PSO implementation for the OSM.

VadereModelTests/TestOSM/scenarios/rimea_06_corner_osm2.scenario

@@ -3,8 +3,15 @@
   "description" : "",
   "release" : "0.2",
   "processWriters" : {
-    "files" : [ ],
-    "processors" : [ ],
+    "files" : [ {
+      "type" : "org.vadere.simulator.projects.dataprocessing.outputfile.TimestepPedestrianIdOutputFile",
+      "filename" : "postvis.trajectories",
+      "processors" : [ 1 ]
+    } ],
+    "processors" : [ {
+      "type" : "org.vadere.simulator.projects.dataprocessing.processor.PedestrianPositionProcessor",
+      "id" : 1
+    } ],
     "isTimestamped" : true
   },
   "scenario" : {

VadereSimulator/src/org/vadere/simulator/models/osm/OptimalStepsModel.java

@@ -7,6 +7,7 @@ import org.vadere.simulator.models.SubModelBuilder;
 import org.vadere.simulator.models.groups.CentroidGroupModel;
 import org.vadere.simulator.models.groups.CentroidGroupPotential;
 import org.vadere.simulator.models.groups.CentroidGroupSpeedAdjuster;
+import org.vadere.simulator.models.osm.optimization.ParticleSwarmOptimizer;
 import org.vadere.simulator.models.osm.optimization.StepCircleOptimizer;
 import org.vadere.simulator.models.osm.optimization.StepCircleOptimizerBrent;
 import org.vadere.simulator.models.osm.optimization.StepCircleOptimizerDiscrete;
@@ -171,6 +172,9 @@ public class OptimalStepsModel implements MainModel, PotentialFieldModel {
 			case POWELL:
 				result = new StepCircleOptimizerPowell(random);
 				break;
+			case PSO:
+				result = new ParticleSwarmOptimizer(movementThreshold, random);
+				break;
 			case GRADIENT:
 				result = new StepCircleOptimizerGradient(topography,
 						potentialFieldTarget, attributesOSM);

VadereSimulator/src/org/vadere/simulator/models/osm/optimization/ParticleSwarmOptimizer.java

+package org.vadere.simulator.models.osm.optimization;
+
+import org.apache.log4j.Logger;
+import org.jetbrains.annotations.NotNull;
+import org.vadere.simulator.models.osm.PedestrianOSM;
+import org.vadere.state.attributes.models.AttributesOSM;
+import org.vadere.state.scenario.Pedestrian;
+import org.vadere.state.types.MovementType;
+import org.vadere.util.geometry.GeometryUtils;
+import org.vadere.util.geometry.Vector2D;
+import org.vadere.util.geometry.shapes.ICircleSector;
+import org.vadere.util.geometry.shapes.VCircle;
+import org.vadere.util.geometry.shapes.VCircleSector;
+import org.vadere.util.geometry.shapes.VPoint;
+import org.vadere.util.math.pso.PSO;
+
+import java.awt.Shape;
+import java.util.*;
+import java.util.List;
+
+/**
+ * @author Benedikt Zoennchen
+ */
+public class ParticleSwarmOptimizer implements StepCircleOptimizer {
+
+	private final double movementThreshold;
+	private final Random random;
+
+	public ParticleSwarmOptimizer(final double movementThreshold, @NotNull final Random random) {
+		this.movementThreshold = movementThreshold;
+		this.random = random;
+	}
+
+	@Override
+	public VPoint getNextPosition(@NotNull final PedestrianOSM pedestrian, @NotNull final Shape reachableArea) {
+		assert reachableArea instanceof VCircle;
+		VCircle circle = ((VCircle) reachableArea);
+		double stepSize = circle.getRadius();
+
+		final PotentialEvaluationFunction potentialEvaluationFunction = new PotentialEvaluationFunction(pedestrian);
+		potentialEvaluationFunction.setStepSize(stepSize);
+
+
+		List<VPoint> positions = StepCircleOptimizerDiscrete.getReachablePositions(pedestrian, random);
+		// maximum possible angle of movement relative to ankerAngle
+		double angle;
+
+		// smallest possible angle of movement
+		double anchorAngle;
+
+		ICircleSector circleSector;
+		// TODO: dupclated code see StepCircleOptimizerDiscrete!
+		if (pedestrian.getAttributesOSM().getMovementType() == MovementType.DIRECTIONAL) {
+			angle = StepCircleOptimizerDiscrete.getMovementAngle(pedestrian);
+			Vector2D velocity = pedestrian.getVelocity();
+			anchorAngle = velocity.angleToZero() - angle;
+			angle = 2 * angle;
+			circleSector = new VCircleSector(circle.getCenter(), circle.getRadius(), anchorAngle, anchorAngle + 2 * angle);
+		} else {
+			angle = 2 * Math.PI;
+			anchorAngle = 0;
+			circleSector = circle;
+		}
+
+		PSO pso = new PSO(p -> getValue(p, pedestrian, stepSize), circleSector, anchorAngle, anchorAngle + 2 * angle, random, stepSize / 5.0, positions);
+
+		VPoint nextPos = pso.getOptimumArg();
+		VPoint curPos = pedestrian.getPosition();
+		double curPosPotential = pedestrian.getPotential(curPos);
+		double potential = pso.getOptimum();
+
+		if (curPosPotential - potential < movementThreshold) {
+			nextPos = curPos;
+		}
+
+		return nextPos;
+	}
+
+	private double getValue(@NotNull final VPoint newPos, @NotNull final PedestrianOSM ped, final double stepSize) {
+		VPoint pedPos = ped.getPosition();
+		double result = 100000;
+
+		// step is not too small nor too large?
+		if (Math.pow(newPos.x - pedPos.x, 2) + Math.pow(newPos.y - pedPos.y, 2) <= Math.pow(stepSize, 2) + 0.00001
+				&& Math.pow(newPos.x - pedPos.x, 2) + Math.pow(newPos.y - pedPos.y, 2) >= Math.pow(ped.getMinStepLength(), 2)
+				- 0.00001) {
+			result = ped.getPotential(newPos);
+		}
+
+		return result;
+	}
+
+	@Override
+	public StepCircleOptimizer clone() {
+		return new ParticleSwarmOptimizer(movementThreshold, random);
+	}
+}

VadereSimulator/src/org/vadere/simulator/models/osm/optimization/StepCircleOptimizer.java

@@ -14,5 +14,5 @@ public interface StepCircleOptimizer {
 	/** Returns the reachable position with the minimal potential. */
 	VPoint getNextPosition(PedestrianOSM pedestrian, Shape reachableArea);
 
-	public StepCircleOptimizer clone();
+	StepCircleOptimizer clone();
 }

VadereSimulator/src/org/vadere/simulator/models/osm/optimization/StepCircleOptimizerDiscrete.java

 package org.vadere.simulator.models.osm.optimization;
 
 import org.apache.log4j.Logger;
+import org.jetbrains.annotations.NotNull;
 import org.vadere.simulator.models.osm.PedestrianOSM;
 import org.vadere.state.attributes.models.AttributesOSM;
 import org.vadere.state.types.MovementType;
+import org.vadere.util.geometry.GeometryUtils;
 import org.vadere.util.geometry.Vector2D;
 import org.vadere.util.geometry.shapes.VCircle;
 import org.vadere.util.geometry.shapes.VPoint;
 
-import java.awt.*;
-import java.util.LinkedList;
+import java.awt.Shape;
+import java.util.List;
 import java.util.Random;
 
 /**
@@ -22,19 +24,19 @@ public class StepCircleOptimizerDiscrete implements StepCircleOptimizer {
 	private final double movementThreshold;
 	private final Random random;
 
-	public StepCircleOptimizerDiscrete(final double movementThreshold, Random random) {
+	public StepCircleOptimizerDiscrete(final double movementThreshold, @NotNull final Random random) {
 		this.movementThreshold = movementThreshold;
 		this.random = random;
 	}
 
 	@Override
-	public VPoint getNextPosition(PedestrianOSM pedestrian, Shape reachableArea) {
-
+	public VPoint getNextPosition(@NotNull final PedestrianOSM pedestrian, @NotNull final Shape reachableArea) {
+		assert reachableArea instanceof VCircle;
 		double stepSize = ((VCircle) reachableArea).getRadius();
-		LinkedList<VPoint> positions = getReachablePositions(pedestrian, random);
 
-		PotentialEvaluationFunction potentialEvaluationFunction = new PotentialEvaluationFunction(
-				pedestrian);
+		List<VPoint> positions = getReachablePositions(pedestrian, random);
+
+		PotentialEvaluationFunction potentialEvaluationFunction = new PotentialEvaluationFunction(pedestrian);
 		potentialEvaluationFunction.setStepSize(stepSize);
 
 		VPoint curPos = pedestrian.getPosition();
@@ -43,8 +45,6 @@ public class StepCircleOptimizerDiscrete implements StepCircleOptimizer {
 		double potential = curPosPotential;
 		double tmpPotential = 0;
 
-
-
 		for (VPoint tmpPos : positions) {
 			try {
 				tmpPotential = potentialEvaluationFunction.getValue(tmpPos);
@@ -53,7 +53,7 @@ public class StepCircleOptimizerDiscrete implements StepCircleOptimizer {
 						|| (Math.abs(tmpPotential - potential) <= 0.0001 && random
 								.nextBoolean())) {
 					potential = tmpPotential;
-					nextPos = tmpPos.clone();
+					nextPos = tmpPos;
 				}
 			} catch (Exception e) {
 				Logger.getLogger(StepCircleOptimizerDiscrete.class).error("Potential evaluation threw an error.");
@@ -63,26 +63,20 @@ public class StepCircleOptimizerDiscrete implements StepCircleOptimizer {
 
 		if (curPosPotential - potential < movementThreshold) {
 			nextPos = curPos;
-			potential = curPosPotential;
 		}
+
 		return nextPos;
 	}
 
+
 	public StepCircleOptimizer clone() {
 		return new StepCircleOptimizerDiscrete(movementThreshold, random);
 	}
 
-	public static LinkedList<VPoint> getReachablePositions(final PedestrianOSM pedestrian, final Random random) {
+	public static List<VPoint> getReachablePositions(@NotNull final PedestrianOSM pedestrian, @NotNull final Random random) {
 
 		final AttributesOSM attributesOSM = pedestrian.getAttributesOSM();
-		double randOffset = attributesOSM.isVaryStepDirection() ? random.nextDouble() : 0;
-
-		VPoint currentPosition = pedestrian.getPosition();
-		LinkedList<VPoint> reachablePositions = new LinkedList<VPoint>();
 		int numberOfCircles = attributesOSM.getNumberOfCircles();
-		double circleOfGrid = 0;
-		int numberOfGridPoints;
-
 		// if number of circle is negative, choose number of circles according to
 		// StepCircleResolution
 		if (attributesOSM.getNumberOfCircles() < 0) {
@@ -107,38 +101,22 @@ public class StepCircleOptimizerDiscrete implements StepCircleOptimizer {
 			anchorAngle = 0;
 		}
 
-		// iterate through all circles
-		for (int j = 1; j <= numberOfCircles; j++) {
-
-			circleOfGrid = pedestrian.getStepSize() * j / numberOfCircles;
+		return GeometryUtils.getDiscDiscretizationPoints(
+				random,
+				attributesOSM.isVaryStepDirection(),
+				new VCircle(pedestrian.getPosition(),
+				pedestrian.getStepSize()),
+				numberOfCircles,
+				attributesOSM.getStepCircleResolution(),
+				anchorAngle,
+				angle);
 
-			numberOfGridPoints = (int) Math.ceil(circleOfGrid / pedestrian.getStepSize()
-					* attributesOSM.getStepCircleResolution());
-
-			// reduce number of grid points proportional to the constraint of direction
-			if (attributesOSM.getMovementType() == MovementType.DIRECTIONAL) {
-				numberOfGridPoints = (int) Math.ceil(numberOfGridPoints * angle / (2 * Math.PI));
-			}
-
-			double angleDelta = angle / numberOfGridPoints;
-
-			// iterate through all angles and compute absolute positions of grid points
-			for (int i = 0; i < numberOfGridPoints; i++) {
-
-				double x = circleOfGrid * Math.cos(anchorAngle + angleDelta * (randOffset + i)) + currentPosition.x;
-				double y = circleOfGrid * Math.sin(anchorAngle + angleDelta * (randOffset + i)) + currentPosition.y;
-				VPoint tmpPos = new VPoint(x, y);
-
-				reachablePositions.add(tmpPos);
-			}
-		}
-		return reachablePositions;
 	}
 
 	/**
 	 * The maximum deviation from the last movement direction given the current speed.
 	 */
-	private static double getMovementAngle(PedestrianOSM pedestrian) {
+	public static double getMovementAngle(@NotNull final PedestrianOSM pedestrian) {
 
 		final double speed = pedestrian.getVelocity().getLength();
 		double result = Math.PI - speed;

VadereSimulator/src/org/vadere/simulator/models/osm/optimization/StepCircleOptimizerEvolStrat.java

@@ -38,7 +38,7 @@ public class StepCircleOptimizerEvolStrat implements StepCircleOptimizer {
 	public VPoint getNextPosition(PedestrianOSM ped, Shape reachableArea) {
 
 		double stepSize = ((VCircle) reachableArea).getRadius();
-		LinkedList<VPoint> positions = StepCircleOptimizerDiscrete.getReachablePositions(ped, random);
+		List<VPoint> positions = StepCircleOptimizerDiscrete.getReachablePositions(ped, random);
 		int numberOfParents = positions.size();
 		int numberOfChildren = numberOfParents * 7;
 

VadereSimulator/src/org/vadere/simulator/models/osm/optimization/StepCircleOptimizerNelderMead.java

@@ -2,6 +2,7 @@ package org.vadere.simulator.models.osm.optimization;
 
 import java.awt.Shape;
 import java.util.LinkedList;
+import java.util.List;
 import java.util.Random;
 
 import org.apache.commons.math.ConvergenceException;
@@ -35,7 +36,7 @@ public class StepCircleOptimizerNelderMead implements StepCircleOptimizer {
 	public VPoint getNextPosition(PedestrianOSM pedestrian, Shape reachableArea) {
 
 		double stepSize = ((VCircle) reachableArea).getRadius();
-		LinkedList<VPoint> positions = StepCircleOptimizerDiscrete.getReachablePositions(pedestrian, random);
+		List<VPoint> positions = StepCircleOptimizerDiscrete.getReachablePositions(pedestrian, random);
 
 		PotentialEvaluationFunction potentialEvaluationFunction = new PotentialEvaluationFunction(pedestrian);
 		potentialEvaluationFunction.setStepSize(stepSize);

VadereSimulator/src/org/vadere/simulator/models/osm/optimization/StepCircleOptimizerPowell.java

@@ -2,6 +2,7 @@ package org.vadere.simulator.models.osm.optimization;
 
 import java.awt.Shape;
 import java.util.LinkedList;
+import java.util.List;
 import java.util.Random;
 
 import org.apache.commons.math3.optimization.direct.BOBYQAOptimizer;
@@ -38,7 +39,7 @@ public class StepCircleOptimizerPowell implements StepCircleOptimizer {
 
 		PointValuePair newMinimum = new PointValuePair(position, potentialEvaluationFunction.value(position));
 
-		LinkedList<VPoint> positions = StepCircleOptimizerDiscrete.getReachablePositions(pedestrian, random);
+		List<VPoint> positions = StepCircleOptimizerDiscrete.getReachablePositions(pedestrian, random);
 
 		try {
 			newMinimum = optimizer.optimize(1000, (MultivariateFunction) potentialEvaluationFunction, GoalType.MINIMIZE,

VadereState/src/org/vadere/state/types/OptimizationType.java

 package org.vadere.state.types;
 
 public enum OptimizationType {
-	NELDER_MEAD, POWELL, EVOLUTION_STRATEGY, BRENT, GRADIENT, DISCRETE, NONE
+	PSO, NELDER_MEAD, POWELL, EVOLUTION_STRATEGY, BRENT, GRADIENT, DISCRETE, NONE
 }

VadereUtils/src/org/vadere/util/geometry/GeometryUtils.java

@@ -8,7 +8,10 @@ import java.util.Collection;
 import java.util.Collections;
 import java.util.LinkedList;
 import java.util.List;
+import java.util.Random;
 
+import org.jetbrains.annotations.NotNull;
+import org.vadere.util.geometry.shapes.VCircle;
 import org.vadere.util.geometry.shapes.VLine;
 import org.vadere.util.geometry.shapes.VPoint;
 import org.vadere.util.geometry.shapes.VPolygon;
@@ -40,6 +43,45 @@ public class GeometryUtils {
 		return false;
 	}
 
+	public static List<VPoint> getDiscDiscretizationPoints(
+			@NotNull final Random random,
+			final boolean varyDirection,
+			@NotNull final VCircle circle,
+			final int numberOfCircles,
+			final int numberOfPointsOfLargestCircle,
+			final double anchorAngle,
+			final double angle) {
+		double randOffset = varyDirection ? random.nextDouble() : 0;
+
+		List<VPoint> reachablePositions = new ArrayList<>();
+
+		// iterate through all circles
+		for (int j = 1; j <= numberOfCircles; j++) {
+
+			double circleOfGrid = circle.getRadius() * j / numberOfCircles;
+
+			int numberOfGridPoints = (int) Math.ceil(circleOfGrid / circle.getRadius() * numberOfPointsOfLargestCircle);
+
+			// reduce number of grid points proportional to the constraint of direction
+			if (angle < 2 * Math.PI) {
+				numberOfGridPoints = (int) Math.ceil(numberOfGridPoints * angle / (2 * Math.PI));
+			}
+
+			double angleDelta = angle / numberOfGridPoints;
+
+			// iterate through all angles and compute absolute positions of grid points
+			for (int i = 0; i < numberOfGridPoints; i++) {
+
+				double x = circleOfGrid * Math.cos(anchorAngle + angleDelta * (randOffset + i)) + circle.getCenter().getX();
+				double y = circleOfGrid * Math.sin(anchorAngle + angleDelta * (randOffset + i)) + circle.getCenter().getY();
+				VPoint tmpPos = new VPoint(x, y);
+
+				reachablePositions.add(tmpPos);
+			}
+		}
+		return reachablePositions;
+	}
+
 	/**
 	 * Computes the point on the line segment that is closest to the given point
 	 * point. from:
@@ -89,6 +131,22 @@ public class GeometryUtils {
 		return orderedList;
 	}
 
+	/**
+	 * Returns the angle between the x-axis, p1 and p2.
+	 * @param p1
+	 * @param p2
+	 * @return
+	 */
+	public static double angleTo(VPoint p1, VPoint p2) {
+		double atan2 = Math.atan2(p1.y - p2.y, p1.x - p2.x);
+
+		if (atan2 < 0.0) {
+			atan2 = Math.PI * 2 + atan2;
+		}
+
+		return atan2;
+	}
+
 	/**
 	 * Calculate the counter clockwise result for the three given points.<br>
 	 * ccw(p1,p2,p3) < 0 if p3 is left of Line(p1,p2)<br>
@@ -150,4 +208,33 @@ public class GeometryUtils {
 	public static VPoint add(VPoint p1, VPoint p2) {
 		return new VPoint(p1.x + p2.x, p1.y + p2.y);
 	}
+
+	public static VPoint lineIntersectionPoint(final double x1,
+	                                           final double y1,
+	                                           final double x2,
+	                                           final double y2,
+	                                           final double x3,
+	                                           final double y3,
+			                                   final double x4,
+			                                   final double y4) {
+		assert new VLine(new VPoint(x1,y1), new VPoint(x2, y2)).intersectsLine(x3, y3, x4, y4);
+		double d = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4);
+		assert d != 0;
+
+		double x = ((x1 * y2 - y1 - x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4)) / d;
+		double y = ((x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (y3 * y4 - y3 * x4)) / d;
+		return new VPoint(x, y);
+	}
+
+	public static VPoint lineIntersectionPoint(final VPoint p1, final VPoint p2, final VPoint q1, final VPoint q2) {
+		return lineIntersectionPoint(p1.x, p1.y, p2.x, p2.y, q1.x, q1.y, q2.x, q2.y);
+	}
+
+	public static VPoint lineIntersectionPoint(final VLine line,
+	                                           final double x3,
+	                                           final double y3,
+	                                           final double x4,
+	                                           final double y4) {
+		return lineIntersectionPoint(line.getX1(), line.getY1(), line.getX2(), line.getY2(), x3, y3, x4, y4);
+	}
 }

VadereUtils/src/org/vadere/util/geometry/Vector2D.java

@@ -85,13 +85,7 @@ public class Vector2D extends VPoint {
 	 * Result is in interval (0,2*PI) according to standard math usage.
 	 */
 	public double angleTo(VPoint center) {
-		double atan2 = Math.atan2(this.y - center.y, this.x - center.x);
-
-		if (atan2 < 0.0) {
-			atan2 = Math.PI * 2 + atan2;
-		}
-
-		return atan2;
+		return GeometryUtils.angleTo(this, center);
 	}
 
 	public Vector2D add(VPoint p) {

VadereUtils/src/org/vadere/util/geometry/shapes/ICircleSector.java

+package org.vadere.util.geometry.shapes;
+
+import com.google.common.collect.ImmutableList;
+
+import org.jetbrains.annotations.NotNull;
+
+import java.util.Optional;
+
+/**
+ * @author Benedikt Zoennchen
+ */
+public interface ICircleSector {
+	boolean contains(VPoint point);
+
+	default ImmutableList<VPoint> getIntersectionPoints(@NotNull final VLine line) {
+		return getIntersectionPoints(line.getX1(), line.getY1(), line.getX2(), line.getY2());
+	}
+
+	default ImmutableList<VPoint> getIntersectionPoints(@NotNull final VPoint p, @NotNull final VPoint q) {
+		return getIntersectionPoints(p.getX(), p.getY(), q.getX(), q.getY());
+	}
+
+	ImmutableList<VPoint> getIntersectionPoints(final double x1, final double y1, final double x2, final double y2);
+
+	default Optional<VPoint> getClosestIntersectionPoint(@NotNull final VLine line, @NotNull final VPoint r) {
+		return getClosestIntersectionPoint(line.getX1(), line.getY1(), line.getX2(), line.getY2(), r.getX(), r.getY());
+	}
+
+	default Optional<VPoint> getClosestIntersectionPoint(@NotNull final VPoint p, @NotNull final VPoint q, @NotNull final VPoint r) {
+		return getClosestIntersectionPoint(p.getX(), p.getY(), q.getX(), q.getY(), r.getX(), r.getY());
+	}
+
+	Optional<VPoint> getClosestIntersectionPoint(final double x1, final double y1, final double x2, final double y2, final double x3, final double y3);
+
+	default boolean intersectsLine(@NotNull VLine intersectingLine) {
+		return intersectsLine(intersectingLine.getX1(), intersectingLine.getY1(), intersectingLine.getX2(), intersectingLine.getY2());
+	}
+
+	default boolean intersectsLine(@NotNull VPoint p, @NotNull VPoint q) {
+		return intersectsLine(p.getX(), p.getY(), q.getX(), q.getY());
+	}
+
+	boolean intersectsLine(final double x1, final double y1, final double x2, final double y2);
+
+	double getRadius();
+
+	VPoint getCenter();
+}

VadereUtils/src/org/vadere/util/geometry/shapes/VCircle.java

 package org.vadere.util.geometry.shapes;
 
+import com.google.common.collect.ImmutableList;
+
 import java.awt.Rectangle;
 import java.awt.geom.AffineTransform;
 import java.awt.geom.Ellipse2D;
 import java.awt.geom.PathIterator;
 import java.awt.geom.Point2D;
 import java.awt.geom.Rectangle2D;
+import java.util.Comparator;
+import java.util.Optional;
 
+import org.jetbrains.annotations.NotNull;
 import org.vadere.util.geometry.ShapeType;
 import org.vadere.util.geometry.Vector2D;
 
-public class VCircle implements VShape {
+public class VCircle implements VShape, ICircleSector {
 
 	private final VPoint center;
 	private final double radius;
@@ -52,9 +57,6 @@ public class VCircle implements VShape {
 		return this.center;
 	}
 
-	/**
-	 * Not implemented.
-	 */
 	@Override
 	public VPoint closestPoint(VPoint point) {
 		Vector2D direction = new Vector2D(point.x - center.x, point.y
@@ -63,6 +65,83 @@ public class VCircle implements VShape {
 		return new VPoint(vector.x + center.x, vector.y + center.y);
 	}
 
+	/**
+	 * Returns zero, one or two points which are the intersection of this circle and the line defined
+	 * by p = (x11, y11) and q = (x22, y22).
+	 *
+	 * @param x11
+	 * @param y11
+	 * @param x22
+	 * @param y22
+	 * @return
+	 */
+	public ImmutableList<VPoint> getIntersectionPoints(final double x11, final double y11, final double x22, final double y22) {
+
+		double x1 = x11 - center.x;
+		double y1 = y11 - center.y;
+		double x2 = x22 - center.x;
+		double y2 = y22 - center.y;
+