question: private static boolean intersectsLatEdge ( S2Point a , S2Point b , double lat , S1Interval lng ) { S2Point z = S2Point . normalize ( S2 . robustCrossProd ( a , b ) ) ; if ( z . z < 0 ) { z = S2Point . neg ( z ) ; } S2Point y = S2Point . normalize ( S2 . robustCrossProd ( z , new S2Point ( 0 , 0 , 1 ) ) ) ; S2Point x = S2Point . crossProd ( y , z ) ; double sinLat = Math . sin ( lat ) ; if ( Math . abs ( sinLat ) >= x . z ) { return false ; } double cosTheta = sinLat / x . z ; double sinTheta = Math . sqrt ( 1 - cosTheta * cosTheta ) ; double theta = Math . atan2 ( sinTheta , cosTheta ) ; S1Interval abTheta = S1Interval . fromPointPair ( Math . atan2 ( a . dotProd ( y ) , a . dotProd ( x ) ) , Math . atan2 ( b . dotProd ( y ) , b . dotProd ( x ) ) ) ; if ( abTheta . contains ( theta ) ) { S2Point isect = S2Point . add ( S2Point . mul ( x , cosTheta ) , S2Point . mul ( y , sinTheta ) ) ; if ( lng . contains ( Math . atan2 ( isect . y , isect . x ) ) ) { return true ; } } if ( abTheta . contains ( - theta ) ) { S2Point intersection = S2Point . sub ( S2Point . mul ( x , cosTheta ) , S2Point . mul ( y , sinTheta ) ) ; if ( lng . contains ( Math . atan2 ( intersection . y , intersection . x ) ) ) { return true ; } } return false ; }
target:  Return true if the edge AB intersects the given edge of constant latitude.