Is there a cleaner / simpler way to calculate the edge in a geometry that a line crosses?

Question

In the code below it is fairly simple to check does the line cross into the geometry or not - it's also trivial to work out the coordinate that the line crosses into the geometry at. However (and I've tried quite a few different ways), it seems way more convoluted to work out which line segment it is on.

final GeometryFactory fact = new GeometryFactory();

// The thing we are testing. 
final Geometry gTestPoly = fact.createPolygon(new Coordinate[] { new Coordinate(0, 0),
  new Coordinate(0, 10), new Coordinate(10, 10),
  new Coordinate(10, 0), new Coordinate(0, 0)}); // a square 

// Preconditions
final Coordinate cOutsideThePoly = new Coordinate(-5, 5);
final Coordinate cInsideThePoly = new Coordinate(5, 5);
final Geometry gOutsideThePoly = fact.createPoint(cOutsideThePoly); 
final Geometry gInsideThePoly = fact.createPoint(cInsideThePoly);
assertTrue(gTestPoly.contains(gInsideThePoly)); 
assertFalse(gTestPoly.contains(gOutsideThePoly));
                
final Geometry gIntersectingLine = fact.createLineString(new Coordinate[] {cOutsideThePoly, cInsideThePoly}); // a line that crosses into the square 
final LineSegment lIntersectingLine = new LineSegment(cOutsideThePoly, cInsideThePoly);
                
// Easy - it crosses the boundary on just 1 edge.
assertTrue(gIntersectingLine.crosses(gTestPoly));
                
// But if I want to see which edge/line segment my intersecting line segment crosses at ?? [this feels quite clunky..]
final Geometry gLineVersionOfTestPoly = LinearComponentExtracter.getGeometry(gTestPoly, true);
final LinearIterator iSegments = new LinearIterator(gLineVersionOfTestPoly);
final LineSegment forTest = new LineSegment();
while (iSegments.hasNext()) {
    final Coordinate from = iSegments.getSegmentStart();
    final Coordinate to = iSegments.getSegmentEnd();
    forTest.setCoordinates(from, to);
    if (forTest.intersection(lIntersectingLine) != null) {
        System.err.println("Matching " + forTest);
    }                   
    iSegments.next(); // move to next step.
}                                        

I get what I expect for output -

Matching LINESTRING( 0.0 0.0, 0.0 10.0)

Yes understand could just grab all the coordinates (via getCoordinates()) and check line segments like that - again seems like I've missed the magic simple method..