Package pygeodesy :: Module sphericalNvector :: Class LatLon |
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# Class LatLon

               object --+
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             named._Named --+
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             named._NamedBase --+
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            latlonBase.LatLonBase --+
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        nvectorBase.LatLonNvectorBase --+
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               object --+               |
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             named._Named --+           |
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             named._NamedBase --+       |
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            latlonBase.LatLonBase --+   |
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    sphericalBase.LatLonSphericalBase --+
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                                       LatLon

New n-vector based point on a spherical earth model.

Tools for working with points and paths on (a spherical model of) the earth's surface using vector-based methods.

Example:

    >>> from sphericalNvector import LatLon
    >>> p = LatLon(52.205, 0.119)

Instance Methods
alongTrackDistanceTo(self, start, end, radius=6371008.77141) Compute the (signed) distance from the start to the closest point on the great circle path defined by a start and an end point. |
bearingTo(self, other, **unused) DEPRECATED, use method `initialBearingTo`. |
crossTrackDistanceTo(self, start, end, radius=6371008.77141) Compute the (signed) distance from this point to great circle defined by a start and end point. |
destination(self, distance, bearing, radius=6371008.77141, height=None) Locate the destination from this point after having travelled the given distance on the given bearing. |
distanceTo(self, other, radius=6371008.77141) Compute the distance from this to an other point. |
greatCircle(self, bearing) Compute the vector normal to great circle obtained by heading on the given bearing from this point. |
greatCircleTo(self, other) Compute the vector normal to great circle obtained by heading from this to an other point or on a given bearing. |
initialBearingTo(self, other, **unused) Compute the initial bearing (forward azimuth) from this to an other point. |
intermediateChordTo(self, other, fraction, height=None) Locate the point projected from the point at given fraction on a straight line (chord) between this and an other point. |
intermediateTo(self, other, fraction, height=None) Locate the point at a given fraction between this and an other point. |
intersection(self, end1, start2, end2, height=None) Locate the intersection point of two paths each defined by two points or a start point and bearing from North. |
isenclosedBy(self, points) Check whether this point is enclosed by a (convex) polygon. |
isEnclosedBy(self, points) DEPRECATED, use method `isenclosedBy`. |
iswithin(self, point1, point2) Check whether this point is between two other points. |
isWithin(self, point1, point2) DEPRECATED, use method `iswithin`. |
midpointTo(self, other, height=None) Find the midpoint between this and an other point. |
nearestOn(self, point1, point2, height=None) Locate the point on the great circle arc between two points closest to this point. |
nearestOn2(self, points, **closed_radius_height) DEPRECATED, use method sphericalNvector.LatLon.nearestOn3. |
nearestOn3(self, points, closed=False, radius=6371008.77141, height=None) Locate the point on a polygon (with great circle arcs joining consecutive points) closest to this point. |
toCartesian(self, **Cartesian_datum_kwds) Convert this point to `Nvector`-based cartesian (ECEF) coordinates. |
toNvector(self, **Nvector_kwds) Convert this point to Nvector components, including height. |
triangulate(self, bearing1, other, bearing2, height=None) Locate a point given this and an other point and a bearing at this and the other point. |
trilaterate(self, distance1, point2, distance2, point3, distance3, radius=6371008.77141, height=None, useZ=False) Locate a point at given distances from this and two other points. |
Inherited from `nvectorBase.LatLonNvectorBase`: `others` Inherited from `sphericalBase.LatLonSphericalBase`: `__init__`, `bearingTo2`, `finalBearingTo`, `maxLat`, `minLat`, `parse`, `rhumbBearingTo`, `rhumbDestination`, `rhumbDistanceTo`, `rhumbMidpointTo`, `toWm` Inherited from `latlonBase.LatLonBase`: `__eq__`, `__ne__`, `__str__`, `antipode`, `bounds`, `boundsOf`, `compassAngle`, `compassAngleTo`, `equals`, `equals3`, `equirectangularTo`, `euclideanTo`, `flatLocalTo`, `flatPolarTo`, `haversineTo`, `isantipode`, `isantipodeTo`, `isequalTo`, `isequalTo3`, `latlon2`, `latlon2round`, `latlon_`, `philam2`, `points`, `points2`, `to2ab`, `to3llh`, `to3xyz`, `toEcef`, `toStr`, `toVector`, `toVector3d`, `vincentysTo` Inherited from `named._NamedBase`: `__repr__`, `toStr2` Inherited from `named._Named`: `_dot_`, `attrs`, `classof`, `copy` Inherited from `object`: `__delattr__`, `__format__`, `__getattribute__`, `__hash__`, `__new__`, `__reduce__`, `__reduce_ex__`, `__setattr__`, `__sizeof__`, `__subclasshook__`

Properties
Inherited from `sphericalBase.LatLonSphericalBase`: `datum`, `isEllipsoidal`, `isSpherical` Inherited from `latlonBase.LatLonBase`: `Ecef`, `height`, `lam`, `lat`, `latlon`, `latlonheight`, `lon`, `phi`, `philam`, `philamheight`, `xyz`, `xyzh` Inherited from `named._Named`: `classname`, `classnaming`, `name`, `named`, `named2` Inherited from `object`: `__class__`

Method Details

### alongTrackDistanceTo (self, start, end, radius=6371008.77141) |
Compute the (signed) distance from the start to the closest point on the great circle path defined by a start and an end point. That is, if a perpendicular is drawn from this point to the great circle path, the along-track distance is the distance from the start point to the point where the perpendicular crosses the path. Arguments: `start` - Start point of great circle path (LatLon). `end` - End point of great circle path (LatLon) or initial bearing from start point (compass `degrees360`). `radius` - Mean earth radius (`meter`). Returns: Distance along the great circle path (positive if after the start toward the end point of the path or negative if before the start point). Raises: `TypeError` - If `start` or `end` point is not LatLon. `Valuerror` - Some points coincide. Example:
    >>> p = LatLon(53.2611, -0.7972)
    >>> s = LatLon(53.3206, -1.7297)
    >>> e = LatLon(53.1887, 0.1334)
    >>> d = p.alongTrackDistanceTo(s, e)  # 62331.58

### crossTrackDistanceTo (self, start, end, radius=6371008.77141) |
Compute the (signed) distance from this point to great circle defined by a start and end point. Arguments: `start` - Start point of great circle path (LatLon). `end` - End point of great circle path (LatLon) or initial bearing from start point (compass `degrees360`). `radius` - Mean earth radius (`meter`). Returns: Distance to great circle (negative if to the left or positive if to the right of the path). Raises: `TypeError` - If `start` or `end` point is not LatLon. `Valuerror` - Some points coincide. Example:
    >>> p = LatLon(53.2611, -0.7972)
    >>> s = LatLon(53.3206, -1.7297)
    >>> d = p.crossTrackDistanceTo(s, 96)  # -305.7
    >>> e = LatLon(53.1887, 0.1334)
    >>> d = p.crossTrackDistanceTo(s, e)  # -307.5

### destination (self, distance, bearing, radius=6371008.77141, height=None) |
Locate the destination from this point after having travelled the given distance on the given bearing. Arguments: `distance` - Distance travelled (`meter`, same units as `radius`). `bearing` - Bearing from this point (compass `degrees360`). `radius` - Mean earth radius (`meter`). `height` - Optional height at destination, overriding the default height (`meter`, same units as `radius`). Returns: Destination point (LatLon). Raises: `Valuerror` - Polar coincidence. Example:
    >>> p = LatLon(51.4778, -0.0015)
    >>> q = p.destination(7794, 300.7)
    >>> q.toStr()  # 51.513546°N, 000.098345°W
JS name: destinationPoint.

### distanceTo (self, other, radius=6371008.77141) |
Compute the distance from this to an other point. Arguments: `other` - The other point (LatLon). `radius` - Mean earth radius (`meter`). Returns: Distance between this and the `other` point (`meter`, same units as `radius`). Raises: `TypeError` - The `other` point is not LatLon. Example:
    >>> p = LatLon(52.205, 0.119)
    >>> q = LatLon(48.857, 2.351);
    >>> d = p.distanceTo(q)  # 404.3 km

### greatCircle (self, bearing) |
Compute the vector normal to great circle obtained by heading on the given bearing from this point. Direction of vector is such that initial bearing vector b = c × n, where n is an n-vector representing this point. Arguments: `bearing` - Bearing from this point (compass `degrees360`). Returns: N-vector representing the great circle (Nvector).

### greatCircleTo (self, other) |
Compute the vector normal to great circle obtained by heading from this to an other point or on a given bearing. Direction of vector is such that initial bearing vector b = c × n, where n is an n-vector representing this point. Arguments: `other` - The other point (LatLon) or the bearing from this point (compass `degrees360`). Returns: N-vector representing the great circle (Nvector). Raises: `TypeError` - The `other` point is not LatLon. `Valuerror` - Points coincide. Example:
    >>> p = LatLon(53.3206, -1.7297)
    >>> gc = p.greatCircle(96.0)
    >>> gc.toStr()  # (-0.79408, 0.12856, 0.59406)
    >>> q = LatLon(53.1887, 0.1334)
    >>> g = p.greatCircleTo(q)
    >>> g.toStr()  # (-0.79408, 0.12859, 0.59406)

### initialBearingTo (self, other, **unused) |
Compute the initial bearing (forward azimuth) from this to an other point. Arguments: `other` - The other point (LatLon). `unused` - Optional keyword argument `wrap` ignored. Returns: Initial bearing (compass `degrees360`). Raises: `Crosserror` - This point coincides with the `other` point or the `NorthPole`, provided crosserrors is `True`. `TypeError` - The `other` point is not LatLon. Example:
    >>> p1 = LatLon(52.205, 0.119)
    >>> p2 = LatLon(48.857, 2.351)
    >>> b = p1.initialBearingTo(p2)  # 156.2
JS name: bearingTo.

### intermediateChordTo (self, other, fraction, height=None) |
Locate the point projected from the point at given fraction on a straight line (chord) between this and an other point. Arguments: `other` - The other point (LatLon). `fraction` - Fraction between both points (float, between 0.0 for this and 1.0 for the other point). `height` - Optional height at the intermediate point, overriding the fractional height (`meter`). Returns: Intermediate point (LatLon). Raises: `TypeError` - The `other` point is not LatLon. Example:
    >>> p = LatLon(52.205, 0.119)
    >>> q = LatLon(48.857, 2.351)
    >>> i = p.intermediateChordTo(q, 0.25)  # 51.3723°N, 000.7072°E
JS name: intermediatePointOnChordTo, intermediatePointDirectlyTo.

### intermediateTo (self, other, fraction, height=None) |
Locate the point at a given fraction between this and an other point. Arguments: `other` - The other point (LatLon). `fraction` - Fraction between both points (float, between 0.0 for this and 1.0 for the other point). `height` - Optional height at the intermediate point, overriding the fractional height (`meter`). Returns: Intermediate point (LatLon). Raises: `TypeError` - The `other` point is not LatLon. `Valuerror` - Points coincide. Example:
    >>> p = LatLon(52.205, 0.119)
    >>> q = LatLon(48.857, 2.351)
    >>> i = p.intermediateTo(q, 0.25)  # 51.3721°N, 000.7074°E
JS name: intermediatePointTo.

### intersection (self, end1, start2, end2, height=None) |
Locate the intersection point of two paths each defined by two points or a start point and bearing from North. Arguments: `end1` - End point of the first path (LatLon) or the initial bearing at this 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 `degrees`). `height` - Optional height at the intersection point, overriding the mean height (`meter`). Returns: The intersection point (LatLon) or `None` if no unique intersection exists. Raises: `TypeError` - If `start2`, `end1` or `end2` point is not LatLon. `ValueError` - Intersection is ambiguous or infinite or the paths are parallel, coincident or null. Example:
    >>> s = LatLon(51.8853, 0.2545)
    >>> e = LatLon(49.0034, 2.5735)
    >>> i = s.intersection(108.55, e, 32.44)  # 50.9076°N, 004.5086°E

### isenclosedBy (self, points) |
Check whether this point is enclosed by a (convex) polygon. Arguments: `points` - The polygon points (LatLon[]). Returns: `True` if the polygon encloses this point, `False` otherwise. Raises: `TypeError` - Some `points` are not LatLon. `ValueError` - Insufficient number of `points`. Example:
    >>> b = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1)
    >>> p = LatLon(45.1, 1.1)
    >>> inside = p.isEnclosedBy(b)  # True
JS name: enclosedBy.

### iswithin (self, point1, point2) |
Check whether this point is between two other points. If this point is not on the great circle arc defined by both points, return whether it is within the area bound by perpendiculars to the great circle at each point (in the same hemispere). Arguments: `point1` - Start point of the arc (LatLon). `point2` - End point of the arc (LatLon). Returns: `True` if this point is within the arc, `False` otherwise. Raises: `TypeError` - If `point1` or `point2` is not LatLon. JS name: isBetween.

### midpointTo (self, other, height=None) |
Find the midpoint between this and an other point. Arguments: `other` - The other point (LatLon). `height` - Optional height at the midpoint, overriding the mean height (`meter`). Returns: Midpoint (LatLon). Raises: `TypeError` - The `other` point is not LatLon. Example:
    >>> p1 = LatLon(52.205, 0.119)
    >>> p2 = LatLon(48.857, 2.351)
    >>> m = p1.midpointTo(p2)  # '50.5363°N, 001.2746°E'

### nearestOn (self, point1, point2, height=None) |
Locate the point on the great circle arc between two points closest to this point. If this point is within the extent of the arc between both end points, return the closest point on the arc. Otherwise, return the closest of the arc's end points. Arguments: `point1` - Start point of the arc (LatLon). `point2` - End point of the arc (LatLon). `height` - Optional height, overriding the mean height for the point within the arc (`meter`). Returns: Closest point on the arc (LatLon). Raises: `TypeError` - If `point1` or `point2` is not LatLon. Example:
    >>> s1 = LatLon(51.0, 1.0)
    >>> s2 = LatLon(51.0, 2.0)
    >>> s = LatLon(51.0, 1.9)
    >>> p = s.nearestOn(s1, s2)  # 51.0004°N, 001.9000°E
    >>> d = p.distanceTo(s)  # 42.71 m
    >>> s = LatLon(51.0, 2.1)
    >>> p = s.nearestOn(s1, s2)  # 51.0000°N, 002.0000°E
JS name: nearestPointOnSegment.

### nearestOn2 (self, points, **closed_radius_height) |
DEPRECATED, use method sphericalNvector.LatLon.nearestOn3. Returns: ... 2-Tuple `(closest, distance)` of the `closest` point (LatLon) on the polygon and the `distance` to that point from this point ...

### nearestOn3 (self, points, closed=False, radius=6371008.77141, height=None) |
Locate the point on a polygon (with great circle arcs joining consecutive points) closest to this point. If this point is within the extent of any great circle arc, the closest point is on that arc. Otherwise, the closest is the nearest of the arc's end points. Arguments: `points` - The polygon points (LatLon[]). `closed` - Optionally, close the polygon (`bool`). `radius` - Mean earth radius (`meter`). `height` - Optional height, overriding the mean height for a point within the arc (`meter`). Returns: A NearestOn3Tuple`(closest, distance, angle)` of the `closest` point (LatLon), the `distance` between this and the `closest` point in `meter`, same units as `radius` and the `angle` from this to the `closest` point in compass `degrees360`. Raises: `TypeError` - Some `points` are not `LatLon`. `ValueError` - No `points`.

### toCartesian (self, **Cartesian_datum_kwds) |
Convert this point to `Nvector`-based cartesian (ECEF) coordinates. Arguments: `Cartesian_datum_kwds` - Optional Cartesian, `datum` or other keyword arguments, ignored if `Cartesian=None`. Use `Cartesian=...` to override this Cartesian class or specify `Cartesian=None`. Returns: The cartesian point (Cartesian) or if `Cartesian` is `None`, an Ecef9Tuple`(x, y, z, lat, lon, height, C, M, datum)` with `C` and `M` if available. Raises: `TypeError` - Invalid `Cartesian_datum_kwds`. Overrides: latlonBase.LatLonBase.toCartesian

### toNvector (self, **Nvector_kwds) |
Convert this point to Nvector components, including height. Arguments: `Nvector_kwds` - Optional Nvector keyword arguments, ignored if `Nvector=None`. Use `Nvector=...` to override this Nvector class or specify `Nvector=None` Returns: The `n-vector` components (Nvector) or a Vector4Tuple`(x, y, z, h)` if `Nvector` is `None`. Raises: `TypeError` - Invalid `Nvector_kwds`. Overrides: latlonBase.LatLonBase.toNvector Example:
    >>> p = LatLon(45, 45)
    >>> n = p.toNvector()
    >>> n.toStr()  # [0.50, 0.50, 0.70710]
JS name: toVector.

### triangulate (self, bearing1, other, bearing2, height=None) |
Locate a point given this and an other point and a bearing at this and the other point. Arguments: `bearing1` - Bearing at this point (compass `degrees360`). `other` - The other point (LatLon). `bearing2` - Bearing at the other point (compass `degrees360`). `height` - Optional height at the triangulated point, overriding the mean height (`meter`). Returns: Triangulated point (LatLon). Raises: `TypeError` - The `other` point is not LatLon. `Valuerror` - Points coincide. Example:
    >>> p = LatLon("47°18.228'N","002°34.326'W")  # Basse Castouillet
    >>> q = LatLon("47°18.664'N","002°31.717'W")  # Basse Hergo
    >>> t = p.triangulate(7, q, 295)  # 47.323667°N, 002.568501°W'

### trilaterate (self, distance1, point2, distance2, point3, distance3, radius=6371008.77141, height=None, useZ=False) |
Locate a point at given distances from this and two other points. See also Trilateration. Arguments: `distance1` - Distance to this point (`meter`, same units as `radius`). `point2` - Second reference point (LatLon). `distance2` - Distance to point2 (`meter`, same units as `radius`). `point3` - Third reference point (LatLon). `distance3` - Distance to point3 (`meter`, same units as `radius`). `radius` - Mean earth radius (`meter`). `height` - Optional height at trilaterated point, overriding the mean height (`meter`, same units as `radius`). `useZ` - Include Z component iff non-NaN, non-zero (`bool`). Returns: Trilaterated point (LatLon). Raises: `TypeError` - Some `points` are not LatLon. `ValueError` - Distance(s) exceeds trilateration or some `points` coincide.