h0ddlmZddlmZmZmZmZddlZddlm Z m Z erddl m Z dZ dZd Zdd Zd e f dd Zdd Ze f ddZddZddZe f ddZdZdZdZdZdZdZd dZd!d"dZy)#) annotations)IterableSequenceOptional TYPE_CHECKINGN)Vec2Vec3)UVecg|=gV瞯z,has_clockwise_orientation..(s9 5BTTBDD[RTTBDD[ )5sAArN)r listlen ValueErroriscloseappendsumzip)verticess rhas_clockwise_orientationr syy"H 8}q899 A;  x| , $  h 5     Tc&|\}}|\}}|j}|j} |j} |j} |j} |j} |j}|j}|| z | |z z|| z | | z zz }tj||kry|| z | | z z|| z || z zz |z }t ||| |z zz| || | z zz}|r|Sd}d}||cxkr|kr,ny| |z | | z z| | z || z zz |z }||cxkr|kr|Syy)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 )line1line2virtualabs_tols1s2c1c2s1xs1ys2xs2yc1xc1yc2xc2ydenusintersection_pointlwruprucs rintersection_line_line_2dr<0sT2FB FB $$C $$C $$C $$C $$C $$C $$C $$C 9s #sSyS3Y&? ?C yy~  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) longitudelatituderqe e_sin_latrsrrs rgps_to_world_mercatorr&s& Y'I||H%HA!A"Q&I # /cIo6C@A DHHTXXj8c>9:Q> ??A I A a4Kr!ct}t}|dz }t}tj| |z z}|dtj |zz } tj ||z} |dtj |d| z d| zz |zzzz } t| |z |krn| }W||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 rwr#) ryrz CONST_PI_2r$ratanr{ridegrees) rrtolrqre2pi2t latitude_rrrs rworld_mercator_to_gpsrDs, A!A SB C A26AcDIIaL((I HHY'!+ tyy # /cIo62= =    x)# $s *   AI << "DLL$: ::r!)rzIterable[UVec]returnbool)r&Sequence[Vec2]r'rrzOptional[Vec2])rfloat)rRSequence[Vec3]rSrrr)r`rrarrr)rjr rkz list[Vec2]rint)rrrrrtuple[float, float])gư>)rrrrrrrr) __future__rtypingrrrrr$_vectorr r ezdxf.mathr TOLERANCErer_r r<rKr]rbrfruryWGS84_SEMI_MINOR_AXISrzCONST_E2rrrrr>r!rrs #>>      >   6 6 6  6r "9B$ $ .$$N<@/87 7$77| $/    <&;r!