# Coverage for pygeodesy/utily.py : 97%

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After I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, see U{Latitude/Longitude<https://www.Movable-Type.co.UK/scripts/latlong.html>} and U{Vector-based geodesy<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. ''' # make sure int/int division yields float quotient, see .basics from __future__ import division from pygeodesy.basics import copysign0, isint, isnear0 from pygeodesy.interns import EPS, EPS0, INF, PI, PI2, PI_2, R_M, \ _edge_, _radians_, _semi_circular_, _SPACE_, \ _0_0, _0_5, _1_0, _90_0, _180_0, _360_0, _400_0 from pygeodesy.lazily import _ALL_LAZY from pygeodesy.units import Feet, Float, Lam, Lam_, Meter from math import acos, asin, atan2, cos, degrees, radians, sin, tan # pow __all__ = _ALL_LAZY.utily __version__ = '21.08.30' # <https://Numbers.Computation.Free.FR/Constants/Miscellaneous/digits.html> _1__90 = _1_0 / _90_0 # 0.01111111111111111111111111111111111111111111111111 _2__PI = _1_0 / PI_2 # 0.63661977236758134307553505349005744813783858296182 # sqrt(2) + 1 <https://WikiPedia.org/wiki/Square_root_of_2> # _1sqrt2 = 2.41421356237309504880 # _16887_24209_69807_85696_71875_37694_80731_76679_73799 def acos1(x): '''Return C{math.acos(max(-1, min(1, B{x})))}. ''' return acos(x) if abs(x) < _1_0 else (PI if x < 0 else _0_0) def acre2ha(acres): '''Convert acres to hectare. @arg acres: Value in acres (C{scalar}). @return: Value in C{hectare} (C{float}). @raise ValueError: Invalid B{C{acres}}. ''' # 0.40468564224 == acre2m2(1) / 10_000 return Float(acres) * 0.40468564224 def acre2m2(acres): '''Convert acres to I{square} meter. @arg acres: Value in acres (C{scalar}). @return: Value in C{meter^2} (C{float}). @raise ValueError: Invalid B{C{acres}}. ''' # 4046.8564224 == chain2m(1) * furlong2m(1) return Float(acres) * 4046.8564224 def asin1(x): '''Return C{math.asin(max(-1, min(1, B{x})))}. ''' return asin(x) if abs(x) < _1_0 else (-PI_2 if x < 0 else PI_2) # -PI_2, not PI3_2! def atand(y_x): '''Return C{atan(B{y_x})} angle in C{degrees}. @see: Function L{atan2d}. ''' return atan2d(y_x, _1_0) def atan2b(y, x): '''Return C{atan2(B{y}, B{x})} in degrees M{[0..+360]}. @see: Function L{atan2d}. ''' d = atan2d(y, x) if d < 0: d += _360_0 return d def atan2d(y, x, reverse=False): '''Return C{atan2(B{y}, B{x})} in degrees M{[-180..+180]}, optionally reversed (by 180 degrees for C{azi2}). @see: I{Karney}'s C++ function U{Math.atan2d <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Math.html>}. ''' if abs(y) > abs(x) > 0: if y < 0: # q = 3 d = degrees(atan2(x, -y)) - _90_0 else: # q = 2 d = _90_0 - degrees(atan2(x, y)) elif x < 0: # q = 1 d = copysign0(_180_0, y) - degrees(atan2(y, -x)) elif x > 0: # q = 0 d = degrees(atan2(y, x)) if y else _0_0 else: # x == 0 d = -_90_0 if y < 0 else (_90_0 if y > 0 else _0_0) if reverse: d += _180_0 if d < 0 else -_180_0 return d def chain2m(chains): '''Convert I{UK} chains to meter. @arg chains: Value in chains (C{scalar}). @return: Value in C{meter} (C{float}). @raise ValueError: Invalid B{C{chains}}. ''' # 20.1168 = 22 * yard2m(1) return Float(chains) * 20.1168 def circle4(earth, lat): '''Get the equatorial or a parallel I{circle of latitude}. @arg earth: The earth radius, ellipsoid or datum (C{meter}, L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}). @arg lat: Geodetic latitude (C{degrees90}, C{str}). @return: A L{Circle4Tuple}C{(radius, height, lat, beta)} instance. @raise RangeError: Latitude B{C{lat}} outside valid range and L{rangerrors} set to C{True}. @raise TypeError: Invalid B{C{earth}}. @raise ValueError: B{C{earth}} or B{C{lat}}. ''' from pygeodesy.datums import _spherical_datum E = _spherical_datum(earth).ellipsoid return E.circle4(lat) def cotd(deg, **error_kwds): '''Return the C{cotangent} of an angle in C{degrees}. @arg deg: Angle (C{degrees}). @kwarg error_kwds: Error to raise (C{ValueError}). @return: C{cot(B{deg})}. @raise ValueError: L{pygeodesy.isnear0}C{(sin(B{deg})}. ''' s, c = sincos2d(deg) if isnear0(s): from pygeodesy.errors import _ValueError, _xkwds raise _ValueError(**_xkwds(error_kwds, cotd=deg)) return c / s def cotd_(*degs, **error_kwds): '''Return the C{cotangent} of angle(s) in C{degrees}. @arg degs: One or more angles (C{degrees}). @kwarg error_kwds: Error to raise (C{ValueError}). @return: Yield the C{cot(B{deg})} for each angle. @raise ValueError: See L{pygeodesy.cotd}. ''' for d in degs: yield cotd(d, **error_kwds) def degrees90(rad): '''Convert radians to degrees and wrap M{[-270..+90]}. @arg rad: Angle (C{radians}). @return: Angle, wrapped (C{degrees90}). ''' return _wrap(degrees(rad), _90_0, _360_0) def degrees180(rad): '''Convert radians to degrees and wrap M{[-180..+180]}. @arg rad: Angle (C{radians}). @return: Angle, wrapped (C{degrees180}). ''' return _wrap(degrees(rad), _180_0, _360_0) def degrees360(rad): '''Convert radians to degrees and wrap M{[0..+360)}. @arg rad: Angle (C{radians}). @return: Angle, wrapped (C{degrees360}). ''' return _wrap(degrees(rad), _360_0, _360_0) def degrees2grades(deg): '''Convert degrees to I{grades} (aka I{gradians} or I{gons}). @arg deg: Angle (C{degrees}). @return: Angle (C{grades}). ''' return deg * _400_0 / _360_0 def degrees2m(deg, radius=R_M, lat=0): '''Convert an angle to a distance along the equator or along the parallel at an other (geodetic) latitude. @arg deg: The angle (C{degrees}). @kwarg radius: Mean earth radius, ellipsoid or datum (C{meter}, L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}). @kwarg lat: Parallel latitude (C{degrees90}, C{str}). @return: Distance (C{meter}, same units as B{C{radius}} or ellipsoidal and polar radii) or C{0} for near-polar B{C{lat}}. @raise RangeError: Latitude B{C{lat}} outside valid range and L{rangerrors} set to C{True}. @raise TypeError: Invalid B{C{radius}}. @raise ValueError: Invalid B{C{deg}}, B{C{radius}} or B{C{lat}}. @see: Function L{radians2m} and L{m2degrees}. ''' return radians2m(Lam_(deg=deg, clip=0), radius=radius, lat=lat) def fathom2m(fathoms): '''Convert I{UK} fathom to meter. @arg fathoms: Value in fathoms (C{scalar}). @return: Value in C{meter} (C{float}). @raise ValueError: Invalid B{C{fathoms}}. ''' # 1.8288 == 2 * yard2m(1) return Float(fathoms) * 1.8288 def ft2m(feet, usurvey=False): '''Convert I{International} or I{US Survey} feet to meter. @arg feet: Value in feet (C{scalar}). @kwarg usurvey: Convert I{US Survey} feet (C{bool}), I{International} feet otherwise. @return: Value in C{meter} (C{float}). @raise ValueError: Invalid B{C{feet}}. ''' # US Survey 1200 / 3937 == 0.3048006096012192 # Int'l 0.3048 == 254 * 12 / 10_000 return Feet(feet) * (0.3048006096 if usurvey else 0.3048) def furlong2m(furlongs): '''Convert a I{UK} furlong to meter. @arg furlongs: Value in furlongs (C{scalar}). @return: Value in C{meter} (C{float}). @raise ValueError: Invalid B{C{furlongs}}. ''' # 201.168 = 220 * yard2m(1) return Float(furlongs) * 201.168 def grades(rad): '''Convert radians to I{grades} (aka I{gradians} or I{gons}). @arg rad: Angle (C{radians}). @return: Angle (C{grades}). ''' return rad * _400_0 / PI2 def grades400(rad): '''Convert radians to I{grades} (aka I{gradians} or I{gons}) and wrap M{[0..+400)}. @arg rad: Angle (C{radians}). @return: Angle, wrapped (C{grades}). ''' return _wrap(grades(rad), _400_0, _400_0) def grades2degrees(gon): '''Convert I{grades} (aka I{gradians} or I{gons}) to C{degrees}. @arg gon: Angle (C{grades}). @return: Angle (C{degrees}). ''' return gon * _360_0 / _400_0 def grades2radians(gon): '''Convert I{grades} (aka I{gradians} or I{gons}) to C{radians}. @arg gon: Angle (C{grades}). @return: Angle (C{radians}). ''' return gon * PI2 / _400_0 def m2degrees(distance, radius=R_M, lat=0): '''Convert a distance to an angle along the equator or along the parallel at an other (geodetic) latitude. @arg distance: Distance (C{meter}, same units as B{C{radius}}). @kwarg radius: Mean earth radius, ellipsoid or datum (C{meter}, an L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}). @kwarg lat: Parallel latitude (C{degrees90}, C{str}). @return: Angle (C{degrees}) or C{INF} for near-polar B{C{lat}}. @raise RangeError: Latitude B{C{lat}} outside valid range and L{rangerrors} set to C{True}. @raise TypeError: Invalid B{C{radius}}. @raise ValueError: Invalid B{C{distance}}, B{C{radius}} or B{C{lat}}. @see: Function L{m2radians} and L{degrees2m}. ''' return degrees(m2radians(distance, radius=radius, lat=lat)) def m2ft(meter, usurvey=False): '''Convert meter to I{International} or I{US Survey} feet (C{ft}). @arg meter: Value in meter (C{scalar}). @kwarg usurvey: Convert to I{US Survey} feet (C{bool}), I{International} feet otherwise. @return: Value in C{feet} (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' # US Survey == 3937 / 1200 == 3.2808333333333333 # Int'l 10_000 / (254 * 12) == 3.2808398950131235 return Meter(meter) * (3.280833333 if usurvey else 3.280839895) def m2km(meter): '''Convert meter to kilo meter (km). @arg meter: Value in meter (C{scalar}). @return: Value in km (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' return Meter(meter) * 1.0e-3 def m2NM(meter): '''Convert meter to nautical miles (NM). @arg meter: Value in meter (C{scalar}). @return: Value in NM (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' return Meter(meter) * 5.39956804e-4 # == * _1_0 / 1852 def m2radians(distance, radius=R_M, lat=0): '''Convert a distance to an angle along the equator or along the parallel at an other (geodetic) latitude. @arg distance: Distance (C{meter}, same units as B{C{radius}}). @kwarg radius: Mean earth radius, ellipsoid or datum (C{meter}, an L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}). @kwarg lat: Parallel latitude (C{degrees90}, C{str}). @return: Angle (C{radians}) or C{INF} for near-polar B{C{lat}}. @raise RangeError: Latitude B{C{lat}} outside valid range and L{rangerrors} set to C{True}. @raise TypeError: Invalid B{C{radius}}. @raise ValueError: Invalid B{C{distance}}, B{C{radius}} or B{C{lat}}. @see: Function L{m2degrees} and L{radians2m}. ''' m = circle4(radius, lat).radius return INF if m < EPS0 else (Float(distance) / m) def m2SM(meter): '''Convert meter to statute miles (SM). @arg meter: Value in meter (C{scalar}). @return: Value in SM (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' return Meter(meter) * 6.21369949e-4 # == _1_0 / 1609.344 def m2yard(meter): '''Convert meter to I{UK} yards. @arg meter: Value in meter (C{scalar}). @return: Value in yards (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' # 1.0936132983377078 == 10_000 / (254 * 12 * 3) return Meter(meter) * 1.09361329833771 def radiansPI(deg): '''Convert and wrap degrees to radians M{[-PI..+PI]}. @arg deg: Angle (C{degrees}). @return: Radians, wrapped (C{radiansPI}) ''' return _wrap(radians(deg), PI, PI2) def radiansPI2(deg): '''Convert and wrap degrees to radians M{[0..+2PI)}. @arg deg: Angle (C{degrees}). @return: Radians, wrapped (C{radiansPI2}) ''' return _wrap(radians(deg), PI2, PI2) def radiansPI_2(deg): '''Convert and wrap degrees to radians M{[-3PI/2..+PI/2]}. @arg deg: Angle (C{degrees}). @return: Radians, wrapped (C{radiansPI_2}) ''' return _wrap(radians(deg), PI_2, PI2) def radians2m(rad, radius=R_M, lat=0): '''Convert an angle to a distance along the equator or along the parallel at an other (geodetic) latitude. @arg rad: The angle (C{radians}). @kwarg radius: Mean earth radius, ellipsoid or datum (C{meter}, L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}). @kwarg lat: Parallel latitude (C{degrees90}, C{str}). @return: Distance (C{meter}, same units as B{C{radius}} or ellipsoidal and polar radii) or C{0} for near-polar B{C{lat}}. @raise RangeError: Latitude B{C{lat}} outside valid range and L{rangerrors} set to C{True}. @raise TypeError: Invalid B{C{radius}}. @raise ValueError: Invalid B{C{rad}}, B{C{radius}} or B{C{lat}}. @see: Function L{degrees2m} and L{m2radians}. ''' m = circle4(radius, lat).radius return _0_0 if m < EPS0 else (Lam(rad=rad, clip=0) * m) def _sincos2(q, r): '''(INTERNAL) 2-tuple (C{sin(r), cos(r)}) in quadrant M{0 <= q <= 3}. ''' if r < EPS: # XXX EPS0 s, c = _0_0, _1_0 elif r < PI_2: s, c = sin(r), cos(r) else: # r == PI_2 s, c = _1_0, _0_0 t = s, c, -s, -c, s # q &= 3 return t[q], t[q + 1] def sincos2(rad): '''Return the C{sine} and C{cosine} of an angle in C{radians}. @arg rad: Angle (C{radians}). @return: 2-Tuple (C{sin(B{rad})}, C{cos(B{rad})}). @see: U{GeographicLib<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1Math.html#sincosd>} function U{sincosd <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ python/geographiclib/geomath.py#l155>} and C++ U{sincosd <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ include/GeographicLib/Math.hpp#l558>}. ''' q = int(rad * _2__PI) # int(math.floor) if rad < 0: q -= 1 return _sincos2(q & 3, rad - q * PI_2) def sincos2_(*rads): '''Return the C{sine} and C{cosine} of angle(s) in {Cradians}. @arg rads: One or more angles (C{radians}). @return: Yield the C{sin(B{rad})} and C{cos(B{rad})} for each angle. @see: function L{sincos2}. ''' for r in rads: s, c = sincos2(r) yield s yield c def sincos2d(deg): '''Return the C{sine} and C{cosine} of an angle in C{degrees}. @arg deg: Angle (C{degrees}). @return: 2-Tuple (C{sin(B{deg})}, C{cos(B{deg})}). @see: U{GeographicLib<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1Math.html#sincosd>} function U{sincosd <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ python/geographiclib/geomath.py#l155>} and C++ U{sincosd <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ include/GeographicLib/Math.hpp#l558>}. ''' q = int(deg * _1__90) # int(math.floor) if deg < 0: q -= 1 return _sincos2(q & 3, radians(deg - q * _90_0)) def sincos2d_(*degs): '''Return the C{sine} and C{cosine} of angle(s) in C{degrees}. @arg degs: One or more angles (C{degrees}). @return: Yield the C{sin(B{deg})} and C{cos(B{deg})} for each angle. @see: Function L{sincos2d}. ''' for d in degs: s, c = sincos2d(d) yield s yield c def tan_2(rad, **semi): # edge=1 '''Compute the tangent of half angle. @arg rad: Angle (C{radians}). @kwarg semi: Angle or edge name and index for semi-circular error. @return: M{tan(rad / 2)} (C{float}). @raise ValueError: If B{C{rad}} is semi-circular and B{C{semi}} is given. ''' # .formy.excessKarney_, .sphericalTrigonometry.areaOf if semi and isnear0(abs(rad) - PI): for n, v in semi.items(): break if isint(v): from pygeodesy.streprs import Fmt n = _SPACE_(Fmt.SQUARE(**semi), _edge_) else: n = _SPACE_(n, _radians_) from pygeodesy.errors import _ValueError raise _ValueError(n, rad, txt=_semi_circular_) return tan(rad * _0_5) def tand(deg, **error_kwds): '''Return the C{tangent} of an angle in C{degrees}. @arg deg: Angle (C{degrees}). @kwarg error_kwds: Error to raise (C{ValueError}). @return: C{tan(B{deg})}. @raise ValueError: If L{pygeodesy.isnear0}C{(cos(B{deg})}. ''' s, c = sincos2d(deg) if isnear0(c): from pygeodesy.errors import _ValueError, _xkwds raise _ValueError(**_xkwds(error_kwds, tand=deg)) return s / c def tand_(*degs, **error_kwds): '''Return the C{tangent} of angle(s) in C{degrees}. @arg degs: One or more angles (C{degrees}). @kwarg error_kwds: Error to raise (C{ValueError}). @return: Yield the C{tan(B{deg})} for each angle. @raise ValueError: See L{pygeodesy.tand}. ''' for d in degs: yield tand(d, **error_kwds) def tanPI_2_2(rad): '''Compute the tangent of half angle, 90 degrees rotated. @arg rad: Angle (C{radians}). @return: M{tan((rad + PI/2) / 2)} (C{float}). ''' return tan((rad + PI_2) * _0_5) def unroll180(lon1, lon2, wrap=True): '''Unroll longitudinal delta and wrap longitude in degrees. @arg lon1: Start longitude (C{degrees}). @arg lon2: End longitude (C{degrees}). @kwarg wrap: Wrap and unroll to the M{(-180..+180]} range (C{bool}). @return: 2-Tuple C{(B{lon2}-B{lon1}, B{lon2})} unrolled (C{degrees}, C{degrees}). @see: Capability C{LONG_UNROLL} in U{GeographicLib <https://GeographicLib.SourceForge.io/html/python/interface.html#outmask>}. ''' d = lon2 - lon1 if wrap and abs(d) > _180_0: u = _wrap(d, _180_0, _360_0) if u != d: return u, lon1 + u return d, lon2 def unrollPI(rad1, rad2, wrap=True): '''Unroll longitudinal delta and wrap longitude in radians. @arg rad1: Start longitude (C{radians}). @arg rad2: End longitude (C{radians}). @kwarg wrap: Wrap and unroll to the M{(-PI..+PI]} range (C{bool}). @return: 2-Tuple C{(B{rad2}-B{rad1}, B{rad2})} unrolled (C{radians}, C{radians}). @see: Capability C{LONG_UNROLL} in U{GeographicLib <https://GeographicLib.SourceForge.io/html/python/interface.html#outmask>}. ''' r = rad2 - rad1 if wrap and abs(r) > PI: u = _wrap(r, PI, PI2) if u != r: return u, rad1 + u return r, rad2 def _wrap(angle, wrap, modulo): '''(INTERNAL) Angle wrapper M{((wrap-modulo)..+wrap]}. @arg angle: Angle (C{degrees}, C{radians} or C{grades}). @arg wrap: Range (C{degrees}, C{radians} or C{grades}). @arg modulo: Upper limit (360 C{degrees}, PI2 C{radians} or 400 C{grades}). @return: The B{C{angle}}, wrapped (C{degrees}, C{radians} or C{grades}). ''' angle = float(angle) if not wrap > angle >= (wrap - modulo): # math.fmod(-1.5, 3.14) == -1.5, but -1.5 % 3.14 == 1.64 # math.fmod(-1.5, 360) == -1.5, but -1.5 % 360 == 358.5 angle %= modulo if angle > wrap: angle -= modulo return angle def wrap90(deg): '''Wrap degrees to M{[-270..+90]}. @arg deg: Angle (C{degrees}). @return: Degrees, wrapped (C{degrees90}). ''' return _wrap(deg, _90_0, _360_0) def wrap180(deg): '''Wrap degrees to M{[-180..+180]}. @arg deg: Angle (C{degrees}). @return: Degrees, wrapped (C{degrees180}). ''' return _wrap(deg, _180_0, _360_0) def wrap360(deg): '''Wrap degrees to M{[0..+360)}. @arg deg: Angle (C{degrees}). @return: Degrees, wrapped (C{degrees360}). ''' return _wrap(deg, _360_0, _360_0) def wrapPI(rad): '''Wrap radians to M{[-PI..+PI]}. @arg rad: Angle (C{radians}). @return: Radians, wrapped (C{radiansPI}). ''' return _wrap(rad, PI, PI2) def wrapPI2(rad): '''Wrap radians to M{[0..+2PI)}. @arg rad: Angle (C{radians}). @return: Radians, wrapped (C{radiansPI2}). ''' return _wrap(rad, PI2, PI2) def wrapPI_2(rad): '''Wrap radians to M{[-3PI/2..+PI/2]}. @arg rad: Angle (C{radians}). @return: Radians, wrapped (C{radiansPI_2}). ''' return _wrap(rad, PI_2, PI2) def yard2m(yards): '''Convert I{UK} yards to meter. @arg yards: Value in yards (C{scalar}). @return: Value in C{meter} (C{float}). @raise ValueError: Invalid B{C{yards}}. ''' # 0.9144 == 254 * 12 * 3 / 10_000 == 3 * ft2m(1) Int'l return Float(yards) * 0.9144 # **) MIT License # # Copyright (C) 2016-2021 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.