Module ellipsoidalExact

Compute the intersections of a circle and a geodesic given as two points or as a point and (forward) bearing.

Arguments:

• center - Center of the circle (LatLon).
• circle - Radius of the circle (meter, conventionally) or a point on the circle (LatLon, as center).
• point - A point of the geodesic (LatLon, as center).
• other - An other point of the geodesic (LatLon, as center) or the (forward) bearing at the point (compass degrees).
• exact_height_wrap_tol - Optional keyword arguments, see below.

Raises:

• NotImplementedError - Method intersecant2 not available.
• TypeError - If center, point or circle or other points not ellipsoidal or not compatible with center.

Check whether a polygon encloses a pole.

Arguments:

• points - The polygon points (LatLon[]).
• wrap - If True, wrap or normalize and unroll the points (bool).

Returns:

True if the polygon encloses a pole, False otherwise.

Raises:

• PointsError - Insufficient number of points
• TypeError - Some points are not LatLon or don't have bearingTo2, initialBearingTo and finalBearingTo methods.

Compute the area of an (ellipsoidal) polygon or composite.

Arguments:

• points - The polygon points (LatLon[], BooleanFHP or BooleanGH).
• datum - Optional datum (Datum).
• wrap - If True, wrap or normalize and unroll the points (bool).

Returns:

Area (meter squared, same units as the datum's ellipsoid axes).

Raises:

• PointsError - Insufficient number of points.
• TypeError - Some points are not LatLon.
• ValueError - Invalid wrap=False, unwrapped, unrolled longitudes not supported.

Iteratively compute the intersection point of two lines, each defined by two (ellipsoidal) points or by an (ellipsoidal) start point and an initial bearing from North.

Arguments:

• start1 - Start point of the first line (LatLon).
• end1 - End point of the first line (LatLon) or the initial bearing at the first point (compass degrees360).
• start2 - Start point of the second line (LatLon).
• end2 - End point of the second line (LatLon) or the initial bearing at the second point (compass degrees360).
• height - Optional height at the intersection (meter, conventionally) or None for the mean height.
• wrap - If True, wrap or normalize and unroll the start2 and end* points (bool).
• equidistant - An azimuthal equidistant projection (class or function pygeodesy.equidistant) or None for the preferred start1.Equidistant.
• tol - Tolerance for convergence and for skew line distance and length (meter, conventionally).
• LatLon - Optional class to return the intersection points (LatLon) or None.
• LatLon_kwds - Optional, additional LatLon keyword arguments, ignored if LatLon is None.

Returns:

An Intersection3Tuple(point, outside1, outside2) with point a LatLon or if LatLon is None, a LatLon4Tuple(lat, lon, height, datum).

Raises:

• IntersectionError - Skew, colinear, parallel or otherwise non-intersecting lines or no convergence for the given tol.
• TypeError - Invalid or non-ellipsoidal start1, end1, start2 or end2 or invalid equidistant.

Iteratively compute the intersection points of two circles, each defined by an (ellipsoidal) center point and a radius.

Arguments:

• center1 - Center of the first circle (LatLon).
• radius1 - Radius of the first circle (meter, conventionally).
• center2 - Center of the second circle (LatLon).
• radius2 - Radius of the second circle (meter, same units as radius1).
• height - Optional height for the intersection points (meter, conventionally) or None for the "radical height" at the radical line between both centers.
• wrap - If True, wrap or normalize and unroll center2 (bool).
• equidistant - An azimuthal equidistant projection (class or function pygeodesy.equidistant) or None for the preferred center1.Equidistant.
• tol - Convergence tolerance (meter, same units as radius1 and radius2).
• LatLon - Optional class to return the intersection points (LatLon) or None.
• LatLon_kwds - Optional, additional LatLon keyword arguments, ignored if LatLon is None.

Returns:

2-Tuple of the intersection points, each a LatLon instance or LatLon4Tuple(lat, lon, height, datum) if LatLon is None. For abutting circles, both points are the same instance, aka the radical center.

Raises:

• IntersectionError - Concentric, antipodal, invalid or non-intersecting circles or no convergence for the tol.
• TypeError - Invalid or non-ellipsoidal center1 or center2 or invalid equidistant.
• UnitError - Invalid radius1, radius2 or height.

Determine the direction of a path or polygon.

Arguments:

• points - The path or polygon points (LatLon[]).
• datum - Optional datum (Datum).
• wrap - If True, wrap or normalize and unroll the points (bool).

Returns:

True if points are clockwise, False otherwise.

Raises:

• PointsError - Insufficient number of points.
• TypeError - Some points are not LatLon.
• ValueError - The points enclose a pole or zero area.

Iteratively locate the closest point on the geodesic between two other (ellispoidal) points.

Arguments:

• point - Reference point (LatLon).
• point1 - Start point of the geodesic (LatLon).
• point2 - End point of the geodesic (LatLon).
• within - If True return the closest point between point1 and point2, otherwise the closest point elsewhere on the geodesic (bool).
• height - Optional height for the closest point (meter, conventionally) or None or False for the interpolated height. If False, the closest takes the heights of the points into account.
• wrap - If True, wrap or normalize and unroll both point1 and point2 (bool).
• equidistant - An azimuthal equidistant projection (class or function pygeodesy.equidistant) or None for the preferred point.Equidistant.
• tol - Convergence tolerance (meter).
• LatLon - Optional class to return the closest point (LatLon) or None.
• LatLon_kwds - Optional, additional LatLon keyword arguments, ignored if LatLon is None.

Returns:

Closest point, a LatLon instance or if LatLon is None, a LatLon4Tuple(lat, lon, height, datum).

Raises:

• TypeError - Invalid or non-ellipsoidal point, point1 or point2 or invalid equidistant.
• ValueError - No convergence for the tol.

Compute the perimeter of an (ellipsoidal) polygon or composite.

Arguments:

• points - The polygon points (LatLon[], BooleanFHP or BooleanGH).
• closed - Optionally, close the polygon (bool).
• datum - Optional datum (Datum).
• wrap - If True, wrap or normalize and unroll the points (bool).

Returns:

Perimeter (meter, same units as the datum's ellipsoid axes).

Raises:

• PointsError - Insufficient number of points.
• TypeError - Some points are not LatLon.
• ValueError - Invalid wrap=False, unwrapped, unrolled longitudes not supported or closed=False with points a composite.