# 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>}. @newfield example: Example, Examples ''' from pygeodesy.basics import EPS, R_M # PYCHOK PI_4 from pygeodesy.lazily import _ALL_LAZY from math import cos, degrees, pi as PI, radians, sin, tan # pow # all public contants, classes and functions __all__ = _ALL_LAZY.utily __version__ = '20.03.09' PI2 = PI * 2.0 #: Two PI, M{PI * 2} aka Tau (C{float}) # PYCHOK expected PI_2 = PI / 2.0 #: Half PI, M{PI / 2} (C{float}) PI_4 = PI / 4.0 #: Quarter PI, M{PI / 4} (C{float}) # <https://Numbers.Computation.Free.FR/Constants/Miscellaneous/digits.html> _1_90 = 1.0 / 90 # 0.011111111111111111111111111111111111111111111111 _2_PI = 2.0 / PI # 0.63661977236758134307553505349005744813783858296182 _iterNumpy2len = 1 # adjustable for testing purposes def degrees90(rad): '''Convert radians to degrees and wrap M{[-270..+90]}. @param rad: Angle (C{radians}). @return: Angle in degrees, wrapped (C{degrees90}). ''' return _wrap(degrees(rad), 90, 360) def degrees180(rad): '''Convert radians to degrees and wrap M{[-180..+180]}. @param rad: Angle (C{radians}). @return: Angle in degrees, wrapped (C{degrees180}). ''' return _wrap(degrees(rad), 180, 360) def degrees360(rad): '''Convert radians to degrees and wrap M{[0..+360)}. @param rad: Angle (C{radians}). @return: Angle in degrees, wrapped (C{degrees360}). ''' return _wrap(degrees(rad), 360, 360) def degrees2m(deg, radius=R_M, lat=0): '''Convert angle to distance along the equator or along a parallel at an other latitude. @param deg: Angle (C{degrees}). @keyword radius: Mean earth radius (C{meter}). @keyword lat: Parallel latitude (C{degrees90}). @return: Distance (C{meter}, same units as B{C{radius}}). @raise RangeError: Latitude B{C{lat}} outside valid range and L{rangerrors} set to C{True}. ''' m = radians(deg) * radius if lat: from pygeodesy.dms import clipDMS m *= cos(radians(clipDMS(lat, 90))) return m def false2f(value, name='value', false=True, Error=ValueError): '''Convert a false east-/northing to non-negative float. @param value: Value to convert (C{scalar}). @keyword name: Optional name of the value (C{str}). @keyword false: Optionally, value includes false origin (C{bool}). @keyword Error: Exception to raise (C{ValueError}). @return: The value (C{float}). @raise Error: Invalid or negative B{C{value}}. ''' try: f = float(value) if f < 0 and false: raise ValueError except (TypeError, ValueError): raise Error('%s invalid: %r' % (name, value)) return f def ft2m(feet, usurvey=False): '''Convert I{International} or I{US Survey} feet to meter. @param feet: Value in feet (C{scalar}). @keyword usurvery: Convert I{US Survey} feet (C{bool}), I{International} feet otherwise. @return: Value in C{meter} (C{float}). ''' # US Survey 1200./3937. == 0.3048006096012192 return feet * (0.3048006096012192 if usurvey else 0.3048) def isNumpy2(obj): '''Check for an B{C{Numpy2LatLon}} points wrapper. @param obj: The object (any C{type}). @return: C{True} if B{C{obj}} is an B{C{Numpy2LatLon}} instance, C{False} otherwise. ''' # isinstance(self, (Numpy2LatLon, ...)) return getattr(obj, 'isNumpy2', False) def isPoints2(obj): '''Check for an B{C{LatLon2psxy}} points wrapper. @param obj: The object (any C{type}). @return: C{True} if B{C{obj}} is an B{C{LatLon2psxy}} instance, C{False} otherwise. ''' # isinstance(self, (LatLon2psxy, ...)) return getattr(obj, 'isPoints2', False) def isTuple2(obj): '''Check for an B{C{Tuple2LatLon}} points wrapper. @param obj: The object (any). @return: C{True} if B{C{obj}} is an B{C{Tuple2LatLon}} instance, C{False} otherwise. ''' # isinstance(self, (Tuple2LatLon, ...)) return getattr(obj, 'isTuple2', False) def iterNumpy2(obj): '''Iterate over Numpy2 wrappers or other sequences exceeding the threshold. @param obj: Points array, list, sequence, set, etc. (any). @return: C{True} do, C{False} don't iterate. ''' try: return isNumpy2(obj) or len(obj) > _iterNumpy2len except TypeError: return False def iterNumpy2over(n=None): '''Get or set the L{iterNumpy2} threshold. @keyword n: Optional, new threshold (C{int}). @return: Previous threshold (C{int}). @raise ValueError: Invalid B{C{n}}. ''' global _iterNumpy2len p = _iterNumpy2len if n is not None: try: i = int(n) if i > 0: _iterNumpy2len = i else: raise ValueError except (TypeError, ValueError): raise ValueError('%s invalid: %r' % ('n', n)) return p def m2degrees(meter, radius=R_M): '''Convert distance to angle along equator. @param meter: Distance (C{meter}, same units as B{C{radius}}). @keyword radius: Mean earth radius (C{meter}). @return: Angle (C{degrees}). @raise ValueError: Invalid B{C{radius}}. ''' if radius < EPS: raise ValueError('%s invalid: %r' % ('radius', radius)) return degrees(float(meter) / radius) def m2ft(meter, usurvey=False): '''Convert meter to I{International} or I{US Survey} feet (C{ft}). @param meter: Value in meter (C{scalar}). @keyword usurvery: Convert to I{US Survey} feet (C{bool}), I{International} feet otherwise. @return: Value in C{feet} (C{float}). ''' # US Survey == 3937./1200. = 3.2808333333333333 return meter * (3.2808333333333333 if usurvey else 3.2808399) def m2km(meter): '''Convert meter to kilo meter (km). @param meter: Value in meter (C{scalar}). @return: Value in km (C{float}). ''' return meter * 1.0e-3 def m2NM(meter): '''Convert meter to nautical miles (NM). @param meter: Value in meter (C{scalar}). @return: Value in NM (C{float}). ''' return meter * 5.39956804e-4 # == * 1.0 / 1852.0 def m2SM(meter): '''Convert meter to statute miles (SM). @param meter: Value in meter (C{scalar}). @return: Value in SM (C{float}). ''' return meter * 6.21369949e-4 # XXX 6.213712e-4 == 1.0 / 1609.344 def radiansPI(deg): '''Convert and wrap degrees to radians M{[-PI..+PI]}. @param 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)}. @param 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]}. @param deg: Angle (C{degrees}). @return: Radians, wrapped (C{radiansPI_2}) ''' return _wrap(radians(deg), PI_2, PI2) def _sincos2(q, r): '''(INTERNAL) 2-tuple (C{sin(r), cos(r)}) in quadrant C{q}. ''' if r: s, c = sin(r), cos(r) t = s, c, -s, -c, s else: # XXX sin(-0.0)? t = 0.0, 1.0, -0.0, -1.0, 0.0 q &= 3 return t[q], t[q + 1] def sincos2(*rad): '''Return the C{sine} and C{cosine} of angle(s). @param rad: One or more angles (C{radians}). @return: The C{sin(rad)} and C{cos(rad)} for each angle. @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>}. ''' for r in rad: q = int(r * _2_PI) # int(math.floor) if r < 0: q -= 1 s, c = _sincos2(q, r - q * PI_2) # 0 <= r < PI_2 yield s yield c def sincos2d(*deg): '''Return the C{sine} and C{cosine} of angle(s) in C{degrees}. @param deg: One or more angles (C{degrees}). @return: The C{sin(rad)} and C{cos(rad)} for each angle. @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>}. ''' for d in deg: q = int(d * _1_90) # int(math.floor) if d < 0: q -= 1 s, c = _sincos2(q, radians(d - q * 90)) # 0 <= r < PI_2 yield s yield c def tan_2(rad): '''Compute the tangent of half angle. @param rad: Angle (C{radians}). @return: M{tan(rad / 2)} (C{float}). ''' return tan(rad * 0.5) def tanPI_2_2(rad): '''Compute the tangent of half angle, 90 degrees rotated. @param 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. @param lon1: Start longitude (C{degrees}). @param lon2: End longitude (C{degrees}). @keyword wrap: Wrap and unroll to the M{(-180..+180]} range (C{bool}). @return: 2-Tuple (delta B{C{lon2}}-B{lon1}, B{C{lon2}}) unrolled (C{degrees}, C{degrees}). @see: Capability B{C{LONG_UNROLL}} in U{GeographicLib <https://GeographicLib.SourceForge.io/html/python/interface.html#outmask>}. ''' d = lon2 - lon1 if wrap and abs(d) > 180: u = _wrap(d, 180, 360) if u != d: return u, lon1 + u return d, lon2 def unrollPI(rad1, rad2, wrap=True): '''Unroll longitudinal delta and wrap longitude in radians. @param rad1: Start longitude (C{radians}). @param rad2: End longitude (C{radians}). @keyword wrap: Wrap and unroll to the M{(-PI..+PI]} range (C{bool}). @return: 2-Tuple (delta B{C{rad2}}-B{rad1}, B{C{rad2}}) unrolled (C{radians}, C{radians}). @see: Capability B{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]}. @param angle: Angle (C{degrees} or C{radians}). @param wrap: Range (C{degrees} or C{radians}). @param modulo: Upper limit (360 C{degrees} or PI2 C{radians}). @return: The B{C{angle}}, wrapped (C{degrees} or C{radians}). ''' 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]}. @param deg: Angle (C{degrees}). @return: Degrees, wrapped (C{degrees90}). ''' return _wrap(deg, 90, 360) def wrap180(deg): '''Wrap degrees to M{[-180..+180]}. @param deg: Angle (C{degrees}). @return: Degrees, wrapped (C{degrees180}). ''' return _wrap(deg, 180, 360) def wrap360(deg): '''Wrap degrees to M{[0..+360)}. @param deg: Angle (C{degrees}). @return: Degrees, wrapped (C{degrees360}). ''' return _wrap(deg, 360, 360) def wrapPI(rad): '''Wrap radians to M{[-PI..+PI]}. @param rad: Angle (C{radians}). @return: Radians, wrapped (C{radiansPI}). ''' return _wrap(rad, PI, PI2) def wrapPI2(rad): '''Wrap radians to M{[0..+2PI)}. @param 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]}. @param rad: Angle (C{radians}). @return: Radians, wrapped (C{radiansPI_2}). ''' return _wrap(rad, PI_2, PI2) # **) MIT License # # Copyright (C) 2016-2020 -- 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.