Package pygeodesy :: Module sphericalTrigonometry |
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# Module sphericalTrigonometry

Trigonometric spherical geodetic (lat-/longitude) class LatLon and functions areaOf, intersection, isPoleEnclosedBy, meanOf, nearestOn2 and perimeterOf.

Pure Python implementation of geodetic (lat-/longitude) methods using spherical trigonometry, transcribed from JavaScript originals by (C) Chris Veness 2011-2016 published under the same MIT Licence**, see Latitude/Longitude.

Version: 19.02.12

Classes
| LatLon New point on spherical model earth model.

Functions
ispolar(points, wrap=False) Check whether a polygon encloses a pole. |
areaOf(points, radius=6371008.77141, wrap=True) Calculate the area of a (spherical) polygon (with great circle arcs joining the points). |
intersection(start1, end1, start2, end2, height=None, wrap=False, LatLon=<class 'pygeodesy.sphericalTrigonometry.LatLon'>) Compute the intersection point of two paths both defined by two points or a start point and bearing from North. |
isPoleEnclosedBy(points, wrap=False) DEPRECATED, use function ispolar. |
meanOf(points, height=None, LatLon=<class 'pygeodesy.sphericalTrigonometry.LatLon'>) Compute the geographic mean of several points. |
nearestOn2(point, points, closed=False, radius=6371008.77141, LatLon=<class 'pygeodesy.sphericalTrigonometry.LatLon'>, **options) DEPRECATED, use function sphericalTrigonometry.nearestOn3. |
nearestOn3(point, points, closed=False, radius=6371008.77141, LatLon=<class 'pygeodesy.sphericalTrigonometry.LatLon'>, **options) Locate the point on a polygon closest to an other, reference point. |
perimeterOf(points, closed=False, radius=6371008.77141, wrap=True) Compute the perimeter of a polygon. |

Function Details

### ispolar(points, wrap=False) |
Check whether a polygon encloses a pole. Parameters: `points` - The polygon points (`LatLon`[]). `wrap` - Wrap and unroll longitudes (`bool`). Returns: `True` if a pole is enclosed by the polygon, `False` otherwise. Raises: `ValueError` - Insufficient number of points. `TypeError` - Some points are not `LatLon` or don't have `bearingTo2`, `initialBearingTo` and `finalBearingTo` methods.

### areaOf(points, radius=6371008.77141, wrap=True) |
Calculate the area of a (spherical) polygon (with great circle arcs joining the points). Parameters: `points` - The polygon points (LatLon[]). `radius` - Optional, mean earth radius (`meter`). `wrap` - Wrap and unroll longitudes (`bool`). Returns: Polygon area (`meter`, same units as radius, squared). Raises: `TypeError` - Some points are not LatLon. `ValueError` - Insufficient number of points. Note: The area is based on Karney's 'Area of a spherical polygon'. See Also: pygeodesy.areaOf, sphericalNvector.areaOf and ellipsoidalKarney.areaOf. Example:
    >>> b = LatLon(45, 1), LatLon(45, 2), LatLon(46, 2), LatLon(46, 1)
    >>> areaOf(b)  # 8666058750.718977
    >>> c = LatLon(0, 0), LatLon(1, 0), LatLon(0, 1)
    >>> areaOf(c)  # 6.18e9

### intersection(start1, end1, start2, end2, height=None, wrap=False, LatLon=<class 'pygeodesy.sphericalTrigonometry.LatLon'>) |
Compute the intersection point of two paths both defined by two points or a start point and bearing from North. Parameters: `start1` - Start point of the first path (LatLon). `end1` - End point ofthe first path (LatLon) or the initial bearing at the first start 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 start point (compass `degrees360`). `height` - Optional height for the intersection point, overriding the mean height (`meter`). `wrap` - Wrap and unroll longitudes (`bool`). `LatLon` - Optional (sub-)class for the intersection point (LatLon) or `None`. Returns: The intersection point (LatLon) or 3-tuple (`degrees90`, `degrees180`, height) if LatLon is `None`. An alternate intersection point might be the antipode to the returned result. Raises: `TypeError` - Start or end point(s) not LatLon. `ValueError` - Intersection is ambiguous or infinite or the paths are parallel, coincident or null. Example:
    >>> p = LatLon(51.8853, 0.2545)
    >>> s = LatLon(49.0034, 2.5735)
    >>> i = intersection(p, 108.547, s, 32.435)  # '50.9078°N, 004.5084°E'

### meanOf(points, height=None, LatLon=<class 'pygeodesy.sphericalTrigonometry.LatLon'>) |
Compute the geographic mean of several points. Parameters: `points` - Points to be averaged (LatLon[]). `height` - Optional height at mean point, overriding the mean height (`meter`). `LatLon` - Optional (sub-)class to return the mean point (LatLon) or `None`. Returns: Point at geographic mean and height (LatLon) or 3-tuple (`degrees90`, `degrees180`, height) if LatLon is `None`. Raises: `TypeError` - Some points are not LatLon. `ValueError` - No points.

### nearestOn2(point, points, closed=False, radius=6371008.77141, LatLon=<class 'pygeodesy.sphericalTrigonometry.LatLon'>, **options) |
DEPRECATED, use function sphericalTrigonometry.nearestOn3. Returns: ... closest as LatLon or a 2-tuple (lat, lon) without the height if LatLon is `None` ...

### nearestOn3(point, points, closed=False, radius=6371008.77141, LatLon=<class 'pygeodesy.sphericalTrigonometry.LatLon'>, **options) |
Locate the point on a polygon closest to an other, reference point. Distances are approximated by function equirectangular_, subject to the supplied options. Parameters: `point` - The other, reference point (LatLon). `points` - The polygon points (LatLon[]). `closed` - Optionally, close the polygon (`bool`). `radius` - Optional, mean earth radius (`meter`). `LatLon` - Optional (sub-)class for the closest point (LatLon) or `None`. `options` - Optional keyword arguments for function equirectangular_. Returns: 3-Tuple (closest, distance, angle) of the closest point (LatLon) on the polygon, the distance and the compass angle to the closest point. The closest is an instance of LatLon or a 3-tuple (lat, lon, height) if LatLon is `None`. The distance is the equirectangular_ distance between the closest and reference point in `meter`, same units as radius. The angle from the reference point to the closest is in compass `degrees360`, like function compassAngle. The height is the (interpolated) height at the closest point. Raises: `LimitError` - Lat- and/or longitudinal delta exceeds limit, see function equirectangular_. `TypeError` - Some points are not `LatLon`. `ValueError` - Insufficient number of points. See Also: Functions equirectangular_ and nearestOn5.

### perimeterOf(points, closed=False, radius=6371008.77141, wrap=True) |
Compute the perimeter of a polygon. Parameters: `points` - The polygon points (LatLon[]). `closed` - Optionally, close the polygon (`bool`). `radius` - Optional, mean earth radius (`meter`). `wrap` - Wrap and unroll longitudes (`bool`). Returns: Polygon perimeter (`meter`, same units as radius). Raises: `TypeError` - Some points are not LatLon. `ValueError` - Insufficient number of points. Note: This perimeter is based on the haversine formula. See Also: pygeodesy.perimeterOf and ellipsoidalKarney.perimeterOf.