Package pygeodesy :: Module utily |
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# Module utily

Various utility functions.

After (C) Chris Veness 2011-2015 published under the same MIT Licence**, see Latitude/Longitude and Vector-based geodesy.

Version: 24.06.03

Functions
degrees(x) Convert angle x from radians to degrees. |
radians(x) Convert angle x from degrees to radians. |
acos1(x) Return `math.acos(max(-1, min(1, x)))`. |
acre2ha(acres) Convert acres to hectare. |
acre2m2(acres) Convert acres to square meter. |
asin1(x) Return `math.asin(max(-1, min(1, x)))`. |
atan1(y, x=1.0) Return `atan(y / x)` angle in `radians` [-PI/2..+PI/2] using `atan2` for consistency and to avoid `ZeroDivisionError`. |
atan1d(y, x=1.0) Return `atan(y / x)` angle in `degrees` [-90..+90] using `atan2d` for consistency and to avoid `ZeroDivisionError`. |
atan2b(y, x) Return `atan2(y, x)` in degrees [0..+360]. |
atan2d(y, x, reverse=False) Return `atan2(y, x)` in degrees [-180..+180], optionally reversed (by 180 degrees for `azimuth`s). |
chain2m(chains) Convert UK chains to meter. |
circle4(earth, lat) Get the equatorial or a parallel circle of latitude. |
cot(rad, **error_kwds) Return the `cotangent` of an angle in `radians`. |
cot_(*rads, **error_kwds) Return the `cotangent` of angle(s) in `radiansresection`. |
cotd(deg, **error_kwds) Return the `cotangent` of an angle in `degrees`. |
cotd_(*degs, **error_kwds) Return the `cotangent` of angle(s) in `degrees`. |
degrees90(rad) Convert radians to degrees and wrap [-90..+90). |
degrees180(rad) Convert radians to degrees and wrap [-180..+180). |
degrees360(rad) Convert radians to degrees and wrap [0..+360). |
degrees2grades(deg) Convert degrees to grades (aka gons or gradians). |
degrees2m(deg, radius=6371008.771415, lat=0) Convert an angle to a distance along the equator or along the parallel at an other (geodetic) latitude. |
fathom2m(fathoms) Convert Imperial fathom to meter. |
ft2m(feet, usurvey=False, pied=False, fuss=False) Convert International, US Survey, French or German `feet` to `meter`. |
furlong2m(furlongs) Convert a furlong to meter. |
grades(rad) Convert radians to grades (aka gons or gradians). |
grades400(rad) Convert radians to grades (aka gons or gradians) and wrap [0..+400). |
grades2degrees(gon) Convert grades (aka gons or gradians) to `degrees`. |
grades2radians(gon) Convert grades (aka gons or gradians) to `radians`. |
km2m(km) Convert kilo meter to meter (m). |
m2chain(meter) Convert meter to UK chains. |
m2degrees(distance, radius=6371008.771415, lat=0) Convert a distance to an angle along the equator or along the parallel at an other (geodetic) latitude. |
m2fathom(meter) Convert meter to Imperial fathoms. |
m2ft(meter, usurvey=False, pied=False, fuss=False) Convert meter to International, US Survey, French or or German feet (`ft`). |
m2furlong(meter) Convert meter to furlongs. |
m2km(meter) Convert meter to kilo meter (Km). |
m2NM(meter) Convert meter to nautical miles (NM). |
m2radians(distance, radius=6371008.771415, lat=0) Convert a distance to an angle along the equator or along the parallel at an other (geodetic) latitude. |
m2SM(meter) Convert meter to statute miles (SM). |
m2toise(meter) Convert meter to French toises. |
m2yard(meter) Convert meter to UK yards. |
NM2m(nm) Convert nautical miles to meter (m). |
radians2m(rad, radius=6371008.771415, lat=0) Convert an angle to a distance along the equator or along the parallel at an other (geodetic) latitude. |
radiansPI(deg) Convert and wrap degrees to radians [-PI..+PI]. |
radiansPI2(deg) Convert and wrap degrees to radians [0..+2PI). |
radiansPI_2(deg) Convert and wrap degrees to radians [-3PI/2..+PI/2]. |
SinCos2(x) Get `sin` and `cos` of typed angle. |
sincos2(rad) Return the `sine` and `cosine` of an angle in `radians`. |
sincos2_(*rads) Return the `sine` and `cosine` of angle(s) in `radians`. |
sincos2d(deg, **adeg) Return the `sine` and `cosine` of an angle in `degrees`. |
sincos2d_(*degs) Return the `sine` and `cosine` of angle(s) in `degrees`. |
sincostan3(rad) Return the `sine`, `cosine` and `tangent` of an angle in `radians`. |
SM2m(sm) Convert statute miles to meter (m). |
tan_2(rad, **semi) Compute the tangent of half angle. |
tand(deg, **error_kwds) Return the `tangent` of an angle in `degrees`. |
tand_(*degs, **error_kwds) Return the `tangent` of angle(s) in `degrees`. |
tanPI_2_2(rad) Compute the tangent of half angle, 90 degrees rotated. |
toise2m(toises) Convert French toises to meter. |
truncate(x, ndigits=None) Truncate to the given number of digits. |
unroll180(lon1, lon2, wrap=True) Unroll longitudinal delta and wrap longitude in degrees. |
unrollPI(rad1, rad2, wrap=True) Unroll longitudinal delta and wrap longitude in radians. |
wrap90(deg) Wrap degrees to [-90..+90]. |
wrap180(deg) Wrap degrees to [-180..+180]. |
wrap360(deg) Wrap degrees to [0..+360). |
wrapPI(rad) Wrap radians to [-PI..+PI]. |
wrapPI2(rad) Wrap radians to [0..+2PI). |
wrapPI_2(rad) Wrap radians to [-PI/2..+PI/2]. |
wrap_normal(*normal) Define the operation for the keyword argument `wrap=True`, across pygeodesy: wrap, normalize or no-op. |
yard2m(yards) Convert UK yards to meter. |

Variables
| __all__ = `_ALL_LAZY.utily`

Function Details

### acre2ha (acres) |
Convert acres to hectare. Arguments: `acres` - Value in acres (`scalar`). Returns: Value in `hectare` (`float`). Raises: `ValueError` - Invalid `acres`.

### acre2m2 (acres) |
Convert acres to square meter. Arguments: `acres` - Value in acres (`scalar`). Returns: Value in `meter^2` (`float`). Raises: `ValueError` - Invalid `acres`.

### atan1d (y, x=1.0) |
Return `atan(y / x)` angle in `degrees` [-90..+90] using `atan2d` for consistency and to avoid `ZeroDivisionError`. See Also: Function pygeodesy.atan2d.

### atan2b (y, x) |
Return `atan2(y, x)` in degrees [0..+360]. See Also: Function pygeodesy.atan2d.

### atan2d (y, x, reverse=False) |
Return `atan2(y, x)` in degrees [-180..+180], optionally reversed (by 180 degrees for `azimuth`s). See Also: Karney's C++ function Math.atan2d.

### chain2m (chains) |
Convert UK chains to meter. Arguments: `chains` - Value in chains (`scalar`). Returns: Value in `meter` (`float`). Raises: `ValueError` - Invalid `chains`.

### circle4 (earth, lat) |
Get the equatorial or a parallel circle of latitude. Arguments: `earth` - The earth radius, ellipsoid or datum (`meter`, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `lat` - Geodetic latitude (`degrees90`, `str`). Returns: A Circle4Tuple`(radius, height, lat, beta)` instance. Raises: `RangeError` - Latitude `lat` outside valid range and pygeodesy.rangerrors set to `True`. `TypeError` - Invalid `earth`. `ValueError` - `earth` or `lat`.

### cot (rad, **error_kwds) |
Return the `cotangent` of an angle in `radians`. Arguments: `rad` - Angle (`radians`). `error_kwds` - Error to raise (`ValueError`). Returns: `cot(rad)`. Raises: `ValueError` - pygeodesy.isnear0`(sin(rad)`.

### cot_ (*rads, **error_kwds) |
Return the `cotangent` of angle(s) in `radiansresection`. Arguments: `rads` - One or more angles (`radians`). `error_kwds` - Error to raise (`ValueError`). Returns: Yield the `cot(rad)` for each angle. Raises: `ValueError` - See pygeodesy.cot.

### cotd (deg, **error_kwds) |
Return the `cotangent` of an angle in `degrees`. Arguments: `deg` - Angle (`degrees`). `error_kwds` - Error to raise (`ValueError`). Returns: `cot(deg)`. Raises: `ValueError` - pygeodesy.isnear0`(sin(deg)`.

### cotd_ (*degs, **error_kwds) |
Return the `cotangent` of angle(s) in `degrees`. Arguments: `degs` - One or more angles (`degrees`). `error_kwds` - Error to raise (`ValueError`). Returns: Yield the `cot(deg)` for each angle. Raises: `ValueError` - See pygeodesy.cotd.

### degrees90 (rad) |
Convert radians to degrees and wrap [-90..+90). Arguments: `rad` - Angle (`radians`). Returns: Angle, wrapped (`degrees90`).

### degrees180 (rad) |
Convert radians to degrees and wrap [-180..+180). Arguments: `rad` - Angle (`radians`). Returns: Angle, wrapped (`degrees180`).

### degrees360 (rad) |
Convert radians to degrees and wrap [0..+360). Arguments: `rad` - Angle (`radians`). Returns: Angle, wrapped (`degrees360`).

### degrees2grades (deg) |
Convert degrees to grades (aka gons or gradians). Arguments: `deg` - Angle (`degrees`). Returns: Angle (`grades`).

### degrees2m (deg, radius=6371008.771415, lat=0) |
Convert an angle to a distance along the equator or along the parallel at an other (geodetic) latitude. Arguments: `deg` - The angle (`degrees`). `radius` - Mean earth radius, ellipsoid or datum (`meter`, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `lat` - Parallel latitude (`degrees90`, `str`). Returns: Distance (`meter`, same units as `radius` or equatorial and polar radii) or `0.0` for near-polar `lat`. Raises: `RangeError` - Latitude `lat` outside valid range and pygeodesy.rangerrors set to `True`. `TypeError` - Invalid `radius`. `ValueError` - Invalid `deg`, `radius` or `lat`. See Also: Function radians2m and m2degrees.

### fathom2m (fathoms) |
Convert Imperial fathom to meter. Arguments: `fathoms` - Value in fathoms (`scalar`). Returns: Value in `meter` (`float`). Raises: `ValueError` - Invalid `fathoms`. See Also: Function toise2m, Fathom and Klafter.

### ft2m (feet, usurvey=False, pied=False, fuss=False) |
Convert International, US Survey, French or German `feet` to `meter`. Arguments: `feet` - Value in feet (`scalar`). `usurvey` - If `True`, convert US Survey foot else ... `pied` - If `True`, convert French pied-du-Roi else ... `fuss` - If `True`, convert German Fuss, otherwise International foot to `meter`. Returns: Value in `meter` (`float`). Raises: `ValueError` - Invalid `feet`.

### furlong2m (furlongs) |
Convert a furlong to meter. Arguments: `furlongs` - Value in furlongs (`scalar`). Returns: Value in `meter` (`float`). Raises: `ValueError` - Invalid `furlongs`.

### grades (rad) |
Convert radians to grades (aka gons or gradians). Arguments: `rad` - Angle (`radians`). Returns: Angle (`grades`).

### grades400 (rad) |
Convert radians to grades (aka gons or gradians) and wrap [0..+400). Arguments: `rad` - Angle (`radians`). Returns: Angle, wrapped (`grades`).

### grades2degrees (gon) |
Convert grades (aka gons or gradians) to `degrees`. Arguments: `gon` - Angle (`grades`). Returns: Angle (`degrees`).

### grades2radians (gon) |
Convert grades (aka gons or gradians) to `radians`. Arguments: `gon` - Angle (`grades`). Returns: Angle (`radians`).

### km2m (km) |
Convert kilo meter to meter (m). Arguments: `km` - Value in kilo meter (`scalar`). Returns: Value in meter (`float`). Raises: `ValueError` - Invalid `km`.

### m2chain (meter) |
Convert meter to UK chains. Arguments: `meter` - Value in meter (`scalar`). Returns: Value in `chains` (`float`). Raises: `ValueError` - Invalid `meter`.

### m2degrees (distance, radius=6371008.771415, lat=0) |
Convert a distance to an angle along the equator or along the parallel at an other (geodetic) latitude. Arguments: `distance` - Distance (`meter`, same units as `radius`). `radius` - Mean earth radius, ellipsoid or datum (`meter`, an Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `lat` - Parallel latitude (`degrees90`, `str`). Returns: Angle (`degrees`) or `INF` for near-polar `lat`. Raises: `RangeError` - Latitude `lat` outside valid range and pygeodesy.rangerrors set to `True`. `TypeError` - Invalid `radius`. `ValueError` - Invalid `distance`, `radius` or `lat`. See Also: Function m2radians and degrees2m.

### m2fathom (meter) |
Convert meter to Imperial fathoms. Arguments: `meter` - Value in meter (`scalar`). Returns: Value in `fathoms` (`float`). Raises: `ValueError` - Invalid `meter`. See Also: Function m2toise, Fathom and Klafter.

### m2ft (meter, usurvey=False, pied=False, fuss=False) |
Convert meter to International, US Survey, French or or German feet (`ft`). Arguments: `meter` - Value in meter (`scalar`). `usurvey` - If `True`, convert to US Survey foot else ... `pied` - If `True`, convert to French pied-du-Roi else ... `fuss` - If `True`, convert to German Fuss, otherwise to International foot. Returns: Value in `feet` (`float`). Raises: `ValueError` - Invalid `meter`.

### m2furlong (meter) |
Convert meter to furlongs. Arguments: `meter` - Value in meter (`scalar`). Returns: Value in `furlongs` (`float`). Raises: `ValueError` - Invalid `meter`.

### m2km (meter) |
Convert meter to kilo meter (Km). Arguments: `meter` - Value in meter (`scalar`). Returns: Value in Km (`float`). Raises: `ValueError` - Invalid `meter`.

### m2NM (meter) |
Convert meter to nautical miles (NM). Arguments: `meter` - Value in meter (`scalar`). Returns: Value in `NM` (`float`). Raises: `ValueError` - Invalid `meter`.

### m2radians (distance, radius=6371008.771415, lat=0) |
Convert a distance to an angle along the equator or along the parallel at an other (geodetic) latitude. Arguments: `distance` - Distance (`meter`, same units as `radius`). `radius` - Mean earth radius, ellipsoid or datum (`meter`, an Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `lat` - Parallel latitude (`degrees90`, `str`). Returns: Angle (`radians`) or `INF` for near-polar `lat`. Raises: `RangeError` - Latitude `lat` outside valid range and pygeodesy.rangerrors set to `True`. `TypeError` - Invalid `radius`. `ValueError` - Invalid `distance`, `radius` or `lat`. See Also: Function m2degrees and radians2m.

### m2SM (meter) |
Convert meter to statute miles (SM). Arguments: `meter` - Value in meter (`scalar`). Returns: Value in `SM` (`float`). Raises: `ValueError` - Invalid `meter`.

### m2toise (meter) |
Convert meter to French toises. Arguments: `meter` - Value in meter (`scalar`). Returns: Value in `toises` (`float`). Raises: `ValueError` - Invalid `meter`. See Also: Function m2fathom.

### m2yard (meter) |
Convert meter to UK yards. Arguments: `meter` - Value in meter (`scalar`). Returns: Value in `yards` (`float`). Raises: `ValueError` - Invalid `meter`.

### NM2m (nm) |
Convert nautical miles to meter (m). Arguments: `nm` - Value in nautical miles (`scalar`). Returns: Value in meter (`float`). Raises: `ValueError` - Invalid `nm`.

### radians2m (rad, radius=6371008.771415, lat=0) |
Convert an angle to a distance along the equator or along the parallel at an other (geodetic) latitude. Arguments: `rad` - The angle (`radians`). `radius` - Mean earth radius, ellipsoid or datum (`meter`, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `lat` - Parallel latitude (`degrees90`, `str`). Returns: Distance (`meter`, same units as `radius` or equatorial and polar radii) or `0.0` for near-polar `lat`. Raises: `RangeError` - Latitude `lat` outside valid range and pygeodesy.rangerrors set to `True`. `TypeError` - Invalid `radius`. `ValueError` - Invalid `rad`, `radius` or `lat`. See Also: Function degrees2m and m2radians.

### radiansPI (deg) |
Convert and wrap degrees to radians [-PI..+PI]. Arguments: `deg` - Angle (`degrees`). Returns: Radians, wrapped (`radiansPI`)

### radiansPI2 (deg) |
Convert and wrap degrees to radians [0..+2PI). Arguments: `deg` - Angle (`degrees`). Returns: Radians, wrapped (`radiansPI2`)

### radiansPI_2 (deg) |
Convert and wrap degrees to radians [-3PI/2..+PI/2]. Arguments: `deg` - Angle (`degrees`). Returns: Radians, wrapped (`radiansPI_2`)

### SinCos2 (x) |
Get `sin` and `cos` of typed angle. Arguments: `x` - Angle (Degrees, Radians or scalar `radians`). Returns: 2-Tuple (`sin(x)`, `cos(x)`).

### sincos2 (rad) |
Return the `sine` and `cosine` of an angle in `radians`. Arguments: `rad` - Angle (`radians`). Returns: 2-Tuple (`sin(rad)`, `cos(rad)`). See Also: GeographicLib function sincosd and C++ sincosd.

### sincos2_ (*rads) |
Return the `sine` and `cosine` of angle(s) in `radians`. Arguments: `rads` - One or more angles (`radians`). Returns: Yield the `sin(rad)` and `cos(rad)` for each angle. See Also: function sincos2.

### sincos2d (deg, **adeg) |
Return the `sine` and `cosine` of an angle in `degrees`. Arguments: `deg` - Angle (`degrees`). `adeg` - Optional correction (`degrees`). Returns: 2-Tuple (`sin(deg_)`, `cos(deg_)`, `deg_ = deg + adeg`). See Also: GeographicLib function sincosd and C++ sincosd.

### sincos2d_ (*degs) |
Return the `sine` and `cosine` of angle(s) in `degrees`. Arguments: `degs` - One or more angles (`degrees`). Returns: Yield the `sin(deg)` and `cos(deg)` for each angle. See Also: Function sincos2d.

### sincostan3 (rad) |
Return the `sine`, `cosine` and `tangent` of an angle in `radians`. Arguments: `rad` - Angle (`radians`). Returns: 3-Tuple (`sin(rad)`, `cos(rad)`, `tan(rad)`). See Also: Function sincos2.

### SM2m (sm) |
Convert statute miles to meter (m). Arguments: `sm` - Value in statute miles (`scalar`). Returns: Value in meter (`float`). Raises: `ValueError` - Invalid `sm`.

### tan_2 (rad, **semi) |
Compute the tangent of half angle. Arguments: `rad` - Angle (`radians`). `semi` - Angle or edge name and index for semi-circular error. Returns: tan(rad / 2) (`float`). Raises: `ValueError` - If `rad` is semi-circular and `semi` is given.

### tand (deg, **error_kwds) |
Return the `tangent` of an angle in `degrees`. Arguments: `deg` - Angle (`degrees`). `error_kwds` - Error to raise (`ValueError`). Returns: `tan(deg)`. Raises: `ValueError` - If pygeodesy.isnear0`(cos(deg)`.

### tand_ (*degs, **error_kwds) |
Return the `tangent` of angle(s) in `degrees`. Arguments: `degs` - One or more angles (`degrees`). `error_kwds` - Error to raise (`ValueError`). Returns: Yield the `tan(deg)` for each angle. Raises: `ValueError` - See pygeodesy.tand.

### tanPI_2_2 (rad) |
Compute the tangent of half angle, 90 degrees rotated. Arguments: `rad` - Angle (`radians`). Returns: tan((rad + PI/2) / 2) (`float`).

### toise2m (toises) |
Convert French toises to meter. Arguments: `toises` - Value in toises (`scalar`). Returns: Value in `meter` (`float`). Raises: `ValueError` - Invalid `toises`. See Also: Function fathom2m.

### truncate (x, ndigits=None) |
Truncate to the given number of digits. Arguments: `x` - Value to truncate (`scalar`). `ndigits` - Number of digits (`int`), aka precision. Returns: Truncated `x` (`float`). See Also: Python function `round`.

### unroll180 (lon1, lon2, wrap=True) |
Unroll longitudinal delta and wrap longitude in degrees. Arguments: `lon1` - Start longitude (`degrees`). `lon2` - End longitude (`degrees`). `wrap` - If `True`, wrap and unroll to the (-180..+180] range (`bool`). Returns: 2-Tuple `(lon2-lon1, lon2)` unrolled (`degrees`, `degrees`). See Also: Capability `LONG_UNROLL` in GeographicLib.

### unrollPI (rad1, rad2, wrap=True) |
Unroll longitudinal delta and wrap longitude in radians. Arguments: `rad1` - Start longitude (`radians`). `rad2` - End longitude (`radians`). `wrap` - If `True`, wrap and unroll to the (-PI..+PI] range (`bool`). Returns: 2-Tuple `(rad2-rad1, rad2)` unrolled (`radians`, `radians`). See Also: Capability `LONG_UNROLL` in GeographicLib.

### wrap90 (deg) |
Wrap degrees to [-90..+90]. Arguments: `deg` - Angle (`degrees`). Returns: Degrees, wrapped (`degrees90`).

### wrap180 (deg) |
Wrap degrees to [-180..+180]. Arguments: `deg` - Angle (`degrees`). Returns: Degrees, wrapped (`degrees180`).

### wrap360 (deg) |
Wrap degrees to [0..+360). Arguments: `deg` - Angle (`degrees`). Returns: Degrees, wrapped (`degrees360`).

### wrapPI (rad) |
Wrap radians to [-PI..+PI]. Arguments: `rad` - Angle (`radians`). Returns: Radians, wrapped (`radiansPI`).

### wrapPI2 (rad) |
Wrap radians to [0..+2PI). Arguments: `rad` - Angle (`radians`). Returns: Radians, wrapped (`radiansPI2`).

### wrapPI_2 (rad) |
Wrap radians to [-PI/2..+PI/2]. Arguments: `rad` - Angle (`radians`). Returns: Radians, wrapped (`radiansPI_2`).

### wrap_normal (*normal) |
Define the operation for the keyword argument `wrap=True`, across pygeodesy: wrap, normalize or no-op. For backward compatibility, the default is wrap. Arguments: `normal` - If `True`, normalize lat- and longitude using normal or normal_, if `False`, wrap the lat- and longitude individually by wrap90 or wrapPI_2 respectively wrap180, wrapPI or if `None`, leave lat- and longitude unchanged. Do not supply any value to get the current setting. Returns: The previous wrap_normal setting (`bool` or `None`).

### yard2m (yards) |
Convert UK yards to meter. Arguments: `yards` - Value in yards (`scalar`). Returns: Value in `meter` (`float`). Raises: `ValueError` - Invalid `yards`.