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: 22.07.07

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) Iteratively compute the intersection point of two paths, each defined by two (ellipsoidal) points or by an (ellipsoidal) start point and a bearing from North. |
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 geodesic 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: Functions pygeodesy.areaOf, ellipsoidalGeodSolve.areaOf, ellipsoidalKarney.areaOf, sphericalNvector.areaOf and sphericalTrigonometry.areaOf. Note: The area of a polygon enclosing a pole can be found by adding half the datum's ellipsoid surface area to the polygon's area.

### intersection3 (start1, end1, start2, end2, height=None, wrap=True, equidistant=None, tol=0.001, LatLon=<class 'pygeodesy.ellipsoidalExact.LatLon'>, **LatLon_kwds) |
Iteratively 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.

### 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 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`. 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 geodesic between two other (ellispoidal) points. Arguments: `point` - Reference point (`LatLon`). `point1` - Start point of the geodesic (`LatLon`). `point2` - End point of the geodesic (`LatLon`). `within` - If `True` return the closest point between `point1` and `point2`, otherwise the closest point elsewhere on the geodesic (`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: `TypeError` - Invalid or non-ellipsoidal `point`, `point1` or `point2` or invalid `equidistant`. `ValueError` - No convergence for the `tol`. See Also: The ellipsoidal case and Karney's paper, pp 20-21, section 14. MARITIME BOUNDARIES for more details about the iteration algorithm.

### 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: Functions pygeodesy.perimeterOf, ellipsoidalGeodSolve.perimeterOf, ellipsoidalKarney.perimeterOf, sphericalNvector.perimeterOf and sphericalTrigonometry.perimeterOf.