Package pygeodesy :: Module ellipsoidalExact |
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# Module ellipsoidalExact

Exact ellipsoidal geodesy using Karney's Exact Geodesic.

Ellipsoidal geodetic (lat-/longitude) LatLon and geocentric (ECEF) Cartesian classes and functions areaOf, intersections2, isclockwise, nearestOn and perimeterOf based on classes GeodesicExact, GeodesicAreaExact and GeodesicLineExact.

Version: 21.06.03

Classes
| Cartesian Extended to convert exact Cartesian to exact LatLon points.
| LatLon An ellipsoidal LatLon like ellipsoidalKarney.LatLon but using exact geodesic classes GeodesicExact and GeodesicLineExact to compute the geodesic distance, initial and final bearing (azimuths) between two given points or the destination point given a start point and an (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) Compute the area of an (ellipsoidal) polygon. |
intersection3(start1, end1, start2, end2, height=None, wrap=True, equidistant=None, tol=0.001, LatLon=<class 'pygeodesy.ellipsoidalExact.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.ellipsoidalExact.LatLon'>, **LatLon_kwds) Iteratively compute the intersection points of two circles each defined by an (ellipsoidal) center point and a radius. |
isclockwise(points, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, wrap=True) Determine the direction of a path or polygon. |
nearestOn(point, point1, point2, within=True, height=None, wrap=False, equidistant=None, tol=0.001, LatLon=<class 'pygeodesy.ellipsoidalExact.LatLon'>, **LatLon_kwds) Iteratively locate the closest point on the arc between two other (ellispoidal) points. |
perimeterOf(points, closed=False, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, wrap=True) Compute the perimeter of an (ellipsoidal) polygon. |

Variables
| __all__ = `_ALL_LAZY.ellipsoidalExact`

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) |
Compute the area of an (ellipsoidal) polygon. Arguments: `points` - The polygon points (LatLon[]). `datum` - Optional datum (Datum). `wrap` - Wrap and unroll longitudes (`bool`). Returns: Area (`meter`, same as units of the `datum`'s ellipsoid axes, squared). Raises: `PointsError` - Insufficient number of `points`. `TypeError` - Some `points` are not LatLon. `ValueError` - Invalid `wrap=False`, unwrapped, unrolled longitudes not supported. See Also: pygeodesy.areaOf, ellipsoidalGeodSolve.areaOf, ellipsoidalKarney.areaOf, sphericalNvector.areaOf and sphericalTrigonometry.areaOf.

### intersection3 (start1, end1, start2, end2, height=None, wrap=True, equidistant=None, tol=0.001, LatLon=<class 'pygeodesy.ellipsoidalExact.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=None`. Returns: An Intersection3Tuple`(point, outside1, outside2)` with `point` a `LatLon` or if `LatLon=None`, a LatLon4Tuple`(lat, lon, height, datum)`. Raises: `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.ellipsoidalExact.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=None`. Returns: 2-Tuple of the intersection points, each a `LatLon` instance or LatLon4Tuple`(lat, lon, height, datum)` if `LatLon=None`. For abutting circles, both intersection points are the same instance. 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`. See Also: The ellipsoidal case, Karney's paper, pp 20-21, section 14. MARITIME BOUNDARIES, circle-circle and sphere-sphere intersections.

### isclockwise (points, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, wrap=True) |
Determine the direction of a path or polygon. Arguments: `points` - The path or polygon points (`LatLon`[]). `datum` - Optional datum (Datum). `wrap` - Wrap and unroll longitudes (`bool`). Returns: `True` if `points` are clockwise, `False` otherwise. Raises: `PointsError` - Insufficient number of `points`. `TypeError` - Some `points` are not `LatLon`. `ValueError` - The `points` enclose a pole or zero area. See Also: pygeodesy.isclockwise.

### nearestOn (point, point1, point2, within=True, height=None, wrap=False, equidistant=None, tol=0.001, LatLon=<class 'pygeodesy.ellipsoidalExact.LatLon'>, **LatLon_kwds) |
Iteratively locate the closest point on the arc between two other (ellispoidal) 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=None`. Returns: Closest point, a `LatLon` instance or if `LatLon=None`, a LatLon4Tuple`(lat, lon, height, datum)`. Raises: `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) |
Compute the perimeter of an (ellipsoidal) polygon. Arguments: `points` - The polygon points (LatLon[]). `closed` - Optionally, close the polygon (`bool`). `datum` - Optional datum (Datum). `wrap` - Wrap and unroll longitudes (`bool`). Returns: Perimeter (`meter`, same as units of the `datum`'s ellipsoid axes). Raises: `PointsError` - Insufficient number of `points`. `TypeError` - Some `points` are not LatLon. `ValueError` - Invalid `wrap=False`, unwrapped, unrolled longitudes not supported. See Also: pygeodesy.perimeterOf, ellipsoidalGeodSolve.perimeterOf, ellipsoidalKarney.perimeterOf, sphericalNvector.perimeterOf and sphericalTrigonometry.perimeterOf.