# Coverage for pygeodesy/formy.py : 93%

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''' return LatLon2Tuple(-wrap90(lat), wrap180(lon + 180)) def bearing(lat1, lon1, lat2, lon2, **options): '''Compute the initial or final bearing (forward or reverse azimuth) between a (spherical) start and end point. @param lat1: Start latitude (C{degrees}). @param lon1: Start longitude (C{degrees}). @param lat2: End latitude (C{degrees}). @param lon2: End longitude (C{degrees}). @keyword options: Optional keyword arguments for function L{bearing_}. @return: Initial or final bearing (compass C{degrees360}) or zero if start and end point coincide. ''' ab4 = map1(radians, lat1, lon1, lat2, lon2) return degrees(bearing_(*ab4, **options)) def bearing_(a1, b1, a2, b2, final=False, wrap=False): '''Compute the initial or final bearing (forward or reverse azimuth) between a (spherical) start and end point. @param a1: Start latitude (C{radians}). @param b1: Start longitude (C{radians}). @param a2: End latitude (C{radians}). @param b2: End longitude (C{radians}). @keyword final: Return final bearing if C{True}, initial otherwise (C{bool}). @keyword wrap: Wrap and L{unrollPI} longitudes (C{bool}). @return: Initial or final bearing (compass C{radiansPI2}) or zero if start and end point coincide. ''' if final: a1, b1, a2, b2 = a2, b2, a1, b1 r = PI + PI2 else: r = PI2 db, _ = unrollPI(b1, b2, wrap=wrap) sa1, ca1, sa2, ca2, sdb, cdb = sincos2(a1, a2, db) # see <https://MathForum.org/library/drmath/view/55417.html> x = ca1 * sa2 - sa1 * ca2 * cdb y = sdb * ca2 return (atan2(y, x) + r) % PI2 # wrapPI2 def compassAngle(lat1, lon1, lat2, lon2, adjust=True, wrap=False): '''Return the angle from North for the direction vector M{(lon2 - lon1, lat2 - lat1)} between two points. Suitable only for short, non-near-polar vectors up to a few hundred Km or Miles. Use function L{bearing} for longer vectors. @param lat1: From latitude (C{degrees}). @param lon1: From longitude (C{degrees}). @param lat2: To latitude (C{degrees}). @param lon2: To longitude (C{degrees}). @keyword adjust: Adjust the longitudinal delta by the cosine of the mean latitude (C{bool}). @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @return: Compass angle from North (C{degrees360}). @note: Courtesy Martin Schultz. @see: U{Local, flat earth approximation <https://www.EdWilliams.org/avform.htm#flat>}. ''' d_lon, _ = unroll180(lon1, lon2, wrap=wrap) if adjust: # scale delta lon d_lon *= _scaled(lat1, lat2) return degrees360(atan2(d_lon, lat2 - lat1)) def equirectangular(lat1, lon1, lat2, lon2, radius=R_M, **options): '''Compute the distance between two points using the U{Equirectangular Approximation / Projection <https://www.Movable-Type.co.UK/scripts/latlong.html>}. @param lat1: Start latitude (C{degrees}). @param lon1: Start longitude (C{degrees}). @param lat2: End latitude (C{degrees}). @param lon2: End longitude (C{degrees}). @keyword radius: Mean earth radius (C{meter}). @keyword options: Optional keyword arguments for function L{equirectangular_}. @return: Distance (C{meter}, same units as B{C{radius}}). @see: Function L{equirectangular_} for more details, the available B{C{options}}, errors, restrictions and other, approximate or accurate distance functions. ''' _, dy, dx, _ = equirectangular_(lat1, lon1, lat2, lon2, **options) # PYCHOK Distance4Tuple return degrees2m(hypot(dx, dy), radius=radius) def equirectangular_(lat1, lon1, lat2, lon2, adjust=True, limit=45, wrap=False): '''Compute the distance between two points using the U{Equirectangular Approximation / Projection <https://www.Movable-Type.co.UK/scripts/latlong.html>}. This approximation is valid for short distance of several hundred Km or Miles, see the B{C{limit}} keyword argument and the L{LimitError}. @param lat1: Start latitude (C{degrees}). @param lon1: Start longitude (C{degrees}). @param lat2: End latitude (C{degrees}). @param lon2: End longitude (C{degrees}). @keyword adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @keyword limit: Optional limit for lat- and longitudinal deltas (C{degrees}) or C{None} or C{0} for unlimited. @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @return: A L{Distance4Tuple}C{(distance2, delta_lat, delta_lon, unroll_lon2)}. @raise LimitError: If the lat- and/or longitudinal delta exceeds the B{C{-limit..+limit}} range and L{limiterrors} set to C{True}. @see: U{Local, flat earth approximation <https://www.EdWilliams.org/avform.htm#flat>}, functions L{equirectangular}, L{euclidean}, L{haversine} and L{vincentys} and methods L{Ellipsoid.distance2}, C{LatLon.distanceTo*} and C{LatLon.equirectangularTo}. ''' d_lat = lat2 - lat1 d_lon, ulon2 = unroll180(lon1, lon2, wrap=wrap) if limit and _limiterrors \ and max(abs(d_lat), abs(d_lon)) > limit > 0: t = fStr((lat1, lon1, lat2, lon2), prec=4) raise LimitError('%s(%s, limit=%s) delta exceeds limit' % ('equirectangular_', t, fStr(limit, prec=2))) if adjust: # scale delta lon d_lon *= _scaled(lat1, lat2) d2 = hypot2(d_lat, d_lon) # degrees squared! return Distance4Tuple(d2, d_lat, d_lon, ulon2 - lon2) def euclidean(lat1, lon1, lat2, lon2, radius=R_M, adjust=True, wrap=False): '''Approximate the C{Euclidian} distance between two (spherical) points. @param lat1: Start latitude (C{degrees}). @param lon1: Start longitude (C{degrees}). @param lat2: End latitude (C{degrees}). @param lon2: End longitude (C{degrees}). @keyword radius: Mean earth radius (C{meter}). @keyword adjust: Adjust the longitudinal delta by the cosine of the mean latitude (C{bool}). @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @return: Distance (C{meter}, same units as B{C{radius}}). @see: U{Distance between two (spherical) points <https://www.EdWilliams.org/avform.htm#Dist>}, functions L{equirectangular}, L{haversine} and L{vincentys} and methods L{Ellipsoid.distance2}, C{LatLon.distanceTo*} and C{LatLon.equirectangularTo}. ''' r = float(radius) if r: d, _ = unroll180(lon1, lon2, wrap=wrap) r *= euclidean_(radians(lat2), radians(lat1), radians(d), adjust=adjust) return r def euclidean_(a2, a1, b21, adjust=True): '''Approximate the I{angular} C{Euclidean} distance between two (spherical) points. @param a2: End latitude (C{radians}). @param a1: Start latitude (C{radians}). @param b21: Longitudinal delta, M{end-start} (C{radians}). @keyword adjust: Adjust the longitudinal delta by the cosine of the mean latitude (C{bool}). @return: Angular distance (C{radians}). @see: Functions L{euclidean}, L{equirectangular_}, L{haversine_} and L{vincentys_}. ''' a, b = abs(a2 - a1), abs(b21) if adjust: b *= _scaler(a2, a1) if a < b: a, b = b, a return a + b * 0.5 # 0.4142135623731 def haversine(lat1, lon1, lat2, lon2, radius=R_M, wrap=False): '''Compute the distance between two (spherical) points using the U{Haversine<https://www.Movable-Type.co.UK/scripts/latlong.html>} formula. @param lat1: Start latitude (C{degrees}). @param lon1: Start longitude (C{degrees}). @param lat2: End latitude (C{degrees}). @param lon2: End longitude (C{degrees}). @keyword radius: Mean earth radius (C{meter}). @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @return: Distance (C{meter}, same units as B{C{radius}}). @see: U{Distance between two (spherical) points <https://www.EdWilliams.org/avform.htm#Dist>}, functions L{equirectangular}, L{euclidean} and L{vincentys} and methods L{Ellipsoid.distance2}, C{LatLon.distanceTo*} and C{LatLon.equirectangularTo}. @note: See note under L{vincentys_}. ''' r = float(radius) if r: d, _ = unroll180(lon1, lon2, wrap=wrap) r *= haversine_(radians(lat2), radians(lat1), radians(d)) return r def haversine_(a2, a1, b21): '''Compute the I{angular} distance between two (spherical) points using the U{Haversine<https://www.Movable-Type.co.UK/scripts/latlong.html>} formula. @param a2: End latitude (C{radians}). @param a1: Start latitude (C{radians}). @param b21: Longitudinal delta, M{end-start} (C{radians}). @return: Angular distance (C{radians}). @see: Functions L{haversine}, L{equirectangular_}, L{euclidean_} and L{vincentys_}. @note: See note under L{vincentys_}. ''' def _hsin(rad): return sin(rad * 0.5)**2 h = _hsin(a2 - a1) + cos(a1) * cos(a2) * _hsin(b21) # haversine try: r = atan2(sqrt(h), sqrt(1 - h)) * 2 # == asin(sqrt(h)) * 2 except ValueError: r = 0 if h < 0.5 else PI return r def heightOf(angle, distance, radius=R_M): '''Determine the height above the (spherical) earth after traveling along a straight line at a given tilt. @param angle: Tilt angle above horizontal (C{degrees}). @param distance: Distance along the line (C{meter} or same units as B{C{radius}}). @keyword radius: Optional mean earth radius (C{meter}). @return: Height (C{meter}, same units as B{C{distance}} and B{C{radius}}). @raise ValueError: Invalid B{C{angle}}, B{C{distance}} or B{C{radius}}. @see: U{MultiDop geog_lib.GeogBeamHt<https://GitHub.com/NASA/MultiDop>} (U{Shapiro et al. 2009, JTECH <https://Journals.AMetSoc.org/doi/abs/10.1175/2009JTECHA1256.1>} and U{Potvin et al. 2012, JTECH <https://Journals.AMetSoc.org/doi/abs/10.1175/JTECH-D-11-00019.1>}). ''' d, r = distance, radius if d > r: d, r = r, d if d > EPS: d = d / float(r) s = sin(radians(angle)) s = fsum_(1, 2 * s * d, d**2) if s > 0: return r * sqrt(s) - float(radius) raise ValueError('%s%r' % (heightOf.__name__, (angle, distance, radius))) def horizon(height, radius=R_M, refraction=False): '''Determine the distance to the horizon from a given altitude above the (spherical) earth. @param height: Altitude (C{meter} or same units as B{C{radius}}). @keyword radius: Optional mean earth radius (C{meter}). @keyword refraction: Consider atmospheric refraction (C{bool}). @return: Distance (C{meter}, same units as B{C{height}} and B{C{radius}}). @raise ValueError: Invalid B{C{height}} or B{C{radius}}. @see: U{Distance to horizon<https://www.EdWilliams.org/avform.htm#Horizon>}. ''' if min(height, radius) < 0: raise ValueError('%s%r' % (horizon.__name__, (height, radius))) if refraction: d2 = 2.415750694528 * height * radius # 2.0 / 0.8279 else: d2 = height * fsum_(radius, radius, height) return sqrt(d2) def isantipode(lat1, lon1, lat2, lon2, eps=EPS): '''Check whether two points are antipodal, on diametrically opposite sides of the earth. @param lat1: Latitude of one point (C{degrees}). @param lon1: Longitude of one point (C{degrees}). @param lat2: Latitude of the other point (C{degrees}). @param lon2: Longitude of the other point (C{degrees}). @keyword eps: Tolerance for near-equality (C{degrees}). @return: C{True} if points are antipodal within the B{C{eps}} tolerance, C{False} otherwise. @see: U{Geosphere<https://CRAN.R-Project.org/web/packages/geosphere/geosphere.pdf>}. ''' return abs(wrap90(lat1) + wrap90(lat2)) < eps and \ abs(abs(wrap180(lon1) - wrap180(lon2)) % 360 - 180) < eps def points2(points, closed=True, base=None, Error=ValueError): '''Check a path or polygon represented by points. @param points: The path or polygon points (C{LatLon}[]) @keyword closed: Optionally, consider the polygon closed, ignoring any duplicate or closing final B{C{points}} (C{bool}). @keyword base: Optionally, check all B{C{points}} against this base class, if C{None} don't check. @keyword Error: Exception to raise (C{ValueError}). @return: A L{Points2Tuple}C{(number, points)} with the number of points and the points C{list} or C{tuple}. @raise TypeError: Some B{C{points}} are not B{C{base}}. @raise Error: Insufficient number of B{C{points}}. ''' n, points = len2(points) if closed: # remove duplicate or closing final points while n > 1 and (points[n-1] == points[0] or points[n-1] == points[n-2]): n -= 1 # XXX following line is unneeded if points # are always indexed as ... i in range(n) points = points[:n] # XXX numpy.array slice is a view! if n < (3 if closed else 1): raise Error('too few %s: %s' % ('points', n)) if base and not (isNumpy2(points) or isTuple2(points)): for i in range(n): base.others(points[i], name='%s[%s]' % ('points', i)) return Points2Tuple(n, points) def vincentys(lat1, lon1, lat2, lon2, radius=R_M, wrap=False): '''Compute the distance between two (spherical) points using U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>} spherical formula. @param lat1: Start latitude (C{degrees}). @param lon1: Start longitude (C{degrees}). @param lat2: End latitude (C{degrees}). @param lon2: End longitude (C{degrees}). @keyword radius: Mean earth radius (C{meter}). @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @return: Distance (C{meter}, same units as B{C{radius}}). @see: Functions L{equirectangular}, L{euclidean} and L{haversine} and methods L{Ellipsoid.distance2}, C{LatLon.distanceTo*} and C{LatLon.equirectangularTo}. @note: See note under L{vincentys_}. ''' d, _ = unroll180(lon1, lon2, wrap=wrap) r = vincentys_(radians(lat2), radians(lat1), radians(d)) return r * float(radius) def vincentys_(a2, a1, b21): '''Compute the I{angular} distance between two (spherical) points using U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>} spherical formula. @param a2: End latitude (C{radians}). @param a1: Start latitude (C{radians}). @param b21: Longitudinal delta, M{end-start} (C{radians}). @return: Angular distance (C{radians}). @see: Functions L{vincentys}, L{equirectangular_}, L{euclidean_} and L{haversine_}. @note: Functions L{vincentys_} and L{haversine_} produce equivalent results, but L{vincentys_} is suitable for antipodal points and slightly more expensive than L{haversine_} (M{3 cos, 3 sin, 1 hypot, 1 atan2, 7 mul, 2 add} versus M{2 cos, 2 sin, 2 sqrt, 1 atan2, 5 mul, 1 add}). ''' sa1, ca1, sa2, ca2, sb21, cb21 = sincos2(a1, a2, b21) x = sa1 * sa2 + ca1 * ca2 * cb21 y = ca1 * sa2 - sa1 * ca2 * cb21 y = hypot(ca2 * sb21, y) return atan2(y, x) # **) 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.