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pygeodesy
Package pygeodesy :: Module sphericalTrigonometry :: Class LatLon
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Class LatLon

           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.LatLonBase --+    
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sphericalBase.LatLonSphericalBase --+
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                                   LatLon

New point on a spherical earth model, based on trigonometry formulae.

Instance Methods
 
alongTrackDistanceTo(self, start, end, radius=6371008.771415, wrap=False)
Compute the (signed) distance from the start to the closest point on the great circle line defined by a start and an end point.
 
bearingTo(self, other, wrap=False, raiser=False)
DEPRECATED, use method initialBearingTo.
 
crossingParallels(self, other, lat, wrap=False)
Return the pair of meridians at which a great circle defined by this and an other point crosses the given latitude.
 
crossTrackDistanceTo(self, start, end, radius=6371008.771415, wrap=False)
Compute the (signed) distance from this point to a great circle from a start to an end point.
 
destination(self, distance, bearing, radius=6371008.771415, height=None)
Locate the destination from this point after having travelled the given distance on a bearing from North.
 
distanceTo(self, other, radius=6371008.771415, wrap=False)
Compute the (angular) distance from this to an other point.
 
greatCircle(self, bearing, Vector=<class 'pygeodesy.vector3d.Vector3d'>, **Vector_kwds)
Compute the vector normal to great circle obtained by heading from this point on the bearing from North.
 
initialBearingTo(self, other, wrap=False, raiser=False)
Compute the initial bearing (forward azimuth) from this to an other point.
 
intermediateTo(self, other, fraction, height=None, wrap=False)
Locate the point at given fraction between (or along) this and an other point.
 
intersection(self, end1, other, end2, height=None, wrap=False)
Compute the intersection point of two lines, each defined by two points or a start point and a bearing from North.
 
intersections2(self, rad1, other, rad2, radius=6371008.771415, eps=0.0, height=None, wrap=True)
Compute the intersection points of two circles, each defined by a center point and a radius.
 
isEnclosedBy(self, points)
DEPRECATED, use method isenclosedBy.
 
isenclosedBy(self, points, wrap=False)
Check whether a (convex) polygon or composite encloses this point.
 
midpointTo(self, other, height=None, fraction=0.5, wrap=False)
Find the midpoint between this and an other point.
 
nearestOn(self, point1, point2, radius=6371008.771415, **wrap_adjust_limit)
Locate the point between two other points closest to this point.
 
nearestOn2(self, points, closed=False, radius=6371008.771415, **options)
DEPRECATED, use method sphericalTrigonometry.LatLon.nearestOn3.
 
nearestOn3(self, points, closed=False, radius=6371008.771415, **wrap_adjust_limit)
Locate the point on a polygon closest to this point.
 
toCartesian(self, **Cartesian_datum_kwds)
Convert this point to Karney-based cartesian (ECEF) coordinates.
 
triangle7(self, otherB, otherC, radius=6371008.771415, wrap=False)
Compute the angles, sides and area of a spherical triangle.
 
triangulate(self, bearing1, other, bearing2, **height_wrap)
Locate a point given this, an other point and a bearing from North at both points.
 
trilaterate5(self, distance1, point2, distance2, point3, distance3, area=True, eps=0.9999999999999998, radius=6371008.771415, wrap=False)
Trilaterate three points by area overlap or perimeter intersection of three corresponding circles.

Inherited from sphericalBase.LatLonSphericalBase: __init__, bearingTo2, finalBearingTo, intersecant2, maxLat, minLat, parse, rhumbAzimuthTo, rhumbBearingTo, rhumbDestination, rhumbDistanceTo, rhumbIntersecant2, rhumbMidpointTo, toNvector

Inherited from latlonBase.LatLonBase: PointsIter, __eq__, __ne__, __str__, antipode, bounds, boundsOf, chordTo, circin6, circum3, circum4_, compassAngle, compassAngleTo, cosineAndoyerLambertTo, cosineForsytheAndoyerLambertTo, cosineLawTo, destinationXyz, equals, equals3, equirectangularTo, euclideanTo, flatLocalTo, flatPolarTo, hartzell, haversineTo, height4, heightStr, hubenyTo, isantipode, isantipodeTo, isequalTo, isequalTo3, latlon2, latlon2round, latlon_, nearestOn6, nearestTo, normal, philam2, points, points2, radii11, rhumbLine, thomasTo, to2ab, to3llh, to3xyz, toDatum, toEcef, toNormal, toStr, toVector, toVector3d, toWm, vincentysTo

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

Inherited from sphericalBase.LatLonSphericalBase: datum, napieradius, sphericalLatLon

Inherited from latlonBase.LatLonBase: clipid, ellipsoidalLatLon, height, isEllipsoidal, isSpherical, isnormal, lam, lat, latlon, latlonheight, lon, phi, philam, philamheight, xyz, xyz3, xyzh

Inherited from named._Named: classname, classnaming, iteration, name, named, named2, named3, named4, sizeof

Inherited from named._NamedLocal: Ecef

Inherited from object: __class__

Method Details

alongTrackDistanceTo (self, start, end, radius=6371008.771415, wrap=False)

 

Compute the (signed) distance from the start to the closest point on the great circle line defined by a start and an end point.

That is, if a perpendicular is drawn from this point to the great circle line, the along-track distance is the distance from the start point to the point where the perpendicular crosses the line.

Arguments:
  • start - Start point of the great circle line (LatLon).
  • end - End point of the great circle line (LatLon).
  • radius - Mean earth radius (meter) or None.
  • wrap - If True, wrap or normalize and unroll the start and end point (bool).
Returns:
Distance along the great circle line (radians if radius is None or meter, same units as radius), positive if after the start toward the end point of the line, negative if before or 0 if at the start point.
Raises:
  • TypeError - Invalid start or end point.
  • ValueError - Invalid radius.

bearingTo (self, other, wrap=False, raiser=False)

 

DEPRECATED, use method initialBearingTo.

Decorators:
  • @deprecated_method

crossingParallels (self, other, lat, wrap=False)

 

Return the pair of meridians at which a great circle defined by this and an other point crosses the given latitude.

Arguments:
  • other - The other point defining great circle (LatLon).
  • lat - Latitude at the crossing (degrees).
  • wrap - If True, wrap or normalize and unroll the other point (bool).
Returns:
2-Tuple (lon1, lon2), both in degrees180 or None if the great circle doesn't reach lat.

crossTrackDistanceTo (self, start, end, radius=6371008.771415, wrap=False)

 

Compute the (signed) distance from this point to a great circle from a start to an end point.

Arguments:
  • start - Start point of the great circle line (LatLon).
  • end - End point of the great circle line (LatLon).
  • radius - Mean earth radius (meter) or None.
  • wrap - If True, wrap or normalize and unroll the start and end point (bool).
Returns:
Distance to the great circle (radians if radius or meter, same units as radius), negative if to the left or positive if to the right of the line.
Raises:
  • TypeError - If start or end is not LatLon.
  • ValueError - Invalid radius.

destination (self, distance, bearing, radius=6371008.771415, height=None)

 

Locate the destination from this point after having travelled the given distance on a bearing from North.

Arguments:
  • distance - Distance travelled (meter, same units as radius).
  • bearing - Bearing from this point (compass degrees360).
  • radius - Mean earth radius (meter).
  • height - Optional height at destination (meter, same units a radius).
Returns:
Destination point (LatLon).
Raises:
  • ValueError - Invalid distance, bearing, radius or height.

distanceTo (self, other, radius=6371008.771415, wrap=False)

 

Compute the (angular) distance from this to an other point.

Arguments:
  • other - The other point (LatLon).
  • radius - Mean earth radius (meter) or None.
  • wrap - If True, wrap or normalize and unroll the other point (bool).
Returns:
Distance between this and the other point (meter, same units as radius or radians if radius is None).
Raises:
  • TypeError - The other point is not LatLon.
  • ValueError - Invalid radius.

greatCircle (self, bearing, Vector=<class 'pygeodesy.vector3d.Vector3d'>, **Vector_kwds)

 

Compute the vector normal to great circle obtained by heading from this point on the bearing from North.

Direction of vector is such that initial bearing vector b = c × n, where n is an n-vector representing this point.

Arguments:
  • bearing - Bearing from this point (compass degrees360).
  • Vector - Vector class to return the great circle, overriding the default Vector3d.
  • Vector_kwds - Optional, additional keyword argunents for Vector.
Returns:
Vector representing great circle (Vector).
Raises:
  • ValueError - Invalid bearing.

initialBearingTo (self, other, wrap=False, raiser=False)

 

Compute the initial bearing (forward azimuth) from this to an other point.

Arguments:
  • other - The other point (spherical LatLon).
  • wrap - If True, wrap or normalize and unroll the other point (bool).
  • raiser - Optionally, raise CrossError (bool), use raiser=True for behavior like sphericalNvector.LatLon.initialBearingTo.
Returns:
Initial bearing (compass degrees360).
Raises:
  • CrossError - If this and the other point coincide and if raiser and crosserrors are both True.
  • TypeError - The other point is not LatLon.

intermediateTo (self, other, fraction, height=None, wrap=False)

 

Locate the point at given fraction between (or along) this and an other point.

Arguments:
  • other - The other point (LatLon).
  • fraction - Fraction between both points (scalar, 0.0 at this and 1.0 at the other point).
  • height - Optional height, overriding the intermediate height (meter).
  • wrap - If True, wrap or normalize and unroll the other point (bool).
Returns:
Intermediate point (LatLon).
Raises:
  • TypeError - The other point is not LatLon.
  • ValueError - Invalid fraction or height.

See Also: Methods midpointTo and rhumbMidpointTo.

intersection (self, end1, other, end2, height=None, wrap=False)

 

Compute the intersection point of two lines, each defined by two points or a start point and a bearing from North.

Arguments:
  • end1 - End point of this line (LatLon) or the initial bearing at this point (compass degrees360).
  • other - Start point of the other line (LatLon).
  • end2 - End point of the other line (LatLon) or the initial bearing at the other point (compass degrees360).
  • height - Optional height for intersection point, overriding the mean height (meter).
  • wrap - If True, wrap or normalize and unroll start2 and both end* points (bool).
Returns:
The intersection point (LatLon). An alternate intersection point might be the antipode to the returned result.
Raises:
  • IntersectionError - Ambiguous or infinite intersection or colinear, parallel or otherwise non-intersecting lines.
  • TypeError - If other is not LatLon or end1 or end2 not scalar nor LatLon.
  • ValueError - Invalid height or null line.

intersections2 (self, rad1, other, rad2, radius=6371008.771415, eps=0.0, height=None, wrap=True)

 

Compute the intersection points of two circles, each defined by a center point and a radius.

Arguments:
  • rad1 - Radius of the this circle (meter or radians, see radius).
  • other - Center point of the other circle (LatLon).
  • rad2 - Radius of the other circle (meter or radians, see radius).
  • radius - Mean earth radius (meter or None if rad1, rad2 and eps are given in radians).
  • eps - Required overlap (meter or radians, see radius).
  • height - Optional height for the intersection points (meter, conventionally) or None for the "radical height" at the radical line between both centers.
  • wrap - If True, wrap or normalize and unroll the other point (bool).
Returns:
2-Tuple of the intersection points, each a LatLon instance. For abutting circles, both intersection points are the same instance, aka the radical center.
Raises:
  • IntersectionError - Concentric, antipodal, invalid or non-intersecting circles.
  • TypeError - If other is not LatLon.
  • ValueError - Invalid rad1, rad2, radius, eps or height.

isEnclosedBy (self, points)

 

DEPRECATED, use method isenclosedBy.

Decorators:
  • @deprecated_method

isenclosedBy (self, points, wrap=False)

 

Check whether a (convex) polygon or composite encloses this point.

Arguments:
  • points - The polygon points or composite (LatLon[], BooleanFHP or BooleanGH).
  • wrap - If True, wrap or normalize and unroll the points (bool).
Returns:
True if this point is inside the polygon or composite, False otherwise.
Raises:
  • PointsError - Insufficient number of points.
  • TypeError - Some points are not LatLon.
  • ValueError - Invalid points, non-convex polygon.

See Also: Functions pygeodesy.isconvex, pygeodesy.isenclosedBy and pygeodesy.ispolar especially if the points may enclose a pole or wrap around the earth longitudinally.

midpointTo (self, other, height=None, fraction=0.5, wrap=False)

 

Find the midpoint between this and an other point.

Arguments:
  • other - The other point (LatLon).
  • height - Optional height for midpoint, overriding the mean height (meter).
  • fraction - Midpoint location from this point (scalar), may be negative or greater than 1.0.
  • wrap - If True, wrap or normalize and unroll the other point (bool).
Returns:
Midpoint (LatLon).
Raises:
  • TypeError - The other point is not LatLon.
  • ValueError - Invalid height.

See Also: Methods intermediateTo and rhumbMidpointTo.

nearestOn (self, point1, point2, radius=6371008.771415, **wrap_adjust_limit)

 

Locate the point between two other points closest to this point.

Distances are approximated by function pygeodesy.equirectangular4, subject to the supplied options.

Arguments:
Returns:
Closest point on the great circle line (LatLon).
Raises:
  • LimitError - Lat- and/or longitudinal delta exceeds limit, see function pygeodesy.equirectangular4.
  • NotImplementedError - Keyword argument within=False is not (yet) supported.
  • TypeError - Invalid point1 or point2.
  • ValueError - Invalid radius or options.

See Also: Functions pygeodesy.equirectangular4 and pygeodesy.nearestOn5 and method sphericalTrigonometry.LatLon.nearestOn3.

nearestOn2 (self, points, closed=False, radius=6371008.771415, **options)

 

DEPRECATED, use method sphericalTrigonometry.LatLon.nearestOn3.

Returns:
... 2-Tuple (closest, distance) of the closest point (LatLon) on the polygon and the distance to that point from this point in meter, same units of radius.
Decorators:
  • @deprecated_method

nearestOn3 (self, points, closed=False, radius=6371008.771415, **wrap_adjust_limit)

 

Locate the point on a polygon closest to this point.

Distances are approximated by function pygeodesy.equirectangular4, subject to the supplied options.

Arguments:
Returns:
A NearestOn3Tuple(closest, distance, angle) of the closest point (LatLon), the pygeodesy.equirectangular4 distance between this and the closest point converted to meter, same units as radius. The angle from this to the closest point is in compass degrees360, like function pygeodesy.compassAngle.
Raises:

See Also: Functions pygeodesy.compassAngle, pygeodesy.equirectangular4 and pygeodesy.nearestOn5.

toCartesian (self, **Cartesian_datum_kwds)

 

Convert this point to Karney-based cartesian (ECEF) coordinates.

Arguments:
  • Cartesian_datum_kwds - Optional Cartesian, datum and other keyword arguments, ignored if Cartesian is None. Use Cartesian=... to override this Cartesian class or specify Cartesian=None.
Returns:
The cartesian point (Cartesian) or if Cartesian is None, an Ecef9Tuple(x, y, z, lat, lon, height, C, M, datum) with C and M if available.
Raises:
  • TypeError - Invalid Cartesian_datum_kwds argument.
Overrides: latlonBase.LatLonBase.toCartesian

triangle7 (self, otherB, otherC, radius=6371008.771415, wrap=False)

 

Compute the angles, sides and area of a spherical triangle.

Arguments:
  • otherB - Second triangle point (LatLon).
  • otherC - Third triangle point (LatLon).
  • radius - Mean earth radius, ellipsoid or datum (meter, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple) or None.
  • wrap - If True, wrap or normalize and unroll points otherB and otherC (bool).
Returns:
Triangle7Tuple(A, a, B, b, C, c, area) or if radius is None, a Triangle8Tuple(A, a, B, b, C, c, D, E).

See Also: Function triangle7 and Spherical trigonometry.

triangulate (self, bearing1, other, bearing2, **height_wrap)

 

Locate a point given this, an other point and a bearing from North at both points.

Arguments:
  • bearing1 - Bearing at this point (compass degrees360).
  • other - The other point (LatLon).
  • bearing2 - Bearing at the other point (compass degrees360).
  • height_wrap_tol - Optional keyword arguments height=None, wrap=False, see method intersection.
Returns:
Triangulated point (LatLon).

See Also: Method intersection for further details.

trilaterate5 (self, distance1, point2, distance2, point3, distance3, area=True, eps=0.9999999999999998, radius=6371008.771415, wrap=False)

 

Trilaterate three points by area overlap or perimeter intersection of three corresponding circles.

Arguments:
  • distance1 - Distance to this point (meter, same units as radius).
  • point2 - Second center point (LatLon).
  • distance2 - Distance to point2 (meter, same units as radius).
  • point3 - Third center point (LatLon).
  • distance3 - Distance to point3 (meter, same units as radius).
  • area - If True, compute the area overlap, otherwise the perimeter intersection of the circles (bool).
  • eps - The required minimal overlap for area=True or the intersection margin if area=False (meter, same units as radius).
  • radius - Mean earth radius (meter, conventionally).
  • wrap - If True, wrap or normalize and unroll point2 and point3 (bool).
Returns:
A Trilaterate5Tuple(min, minPoint, max, maxPoint, n) with min and max in meter, same units as eps, the corresponding trilaterated points minPoint and maxPoint as spherical LatLon and n, the number of trilatered points found for the given eps.

If only a single trilaterated point is found, min is max, minPoint is maxPoint and n = 1.

For area=True, min and max are the smallest respectively largest radial overlap found.

For area=False, min and max represent the nearest respectively farthest intersection margin.

If area=True and all 3 circles are concentric, n=0 and minPoint and maxPoint are both the point# with the smallest distance# min and max the largest distance#.

Raises:
  • IntersectionError - Trilateration failed for the given eps, insufficient overlap for area=True or no intersection or all (near-)concentric if area=False.
  • TypeError - Invalid point2 or point3.
  • ValueError - Coincident point2 or point3 or invalid distance1, distance2, distance3 or radius.

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