Module ellipsoidalVincenty
Ellipsoidal, Vincenty-based geodesy.
Thaddeus Vincenty's geodetic (lat-/longitude) LatLon, geocentric (ECEF) Cartesian and VincentyError classes and functions areaOf, intersections2, nearestOn and perimeterOf.
Pure Python implementation of geodesy tools for ellipsoidal earth
models, transcoded from JavaScript originals by (C) Chris Veness
2005-2016 and published under the same MIT Licence**, see Vincenty geodesics. More at geographiclib and GeoPy.
Calculate geodesic distance between two points using the Vincenty formulae and one of several ellipsoidal earth
models. The default model is WGS-84, the most accurate and widely used
globally-applicable model for the earth ellipsoid.
Other ellipsoids offering a better fit to the local geoid include Airy
(1830) in the UK, Clarke (1880) in Africa, International 1924 in much of
Europe, and GRS-67 in South America. North America (NAD83) and Australia
(GDA) use GRS-80, which is equivalent to the WGS-84 model.
Great-circle distance uses a spherical model of the earth with the
mean earth radius defined by the International Union of Geodesy and
Geophysics (IUGG) as (2 * a + b) / 3 =
6371008.7714150598 meter or approx. 6371009 meter (for WGS-84,
resulting in an error of up to about 0.5%).
Here's an example usage of ellipsoidalVincenty
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>>> from pygeodesy.ellipsoidalVincenty import LatLon
>>> Newport_RI = LatLon(41.49008, -71.312796)
>>> Cleveland_OH = LatLon(41.499498, -81.695391)
>>> Newport_RI.distanceTo(Cleveland_OH)
866,455.4329158525 # meter
You can change the ellipsoid model used by the Vincenty formulae as
follows:
>>> from pygeodesy import Datums
>>> from pygeodesy.ellipsoidalVincenty import LatLon
>>> p = LatLon(0, 0, datum=Datums.OSGB36)
or by converting to anothor datum:
>>> p = p.toDatum(Datums.OSGB36)
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VincentyError
Error raised from Vincenty's direct and
inverse methods for coincident points or lack of
convergence.
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Cartesian
Extended to convert geocentric, Cartesian points to Vincenty-based, ellipsoidal,
geodetic LatLon.
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LatLon
Using the formulae devised by Thaddeus Vincenty (1975) for an (oblate)
ellipsoidal model of the earth to compute the geodesic distance and
bearings between two given points or the destination point given an
start point and (initial) bearing.
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ispolar(points,
wrap=False)
Check whether a polygon encloses a pole. |
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intersection3(start1,
end1,
start2,
end2,
height=None,
wrap=True,
equidistant=None,
tol=0.001,
LatLon=<class 'pygeodesy.ellipsoidalVincenty.LatLon'>,
**LatLon_kwds)
Interatively compute the intersection point of two paths, each
defined by two (ellipsoidal) points or by an (ellipsoidal) start
point and a bearing from North. |
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intersections2(center1,
radius1,
center2,
radius2,
height=None,
wrap=True,
equidistant=None,
tol=0.001,
LatLon=<class 'pygeodesy.ellipsoidalVincenty.LatLon'>,
**LatLon_kwds)
Iteratively compute the intersection points of two circles, each
defined by an (ellipsoidal) center point and a radius. |
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nearestOn(point,
point1,
point2,
within=True,
height=None,
wrap=False,
equidistant=None,
tol=0.001,
LatLon=<class 'pygeodesy.ellipsoidalVincenty.LatLon'>,
**LatLon_kwds)
Iteratively locate the closest point on the geodesic between two
other (ellipsoidal) points. |
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__all__ = _ALL_LAZY.ellipsoidalVincenty
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ispolar (points,
wrap=False)
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Check whether a polygon encloses a pole.
- Arguments:
points - The polygon points (LatLon []).
wrap - Wrap and unroll longitudes (bool ).
- Returns:
True if the polygon encloses a pole,
False otherwise.
- Raises:
PointsError - Insufficient number of points
TypeError - Some points are not LatLon or
don't have bearingTo2 , initialBearingTo
and finalBearingTo methods.
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intersection3 (start1,
end1,
start2,
end2,
height=None,
wrap=True,
equidistant=None,
tol=0.001,
LatLon=<class 'pygeodesy.ellipsoidalVincenty.LatLon'>,
**LatLon_kwds)
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Interatively compute the intersection point of two paths, each defined
by two (ellipsoidal) points or by an (ellipsoidal) start point and a
bearing from North.
- Arguments:
start1 - Start point of the first path (LatLon).
end1 - End point of the first path (LatLon) or the initial bearing at the first
point (compass degrees360 ).
start2 - Start point of the second path (LatLon).
end2 - End point of the second path (LatLon) or the initial bearing at the second
point (compass degrees360 ).
height - Optional height at the intersection (meter ,
conventionally) or None for the mean height.
wrap - Wrap and unroll longitudes (bool ).
equidistant - An azimuthal equidistant projection (class or function pygeodesy.equidistant) or None for
the preferred start1.Equidistant .
tol - Tolerance for convergence and for skew line distance and length
(meter , conventionally).
LatLon - Optional class to return the intersection points (LatLon) or None .
LatLon_kwds - Optional, additional LatLon keyword
arguments, ignored if LatLon is None .
- Returns:
- An Intersection3Tuple
(point, outside1,
outside2) with point a
LatLon or if LatLon is
None , a LatLon4Tuple(lat, lon, height,
datum) .
- Raises:
IntersectionError - Skew, colinear, parallel or otherwise non-intersecting paths or no
convergence for the given tol .
TypeError - Invalid or non-ellipsoidal start1 ,
end1 , start2 or
end2 or invalid
equidistant .
Note:
For each path specified with an initial bearing, a pseudo-end point
is computed as the destination along that bearing at
about 1.5 times the distance from the start point to an initial
gu-/estimate of the intersection point (and between 1/8 and 3/8 of
the authalic earth perimeter).
See Also:
The ellipsoidal case and Karney's
paper, pp 20-21, section 14. MARITIME BOUNDARIES for
more details about the iteration algorithm.
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intersections2 (center1,
radius1,
center2,
radius2,
height=None,
wrap=True,
equidistant=None,
tol=0.001,
LatLon=<class 'pygeodesy.ellipsoidalVincenty.LatLon'>,
**LatLon_kwds)
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Iteratively compute the intersection points of two circles, each
defined by an (ellipsoidal) center point and a radius.
- Arguments:
center1 - Center of the first circle (LatLon).
radius1 - Radius of the first circle (meter , conventionally).
center2 - Center of the second circle (LatLon).
radius2 - Radius of the second circle (meter , same units as
radius1 ).
height - Optional height for the intersection points (meter ,
conventionally) or None for the "radical
height" at the radical line between both centers.
wrap - Wrap and unroll longitudes (bool ).
equidistant - An azimuthal equidistant projection (class or function pygeodesy.equidistant) or None for
the preferred center1.Equidistant .
tol - Convergence tolerance (meter , same units as
radius1 and radius2 ).
LatLon - Optional class to return the intersection points (LatLon) or None .
LatLon_kwds - Optional, additional LatLon keyword
arguments, ignored if LatLon is None .
- Returns:
- 2-Tuple of the intersection points, each a
LatLon instance or LatLon4Tuple(lat, lon, height,
datum) if LatLon is None . For
abutting circles, both points are the same instance, aka the
radical center.
- Raises:
IntersectionError - Concentric, antipodal, invalid or non-intersecting circles or no
convergence for the tol .
TypeError - Invalid or non-ellipsoidal center1 or
center2 or invalid
equidistant .
UnitError - Invalid radius1 , radius2 or
height .
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nearestOn (point,
point1,
point2,
within=True,
height=None,
wrap=False,
equidistant=None,
tol=0.001,
LatLon=<class 'pygeodesy.ellipsoidalVincenty.LatLon'>,
**LatLon_kwds)
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Iteratively locate the closest point on the geodesic between two other
(ellipsoidal) points.
- Arguments:
point - Reference point (LatLon ).
point1 - Start point of the arc (LatLon ).
point2 - End point of the arc (LatLon ).
within - If True return the closest point between
point1 and point2 ,
otherwise the closest point elsewhere on the arc
(bool ).
height - Optional height for the closest point (meter ,
conventionally) or None or False for
the interpolated height. If False , the closest
takes the heights of the points into account.
wrap - Wrap and unroll longitudes (bool ).
equidistant - An azimuthal equidistant projection (class or function pygeodesy.equidistant) or None for
the preferred point.Equidistant .
tol - Convergence tolerance (meter ).
LatLon - Optional class to return the closest point (LatLon) or None .
LatLon_kwds - Optional, additional LatLon keyword
arguments, ignored if LatLon is None .
- Returns:
- Closest point, a
LatLon instance or if
LatLon is None , a LatLon4Tuple(lat, lon, height,
datum) .
- Raises:
ImportError - Package geographiclib not installed or not found, but
only if equidistant= EquidistantKarney.
TypeError - Invalid or non-ellipsoidal point ,
point1 or point2 or invalid
equidistant .
ValueError - No convergence for the tol .
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