'jS/ddlmZddlmZmZmZmZddlZddlm Z m Z erddl m Z dZ dZd Zd4dZde fd5dZd6dZe fd7dZd8dZd8dZe fd9d$Zd%Zd&Zd'Zd(Zd)Zd*Zd:d.Zd;dz,has_clockwise_orientation..(sO  BTBD[RTBD[ )      rN)r listlen ValueErroriscloseappendsumzip)r s rhas_clockwise_orientationr$sy""H 8}}q8999 A;  x| , ,% $$$   h 55        rTline1Sequence[Vec2]line2Optional[Vec2]c|\}}|\}}|j}|j} |j} |j} |j} |j} |j}|j}|| z | |z z|| z | | z zz }tj||krdS|| z | | z z|| z || z zz |z }t ||| |z zz| || | z zz}|r|Sd}d}||cxkr|kr/nn,| |z | | z z| | z || z zz |z }||cxkr|krnn|SdS)a9 Compute the intersection of two lines in the xy-plane. Args: line1: start- and end point of first line to test e.g. ((x1, y1), (x2, y2)). line2: start- and end point of second line to test e.g. ((x3, y3), (x4, y4)). virtual: ``True`` returns any intersection point, ``False`` returns only real intersection points. abs_tol: tolerance for intersection test. Returns: ``None`` if there is no intersection point (parallel lines) or intersection point as :class:`Vec2` Nr?)rrmathfabsr )r%r'virtualabs_tols1s2c1c2s1xs1ys2xs2yc1xc1yc2xc2ydenusintersection_pointlwruprucs rintersection_line_line_2drA0sq2FB FB $C $C $C $C $C $C $C $C 9s #sSyS3Y&? ?C y~~  t 9s #sSyS3Y&? ?3 FBcB#)$44cB#)`_ location given as latitude and longitude in decimal degrees as used by GPS into World Mercator cartesian 2D coordinates in meters `EPSG:3395 `_. Args: longitude: represents the longitude value (East-West) in decimal degrees latitude: represents the latitude value (North-South) in decimal degrees. .. versionadded:: 1.3.0 r*@) r+radiansWGS84_SEMI_MAJOR_AXISWGS84_ELLIPSOID_ECCENTRICsinpowlogtan CONST_PI_4)rrrze e_sin_latr|rrs rgps_to_world_mercatorr&s& Y''I|H%%HA!A""Q&I # /cIo6C@@A DHTXj8c>9::Q> ? ??A I A a4Krư>rrtolct}t}|dz }t}tj| |z z}|dtj|zz } tj||z} |dtj|d| z d| zz |zzzz } t| |z |krn| }Z||z } tj| tj| fS)aTransform World Mercator to GPS. Transform WGS84 World Mercator `EPSG:3395 `_ location given as cartesian 2D coordinates x, y in meters into WGS84 decimal degrees as longitude and latitude `EPSG:4326 `_ as used by GPS. Args: x: coordinate WGS84 World Mercator y: coordinate WGS84 World Mercator tol: accuracy for latitude calculation .. versionadded:: 1.3.0 rTr*) rr CONST_PI_2r+ratanrrtdegrees) rrrrzre2pi2t latitude_rrrs rworld_mercator_to_gpsrDs, A!A SB C A26AcDIaLL((IHY''!+ ty # /cIo62= =     x)# $ $s * *  AI < " "DL$:$: ::r)r r rr)r%r&r'r&rr()rrB)rRrSrTrSrrS)rerBrfrBrrB)rnr rorprrq)rrBrrBrr)r)rrBrrBrrBrr) __future__rtypingrrrrr+_vectorr r ezdxf.mathr TOLERANCErlrhr$rArQrdrirmr~rWGS84_SEMI_MINOR_AXISrCONST_E2rrrrrDrrrs #""""">>>>>>>>>>>>       >   66666r    "9B$$$$$N<@/877777| $/    <&;&;&;&;&;&;&;r