Coverage for pygeodesy/ellipsoidalExact.py : 100%

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# -*- coding: utf-8 -*-
Ellipsoidal geodetic (lat-/longitude) L{LatLon} and geocentric (ECEF) L{Cartesian} classes and functions L{areaOf}, L{intersections2}, L{isclockwise}, L{nearestOn} and L{perimeterOf} based on classes L{GeodesicExact}, L{GeodesicAreaExact} and L{GeodesicLineExact}. '''
_intersection3, _intersections2 # from pygeodesy.errors import _xkwds # from .karney # from pygeodesy.props import Property_RO # from .karney
'''Extended to convert exact L{Cartesian} to exact L{LatLon} points. '''
'''Convert this cartesian point to an exact geodetic point.
@kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword arguments as C{datum}. Use C{B{LatLon}=..., B{datum}=...} to override this L{LatLon} class or specify C{B{LatLon}=None}.
@return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C} and C{M} if available.
@raise TypeError: Invalid B{C{LatLon_and_kwds}} argument. '''
'''An ellipsoidal L{LatLon} like L{ellipsoidalKarney.LatLon} but using exact geodesic classes L{GeodesicExact} and L{GeodesicLineExact} to compute the geodesic distance, initial and final bearing (azimuths) between two given points or the destination point given a start point and an (initial) bearing. '''
'''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantExact}). '''
'''Get this C{LatLon}'s exact geodesic (L{GeodesicExact}). '''
'''Convert this point to exact cartesian (ECEF) coordinates.
@kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} and other keyword arguments, ignored if C{B{Cartesian} is None}. Use C{B{Cartesian}=...} to override this L{Cartesian} class or set C{B{Cartesian} is None}.
@return: The cartesian (ECEF) coordinates (L{Cartesian}) or if B{C{Cartesian}} is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C} and C{M} if available.
@raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other B{C{Cartesian_datum_kwds}}. '''
'''Compute the area of an (ellipsoidal) polygon.
@arg points: The polygon points (L{LatLon}[]). @kwarg datum: Optional datum (L{Datum}). @kwarg wrap: Wrap and unroll longitudes (C{bool}).
@return: Area (C{meter}, same as units of the B{C{datum}}'s ellipsoid axes, I{squared}).
@raise PointsError: Insufficient number of B{C{points}}.
@raise TypeError: Some B{C{points}} are not L{LatLon}.
@raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled longitudes not supported.
@see: Functions L{pygeodesy.areaOf}, L{ellipsoidalGeodSolve.areaOf}, L{ellipsoidalKarney.areaOf}, L{sphericalNvector.areaOf} and L{sphericalTrigonometry.areaOf}. '''
equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds): '''Interatively compute the intersection point of two paths, each defined by two (ellipsoidal) points or by an (ellipsoidal) start point and a bearing from North.
@arg start1: Start point of the first path (L{LatLon}). @arg end1: End point of the first path (L{LatLon}) or the initial bearing at the first point (compass C{degrees360}). @arg start2: Start point of the second path (L{LatLon}). @arg end2: End point of the second path (L{LatLon}) or the initial bearing at the second point (compass C{degrees360}). @kwarg height: Optional height at the intersection (C{meter}, conventionally) or C{None} for the mean height. @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg equidistant: An azimuthal equidistant projection (I{class} or function L{pygeodesy.equidistant}) or C{None} for the preferred C{B{start1}.Equidistant}. @kwarg tol: Tolerance for convergence and for skew line distance and length (C{meter}, conventionally). @kwarg LatLon: Optional class to return the intersection points (L{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon} is None}.
@return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point} a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
@raise IntersectionError: Skew, colinear, parallel or otherwise non-intersecting paths or no convergence for the given B{C{tol}}.
@raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}}, B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.
@note: For each path specified with an initial bearing, a pseudo-end point is computed as the C{destination} along that bearing at about 1.5 times the distance from the start point to an initial gu-/estimate of the intersection point (and between 1/8 and 3/8 of the authalic earth perimeter).
@see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ calculating-intersection-of-two-circles>} and U{Karney's paper <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES} for more details about the iteration algorithm. ''' equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds): '''Iteratively compute the intersection points of two circles, each defined by an (ellipsoidal) center point and a radius.
@arg center1: Center of the first circle (L{LatLon}). @arg radius1: Radius of the first circle (C{meter}, conventionally). @arg center2: Center of the second circle (L{LatLon}). @arg radius2: Radius of the second circle (C{meter}, same units as B{C{radius1}}). @kwarg height: Optional height for the intersection points (C{meter}, conventionally) or C{None} for the I{"radical height"} at the I{radical line} between both centers. @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg equidistant: An azimuthal equidistant projection (I{class} or function L{pygeodesy.equidistant}) or C{None} for the preferred C{B{center1}.Equidistant}. @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}} and B{C{radius2}}). @kwarg LatLon: Optional class to return the intersection points (L{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon} is None}.
@return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is None}. For abutting circles, both points are the same instance, aka the I{radical center}.
@raise IntersectionError: Concentric, antipodal, invalid or non-intersecting circles or no convergence for the B{C{tol}}.
@raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}} or invalid B{C{equidistant}}.
@raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
@see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ calculating-intersection-of-two-circles>}, U{Karney's paper <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES}, U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>} intersections. ''' equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
'''Determine the direction of a path or polygon.
@arg points: The path or polygon points (C{LatLon}[]). @kwarg datum: Optional datum (L{Datum}). @kwarg wrap: Wrap and unroll longitudes (C{bool}).
@return: C{True} if B{C{points}} are clockwise, C{False} otherwise.
@raise PointsError: Insufficient number of B{C{points}}.
@raise TypeError: Some B{C{points}} are not C{LatLon}.
@raise ValueError: The B{C{points}} enclose a pole or zero area.
@see: L{pygeodesy.isclockwise}. ''' raise _areaError(points)
equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds): '''Iteratively locate the closest point on the geodesic between two other (ellispoidal) points.
@arg point: Reference point (C{LatLon}). @arg point1: Start point of the arc (C{LatLon}). @arg point2: End point of the arc (C{LatLon}). @kwarg within: If C{True} return the closest point I{between} B{C{point1}} and B{C{point2}}, otherwise the closest point elsewhere on the arc (C{bool}). @kwarg height: Optional height for the closest point (C{meter}, conventionally) or C{None} or C{False} for the interpolated height. If C{False}, the closest takes the heights of the points into account. @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg equidistant: An azimuthal equidistant projection (I{class} or function L{pygeodesy.equidistant}) or C{None} for the preferred C{B{point}.Equidistant}. @kwarg tol: Convergence tolerance (C{meter}). @kwarg LatLon: Optional class to return the closest point (L{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon} is None}.
@return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
@raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}} or B{C{point2}} or invalid B{C{equidistant}}.
@raise ValueError: No convergence for the B{C{tol}}.
@see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ calculating-intersection-of-two-circles>} and U{Karney's paper <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES} for more details about the iteration algorithm. ''' equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
'''Compute the perimeter of an (ellipsoidal) polygon.
@arg points: The polygon points (L{LatLon}[]). @kwarg closed: Optionally, close the polygon (C{bool}). @kwarg datum: Optional datum (L{Datum}). @kwarg wrap: Wrap and unroll longitudes (C{bool}).
@return: Perimeter (C{meter}, same as units of the B{C{datum}}'s ellipsoid axes).
@raise PointsError: Insufficient number of B{C{points}}.
@raise TypeError: Some B{C{points}} are not L{LatLon}.
@raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled longitudes not supported.
@see: Functions L{pygeodesy.perimeterOf}, L{ellipsoidalGeodSolve.perimeterOf}, L{ellipsoidalKarney.perimeterOf}, L{sphericalNvector.perimeterOf} and L{sphericalTrigonometry.perimeterOf}. '''
areaOf, # functions intersection3, intersections2, isclockwise, ispolar, nearestOn, perimeterOf)
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