Package pygeodesy :: Module ktm :: Class KTransverseMercator |
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# Class KTransverseMercator

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                      KTransverseMercator

Transverse Mercator projection based on Krüger's method which evaluates the projection and its inverse in terms of a series.

There's a singularity in the projection at phi = 0, lam - lam0 = +/- (1 - e) 90, about +/- 82.6 degrees for WGS84, where e is the eccentricity. Beyond this point, the series ceases to converge and the results from this method will be garbage. To be on the safe side, don't use this method if the angular distance from the central meridian exceeds (1 - 2e) x 90, about 75 degrees for the WGS84 ellipsoid.

Class ExactTransverseMercator is an alternative implementation of the projection using exact formulas which yield accurate (to 8 nm) results over the entire ellipsoid.

The ellipsoid parameters and the central scale are set in the constructor. The central meridian (which is a trivial shift of the longitude) is specified as the `lon0` keyword argument of the KTransverseMercator.forward and KTransverseMercator.reverse methods. The latitude of origin is taken to be the equator. There is no provision in this class for specifying a false easting or false northing or a different latitude of origin. However these are can be simply included by the calling function.

The KTransverseMercator.forward and KTransverseMercator.reverse methods also return the meridian convergence `gamma` and scale `k`. The meridian convergence is the bearing of grid North, the `y axis`, measured clockwise from true North.

Instance Methods
__init__(self, a_earth=Ellipsoid(name='WGS84', a=6378137, b=6356752.31424518, f_=298.`...`, f=None, lon0=0, k0=0.9996, name='', raiser=False, **TMorder) New KTransverseMercator. |
forward(self, lat, lon, lon0=None, name='') Forward projection, from geographic to transverse Mercator. |
reverse(self, x, y, lon0=None, name='') Reverse projection, from transverse Mercator to geographic. |
toStr(self, **kwds) Return a `str` representation. |
Inherited from `named._NamedBase`: `__repr__`, `__str__`, `others`, `toRepr` Inherited from `named._Named`: `__imatmul__`, `__matmul__`, `__rmatmul__`, `attrs`, `classof`, `copy`, `dup`, `rename`, `toStr2` Inherited from `object`: `__delattr__`, `__format__`, `__getattribute__`, `__hash__`, `__new__`, `__reduce__`, `__reduce_ex__`, `__setattr__`, `__sizeof__`, `__subclasshook__`

Properties
| ellipsoid Get the ellipsoid (Ellipsoid).
| equatoradius Get the `ellipsoid`'s equatorial radius, semi-axis (`meter`).
| a Get the `ellipsoid`'s equatorial radius, semi-axis (`meter`).
| flattening Get the `ellipsoid`'s flattening (`float`).
| f Get the `ellipsoid`'s flattening (`float`).
| k0 Class `property` with retrievable name.
| lon0 Class `property` with retrievable name.
| raiser Class `property` with retrievable name.
| TMorder Get the Transverse Mercator order (`int`, 4, 5, 6, 7 or 8).
Inherited from `named._Named`: `classname`, `classnaming`, `iteration`, `name`, `named`, `named2`, `named3`, `named4` Inherited from `object`: `__class__`

Method Details

### __init__ (self, a_earth=Ellipsoid(name='WGS84', a=6378137, b=6356752.31424518, f_=298.`...`, f=None, lon0=0, k0=0.9996, name='', raiser=False, **TMorder) (Constructor) |
New KTransverseMercator. Arguments: `a_earth` - This rhumb's earth (Ellipsoid, Ellipsoid2, a_f2Tuple, Datum, 2-tuple (`a, f`)) or the equatorial radius (`scalar`, `meter`). `f` - The ellipsoid's flattening (`scalar`), iff `a_earth` is a `scalar`, ignored otherwise. `lon0` - The central meridian (`degrees180`). `k0` - Central scale factor (`scalar`). `name` - Optional name (`str`). `raiser` - If `True`, throw a KTMError for `forward` singularities (`bool`). `TMorder` - Keyword argument `TMorder`, see property `TMorder`. Raises: `KTMError` - Invalid `a_earth`, `f` or `TMorder`. Overrides: object.__init__

### forward (self, lat, lon, lon0=None, name='') |
Forward projection, from geographic to transverse Mercator. Arguments: `lat` - Latitude of point (`degrees90`). `lon` - Longitude of point (`degrees180`). `lon0` - Central meridian of the projection (`degrees180`). `name` - Optional name (`str`). Returns: Forward4Tuple`(easting, northing, convergence, scale)` with `easting` and `northing` in `meter`, unfalsed, the gamma meridian `convergence` at point in `degrees180` and k `scale` of projection at point `scalar`. Any value may be `NAN`, `NINF` or `INF` for singularities. Raises: `KTMError` - For singularities, iff property `raiser` is `True`.

### reverse (self, x, y, lon0=None, name='') |
Reverse projection, from transverse Mercator to geographic. Arguments: `x` - Easting of point (`meter`). `y` - Northing of point (`meter`). `lon0` - Central meridian of the projection (`degrees180`). Returns: Reverse4Tuple`(lat, lon, convergence, scale)` with `lat`- and `lon`gitude in `degrees`, unfalsed.

### toStr (self, **kwds) |
Return a `str` representation. Arguments: `kwds` - Optional, overriding keyword arguments. Overrides: named._Named.toStr

Property Details

### ellipsoid Get the ellipsoid (Ellipsoid). Get method: ellipsoid(self) - Get the ellipsoid (Ellipsoid). Set method: ellipsoid(self, a_earth_f) - Set this rhumb's ellipsoid (Ellipsoid, Ellipsoid2, Datum, a_f2Tuple or 2-tuple `(a, f)`). Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### equatoradius Get the `ellipsoid`'s equatorial radius, semi-axis (`meter`). Get method: equatoradius(self) - Get the `ellipsoid`'s equatorial radius, semi-axis (`meter`). Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### a Get the `ellipsoid`'s equatorial radius, semi-axis (`meter`). Get method: equatoradius(self) - Get the `ellipsoid`'s equatorial radius, semi-axis (`meter`). Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### flattening Get the `ellipsoid`'s flattening (`float`). Get method: flattening(self) - Get the `ellipsoid`'s flattening (`float`). Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### f Get the `ellipsoid`'s flattening (`float`). Get method: flattening(self) - Get the `ellipsoid`'s flattening (`float`). Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### k0 Class `property` with retrievable name. Get method: k0(self) - Get the central scale factor (`float`), aka `scale0`. Set method: k0(self, k0) - Set the central scale factor (`float`), aka `scale0`.

### lon0 Class `property` with retrievable name. Get method: lon0(self) - Get the central meridian (`degrees180`). Set method: lon0(self, lon0) - Set the central meridian (`degrees180`).

### raiser Class `property` with retrievable name. Get method: raiser(self) - Get the error setting (`bool`). Set method: raiser(self, raiser) - Set the error setting (`bool`), to `True` to throw a KTMError for `forward` singularities.

### TMorder Get the Transverse Mercator order (`int`, 4, 5, 6, 7 or 8). Get method: TMorder(self) - Get the Transverse Mercator order (`int`, 4, 5, 6, 7 or 8). Set method: TMorder(self, order) - Set the Transverse Mercator order (`int`, 4, 5, 6, 7 or 8). Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.