, wide, tall, radius=6371008.771415, height=None, **name)

chordTo (self, other, height=None, wrap=False)

circin6 (self, point2, point3, eps=8.881784197001252e-16, **wrap_name)

circum3 (self, point2, point3, circum=True, eps=8.881784197001252e-16, **wrap_name)

circum4_ (self, *points, **wrap_name)

compassAngle (self, other, **adjust_wrap)

compassAngleTo (self, other, **adjust_wrap)

cosineAndoyerLambertTo (self, other, **wrap)

cosineForsytheAndoyerLambertTo (self, other, **wrap)

cosineLawTo (self, other, **radius__corr_wrap)

destinationXyz (self, delta, LatLon=None, **LatLon_kwds)

equals (self, other, eps=None)

equals3 (self, other, eps=None)

equirectangularTo (self, other, **radius_adjust_limit_wrap)

euclideanTo (self, other, **radius_adjust_wrap)

flatLocalTo (self, other, radius=None, **wrap)

flatPolarTo (self, other, **radius_wrap)

hartzell (self, los=False, earth=None)

haversineTo (self, other, **radius_wrap)

height4 (self, earth=None, normal=True, LatLon=None, **LatLon_kwds)

heightStr (self, prec=-2, m='m')

hubenyTo (self, other, radius=None, **wrap)

isantipode (self, other, eps=2.220446049250313e-16)

isantipodeTo (self, other, eps=2.220446049250313e-16)

isequalTo (self, other, eps=None)

isequalTo3 (self, other, eps=None)

latlon2 (self, ndigits=0)

latlon2round (self, ndigits=0)

latlon_ (self, ndigits=0)

nearestOn6 (self, points, closed=False, height=None, wrap=False)

normal (self)

philam2 (self, ndigits=0)

points (self, points, **closed)

points2 (self, points, closed=True)

radii11 (self, point2, point3, wrap=False)

rhumbAzimuthTo (self, other, exact=False, radius=None, wrap=False, b360=False)

rhumbDestination (self, distance, azimuth, radius=None, height=None, exact=False, **name)

rhumbDistanceTo (self, other, exact=False, radius=None, wrap=False)

rhumbIntersecant2 (self, circle, point, other, height=None, **exact_radius_wrap_eps_tol)

rhumbLine (self, other, exact=False, radius=None, wrap=False, **name_caps)

rhumbMidpointTo (self, other, exact=False, radius=None, height=None, fraction=0.5, **wrap_name)

thomasTo (self, other, **wrap)

to2ab (self)

to3llh (self, height=None)

to3xyz (self)

toCartesian (self, height=None, Cartesian=None, **Cartesian_kwds)

toEcef (self, height=None, M=False)

toNormal (self, deep=False, **name)

toNvector (self, h=None, Nvector=None, **name_Nvector_kwds)

toStr (self, form='dms', joined=', ', m='m', **prec_sep_s_D_M_S)

toVector (self, Vector=None, **Vector_kwds)

toVector3d (self, norm=True, **Vector3d_kwds)

toWm (self, **toWm_kwds)

vincentysTo (self, other, **radius_wrap)

clipid

datum

ellipsoidalLatLon

height

isEllipsoidal

isSpherical

isnormal

lam

lat

latlon

latlonheight

lon

phi

philam

philamheight

sphericalLatLon

xyz

xyz3

xyzh

init (self, lat_llh, lon=None, height=0, datum=None, **wrap_name)
(Constructor)

str (self)
(Informal representation operator)

heightStr (self, prec=-2, m=`'m'`)

toStr (self, form=`'dms'`, joined=', ', m=`'m'`, **prec_sep_s_D_M_S)