Two polylines cross if they meet at (a) point/s only, and at least one of the shared points is internal to both polylines. A polyline and polygon cross if a connected part of the polyline is partly inside and partly outside the polygon.

Example 1: Does Geometry A cross Geometry B?

static boolean geometryCrosses(Geometry geometryA, Geometry geometryB, SpatialReference sr)
 boolean crosses = OperatorCrosses.local().execute(geometryA, geometryB, sr, null);
 return crosses;