To calculate the line intersection points between two shapes we use the ILcd2DLineIntersectionTopology interface, as illustrated in the example below:

import java.util.Formatter;
import java.util.Locale;

import com.luciad.geodesy.TLcdEllipsoid;
import com.luciad.geometry.topology.ILcd2DLineIntersectionTopology;
import com.luciad.geometry.topology.ellipsoidal.TLcdEllipsoidalBasicBinaryTopology;
import com.luciad.shape.ILcdPoint;
import com.luciad.shape.shape2D.ILcd2DEditablePoint;
import com.luciad.shape.shape2D.TLcd2DEditablePointList;
import com.luciad.shape.shape2D.TLcdLonLatPoint;
import com.luciad.shape.shape2D.TLcdLonLatPolygon;

public class LineIntersectionTutorial {
  public static void main(String[] args) {
    // Create the ellipsoid.
    // For this sample, it is hardcoded here.
    // In practice, the ellipsoid used by all shapes in the program should be used.
    // In a cartesian topology, no ellipsoid is needed.
    TLcdEllipsoid ellipsoid = new TLcdEllipsoid();

    // Create two shapes.
    // For this sample two simple triangles are created.
    // In practice, these ILcdShape instances could originate from any source.
    TLcdLonLatPolygon polygon1 = new TLcdLonLatPolygon(new TLcd2DEditablePointList(
        new ILcd2DEditablePoint[]{
            new TLcdLonLatPoint(0.0, 0.0),
            new TLcdLonLatPoint(10.0, 20.0),
            new TLcdLonLatPoint(20.0, 10.0)
        }, false), ellipsoid);
    TLcdLonLatPolygon polygon2 = new TLcdLonLatPolygon(new TLcd2DEditablePointList(
        new ILcd2DEditablePoint[]{
            new TLcdLonLatPoint(11.0, 12.0),
            new TLcdLonLatPoint(5.0, 4.0),
            new TLcdLonLatPoint(12.0, 0.0)
        }, false), ellipsoid);

    // Create the topology.
    ILcd2DLineIntersectionTopology topology = new TLcdEllipsoidalBasicBinaryTopology(ellipsoid);

    // Find the line intersections points.
    ILcdPoint[] intersectionPoints = topology.lineIntersection(polygon1, polygon2);

    System.out.println("Intersection points:");
    for (ILcdPoint intersectionPoint : intersectionPoints) {
      // always use points to avoid confusion with the coordinate separator
      Formatter formatter = new Formatter(Locale.US);
      System.out.println(formatter.format("(%.2f, %.2f)", intersectionPoint.getX(), intersectionPoint.getY()));