Package pygeodesy :: Module ellipsoidalVincenty |
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# 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`:

    >>> 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)

Version: 21.08.24

Classes
| VincentyError Error raised from Vincenty's `direct` and `inverse` methods for coincident points or lack of convergence.
| Cartesian Extended to convert geocentric, Cartesian points to Vincenty-based, ellipsoidal, geodetic LatLon.
| 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.

Functions
ispolar(points, wrap=False) Check whether a polygon encloses a pole. |
areaOf(points, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, wrap=True) DEPRECATED, use function ellipsoidalExact.areaOf or ellipsoidalKarney.areaOf. |
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 an (ellipsoidal) start and end point. |
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. |
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 arc between two other (ellipsoidal) points. |
perimeterOf(points, closed=False, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, wrap=True) DEPRECATED, use function ellipsoidalExact.perimeterOf or ellipsoidalKarney.perimeterOf. |

Variables
| __all__ = `_ALL_LAZY.ellipsoidalVincenty`

Function Details

### ispolar (points, wrap=False) |
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.

### areaOf (points, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, wrap=True) |
DEPRECATED, use function ellipsoidalExact.areaOf or ellipsoidalKarney.areaOf. Decorators: `@deprecated_function`

### 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 an (ellipsoidal) start and end point. Arguments: `start1` - Start point of the first path (LatLon). `end1` - End point of the first path (LatLon). `start2` - Start point of the second path (LatLon). `end2` - End point of the second path (LatLon). `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 equidistant) or `None` for the preferred `start1.Equidistant`. `tol` - Tolerance for skew line distance and length and for convergence (`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: `ImportError` - Package geographiclib not installed or not found, but only if `equidistant=`EquidistantKarney. `IntersectionError` - Skew, colinear, parallel or otherwise non-intersecting paths or no convergence for the `tol`. `TypeError` - Invalid or non-ellipsoidal `start1`, `end1`, `start2` or `end2` or invalide `equidistant`.

### 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. 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 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 radical center. Raises: `ImportError` - Package geographiclib not installed or not found, but only if `equidistant=`EquidistantKarney. `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`. See Also: The ellipsoidal case, Karney's paper, pp 20-21, section 14. MARITIME BOUNDARIES, circle-circle and sphere-sphere intersections.

### 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 arc 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 distance between points takes height into account. `wrap` - Wrap and unroll longitudes (`bool`). `equidistant` - An azimuthal equidistant projection (class or function 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`.

### perimeterOf (points, closed=False, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, wrap=True) |
DEPRECATED, use function ellipsoidalExact.perimeterOf or ellipsoidalKarney.perimeterOf. Decorators: `@deprecated_function`