software architecture improvement for the triangulation

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

@@ -534,6 +534,22 @@ public class GeometryUtils {
 		return new VRectangle(pMin.getX(), pMin.getY(), pMax.getX() - pMin.getX(), pMax.getY() - pMin.getY());
 	}
 
+	public static double sign(final double x1, final double y1, final double x2, final double y2, final double x3, final double y3) {
+		return (x1 - x3) * (y2 - y3) - (x2 -x3) * (y1 - y3);
+	}
+
+	public static <P extends IPoint> VRectangle bound(final Collection<P> points) {
+
+		if(points.isEmpty()) {
+			throw new IllegalArgumentException("the point collection is empty.");
+		}
+
+		VPoint pMax = points.stream().map(p -> new VPoint(p.getX(), p.getY())).reduce((p1, p2) -> new VPoint(Math.max(p1.getX(), p2.getX()), Math.max(p1.getY(), p2.getY()))).get();
+		VPoint pMin = points.stream().map(p -> new VPoint(p.getX(), p.getY())).reduce((p1, p2) -> new VPoint(Math.min(p1.getX(), p2.getX()), Math.min(p1.getY(), p2.getY()))).get();
+
+		return new VRectangle(pMin.getX(), pMin.getY(), pMax.getX() - pMin.getX(), pMax.getY() - pMin.getY());
+	}
+    
 	/**
 	 * This method follows the construction from
 	 * https://proofwiki.org/wiki/Obtuse_Triangle_Divided_into_Acute_Triangles

VadereUtils/src/org/vadere/util/geometry/mesh/impl/PMesh.java

@@ -82,16 +82,6 @@ public class PMesh<P extends IPoint> implements IMesh<P, PHalfEdge<P>, PFace<P>>
 		return halfEdge.isBoundary();
 	}
 
-	@Override
-	public boolean isHole(@NotNull PFace<P> face) {
-		return false;
-	}
-
-	@Override
-	public boolean isHole(@NotNull PHalfEdge<P> halfEdge) {
-		return false;
-	}
-
 	@Override
 	public boolean isDestroyed(@NotNull PFace<P> face) {
 		return face.isDestroyed();
@@ -152,6 +142,11 @@ public class PMesh<P extends IPoint> implements IMesh<P, PHalfEdge<P>, PFace<P>>
 		return vertices.size();
 	}
 
+	@Override
+	public int getNumberOfFaces() {
+		return faces.size();
+	}
+
 	@Override
 	public PHalfEdge<P> createEdge(@NotNull P vertex) {
 		PHalfEdge<P> edge = new PHalfEdge<>(vertex);
@@ -190,6 +185,11 @@ public class PMesh<P extends IPoint> implements IMesh<P, PHalfEdge<P>, PFace<P>>
 		return vertex;
 	}
 
+	@Override
+	public PFace<P> getBoundary() {
+		return boundary;
+	}
+
 	@Override
 	public void insert(P vertex) {
 		vertices.add(vertex);

VadereUtils/src/org/vadere/util/geometry/mesh/inter/IPolyConnectivity.java

@@ -33,7 +33,7 @@ public interface IPolyConnectivity<P extends IPoint, E extends IHalfEdge<P>, F e
 		return Optional.empty();
 	}
 
-	default Optional<F> locate(final IPoint point) {
+	default Optional<F> locate(final P point) {
 		return locate(point.getX(), point.getY());
 	}
 

VadereUtils/src/org/vadere/util/geometry/mesh/inter/ITriConnectivity.java

@@ -26,7 +26,7 @@ public interface ITriConnectivity<P extends IPoint, E extends IHalfEdge<P>, F ex
 
 	default void flipEdgeEvent(F f1, F f2) {}
 
-	default void insertEvent(P vertex) {};
+	default void insertEvent(E vertex) {};
 
 	boolean isIllegal(E edge);
 
@@ -381,13 +381,18 @@ public interface ITriConnectivity<P extends IPoint, E extends IHalfEdge<P>, F ex
 	}
 
 	@Override
-	default Optional<F> locate(final IPoint point) {
+	default Optional<F> locate(final P point) {
 		return this.locate(point.getX(), point.getY());
 	}
 
 	@Override
 	default Optional<F> locate(final double x, final double y) {
-		return locate(x, y, getMesh().getFace());
+		if(getMesh().getNumberOfFaces() > 0) {
+			return locate(x, y, getMesh().getFace());
+		}
+		else {
+			return Optional.empty();
+		}
 	}
 
 	/*default Optional<P> locateVertex(double x, double y, F startFace) {

VadereUtils/src/org/vadere/util/geometry/mesh/triangulations/BasePointLocator.java

@@ -26,7 +26,7 @@ import java.util.Optional;
  */
 public class BasePointLocator<P extends IPoint, E extends IHalfEdge<P>, F extends IFace<P>> implements IPointLocator<P, E, F> {
 
-	private final ITriConnectivity<P, E, F> triConnectivity;
+	private ITriConnectivity<P, E, F> triConnectivity;
 
 	public BasePointLocator(final ITriConnectivity<P, E, F> triConnectivity) {
 		this.triConnectivity = triConnectivity;
@@ -39,7 +39,7 @@ public class BasePointLocator<P extends IPoint, E extends IHalfEdge<P>, F extend
 	public void flipEdgeEvent(final F f1, final F f2) {}
 
 	@Override
-	public void insertEvent(final P vertex) {}
+	public void insertEvent(E vertex) {}
 
 	@Override
 	public void deleteBoundaryFace(final F face) {}

VadereUtils/src/org/vadere/util/geometry/mesh/triangulations/DelaunayHierarchy.java

@@ -2,24 +2,50 @@ package org.vadere.util.geometry.mesh.triangulations;
 
 import org.vadere.util.geometry.mesh.inter.IFace;
 import org.vadere.util.geometry.mesh.inter.IHalfEdge;
+import org.vadere.util.geometry.mesh.inter.IMesh;
 import org.vadere.util.geometry.mesh.inter.IPointLocator;
 import org.vadere.util.geometry.mesh.inter.ITriConnectivity;
+import org.vadere.util.geometry.mesh.inter.ITriangulation;
 import org.vadere.util.geometry.shapes.IPoint;
 
+import java.util.ArrayList;
 import java.util.Collection;
+import java.util.HashMap;
+import java.util.List;
+import java.util.Map;
 import java.util.Optional;
+import java.util.Random;
+import java.util.function.Supplier;
 
 /**
- * Created by bzoennchen on 21.04.17.
+ * @author Benedikt Zoennchen
+ *
+ * @param <P>
+ * @param <E>
+ * @param <F>
  */
 public class DelaunayHierarchy<P extends IPoint, E extends IHalfEdge<P>, F extends IFace<P>> implements IPointLocator<P, E, F>  {
 
-	//private List<ITriangulation<P, E, F>>
+	private List<ITriangulation<P, E, F>> hierarchySets;
 
-	private ITriConnectivity<P, E, F> triConnectivity;
+	private List<Map<E, E>> hierarchyConnector;
 
-	public DelaunayHierarchy(final ITriConnectivity<P, E, F> triConnectivity) {
-		this.triConnectivity = triConnectivity;
+	private ITriConnectivity<P, E, F> base;
+
+	private Supplier<ITriangulation<P, E, F>> triangulationSupplier;
+
+	private double alpha;
+
+	private Random random;
+
+	public DelaunayHierarchy(final ITriangulation<P, E, F> base, final Supplier<ITriangulation<P, E, F>> triangulationSupplier) {
+		this.hierarchySets = new ArrayList<>();
+		this.hierarchyConnector = new ArrayList<>();
+		this.random = new Random();
+		this.triangulationSupplier = triangulationSupplier;
+
+		hierarchySets.add(base);
+		hierarchyConnector.add(new HashMap<>());
 	}
 
 	@Override
@@ -29,8 +55,31 @@ public class DelaunayHierarchy<P extends IPoint, E extends IHalfEdge<P>, F exten
 	public void flipEdgeEvent(F f1, F f2) {}
 
 	@Override
-	public void insertEvent(P vertex) {
+	public void insertEvent(final E halfEdge) {
+		P vertex = base.getMesh().getVertex(halfEdge);
+		E lastEdge = halfEdge;
+		for(int i = 1; i < hierarchySets.size(); ++i) {
+
+			if(random.nextDouble() < alpha) {
+
+				if(hierarchySets.size() <= i) {
+					hierarchySets.add(triangulationSupplier.get());
+				}
+
+				E edge = hierarchySets.get(i).insert(vertex);
 
+				if(hierarchyConnector.size() < i) {
+					hierarchyConnector.add(new HashMap<>());
+				}
+
+				hierarchyConnector.get(i-1).put(lastEdge, edge);
+				lastEdge = edge;
+
+			}
+			else {
+				break;
+			}
+		}
 	}
 
 	@Override
@@ -39,12 +88,33 @@ public class DelaunayHierarchy<P extends IPoint, E extends IHalfEdge<P>, F exten
 	}
 
 	@Override
-	public Collection<F> locatePoint(IPoint point, boolean insertion) {
+	public Collection<F> locatePoint(P point, boolean insertion) {
 		return null;
 	}
 
 	@Override
-	public Optional<F> locate(IPoint point) {
-		return null;
+	public Optional<F> locate(final P point) {
+		Optional<F> optStartFace = Optional.empty();
+		for(int i = hierarchySets.size()-1; i >= 0; --i) {
+			if(!optStartFace.isPresent()) {
+				optStartFace = hierarchySets.get(i).locate(point.getX(), point.getY());
+			}
+			else {
+				E edge = getNearestPoint(hierarchySets.get(i-1), optStartFace.get(), point);
+				E newEdge = hierarchyConnector.get(i-1).get(edge);
+				optStartFace = hierarchySets.get(i).locate(point.getX(), point.getY(), hierarchySets.get(i).getMesh().getFace(newEdge));
+
+				if(!optStartFace.isPresent()) {
+					return Optional.empty();
+				}
+			}
+		}
+
+		return optStartFace;
+	}
+
+	public E getNearestPoint(final ITriangulation<P, E, F> triangulation, final F face, final P point) {
+		IMesh<P, E, F> mesh = triangulation.getMesh();
+		return triangulation.getMesh().streamEdges(face).reduce((p1, p2) -> mesh.getVertex(p1).distance(point) > mesh.getVertex(p2).distance(point) ? p2 : p1).get();
 	}
 }

VadereUtils/src/org/vadere/util/geometry/mesh/triangulations/DelaunayTree.java

@@ -24,16 +24,27 @@ public class DelaunayTree<P extends IPoint, E extends IHalfEdge<P>, F extends IF
 	private final IMesh<P, E, F> mesh;
 	private double eps = 0.0000001;
 
-	public DelaunayTree(final ITriangulation<P, E, F> triangulation, final F superTriangle) {
+	public DelaunayTree(final ITriangulation<P, E, F> triangulation) {
 		this.mesh = triangulation.getMesh();
 		this.map = new HashMap<>();
+	}
+
+	private void checkRoot() {
+		if(dag == null) {
+			F face = mesh.getFace();
 
-		this.dag = new DAG<>(new DAGElement<>(superTriangle, mesh.toTriple(superTriangle)));
-		this.map.put(superTriangle, dag);
+			if(mesh.isBoundary(face)) {
+				face = mesh.getTwinFace(mesh.getEdge(face));
+			}
+			this.dag = new DAG<>(new DAGElement<>(face, mesh.toTriple(face)));
+			this.map.put(face, dag);
+		}
 	}
 
 	@Override
-	public Collection<F> locatePoint(final IPoint point, final boolean insertion) {
+	public Collection<F> locatePoint(final P point, final boolean insertion) {
+		checkRoot();
+
 
 		Set<DAG<DAGElement<P, F>>> leafs = new HashSet<>();
 		LinkedList<DAG<DAGElement<P, F>>> nodesToVisit = new LinkedList<>();
@@ -60,7 +71,8 @@ public class DelaunayTree<P extends IPoint, E extends IHalfEdge<P>, F extends IF
 	}
 
 	@Override
-	public Optional<F> locate(final IPoint point) {
+	public Optional<F> locate(final P point) {
+		checkRoot();
 		Optional<F> optFace = locatePoint(point, false).stream().findAny();
 		if(optFace.isPresent()) {
 			return Optional.of(optFace.get());
@@ -72,6 +84,7 @@ public class DelaunayTree<P extends IPoint, E extends IHalfEdge<P>, F extends IF
 
 	@Override
 	public void splitFaceEvent(F original, F[] faces) {
+		checkRoot();
 		DAG<DAGElement<P, F>> faceDag = map.remove(original);
 		for(F face : faces) {
 			List<P> points = mesh.getVertices(face);
@@ -83,6 +96,7 @@ public class DelaunayTree<P extends IPoint, E extends IHalfEdge<P>, F extends IF
 
 	@Override
 	public void flipEdgeEvent(final F f1, final F f2) {
+		checkRoot();
 		DAG<DAGElement<P, F>> f1Dag = map.remove(f1);
 		DAG<DAGElement<P, F>> f2Dag = map.remove(f2);
 		List<P> points1 = mesh.getVertices(f1);
@@ -102,10 +116,11 @@ public class DelaunayTree<P extends IPoint, E extends IHalfEdge<P>, F extends IF
 	}
 
 	@Override
-	public void insertEvent(P vertex) {}
+	public void insertEvent(E vertex) {}
 
 	@Override
 	public void deleteBoundaryFace(F face) {
+		checkRoot();
 		assert mesh.isBoundary(face);
 		map.remove(face);
 	}

VadereUtils/src/org/vadere/util/geometry/mesh/triangulations/IncrementalTriangulation.java

@@ -3,7 +3,7 @@ package org.vadere.util.geometry.mesh.triangulations;
 import org.apache.commons.collections.IteratorUtils;
 import org.apache.log4j.LogManager;
 import org.apache.log4j.Logger;
-import org.jetbrains.annotations.NotNull;
+import org.vadere.util.geometry.GeometryUtils;
 import org.vadere.util.geometry.mesh.impl.PFace;
 import org.vadere.util.geometry.mesh.iterators.FaceIterator;
 import org.vadere.util.geometry.mesh.inter.IFace;
@@ -51,11 +51,13 @@ public class IncrementalTriangulation<P extends IPoint, E extends IHalfEdge<P>,
 	private E he0;
 	private E he1;
 	private E he2;
-	private P p_max;
-	private P p_min;
-	private boolean finalized;
+	private final VRectangle bound;
+	private boolean finalized = false;
 	private IMesh<P, E, F> mesh;
 	private IPointLocator<P, E, F> pointLocator;
+	private boolean initialized = false;
+
+	// TODO this epsilon it hard coded!!! => replace it with a user choice
 	private double epsilon = 0.0001;
 
 	protected F superTriangle;
@@ -64,48 +66,43 @@ public class IncrementalTriangulation<P extends IPoint, E extends IHalfEdge<P>,
 	private static Logger log = LogManager.getLogger(IncrementalTriangulation.class);
 
 	public IncrementalTriangulation(
-			final IMesh<P, E, F> mesh,
 			final Set<P> points,
 			final Predicate<E> illegalPredicate) {
-		this.mesh = mesh;
 		this.points = points;
 		this.illegalPredicate = illegalPredicate;
-		P p_max = points.parallelStream().reduce(mesh.createVertex(Double.MIN_VALUE, Double.MIN_VALUE), (a, b) -> mesh.createVertex(Math.max(a.getX(), b.getX()), Math.max(a.getY(), b.getY())));
-		P p_min = points.parallelStream().reduce(mesh.createVertex(Double.MIN_VALUE, Double.MIN_VALUE), (a, b) -> mesh.createVertex(Math.min(a.getX(), b.getX()), Math.min(a.getY(), b.getY())));
-		init(p_max, p_min);
+		this.bound = GeometryUtils.bound(points);
 	}
 
-	public IncrementalTriangulation(final IMesh<P, E, F> mesh, final Set<P> points) {
-		this(mesh, points, halfEdge -> true);
+	public IncrementalTriangulation(final Set<P> points) {
+		this(points, halfEdge -> true);
 	}
 
 	public IncrementalTriangulation(
-			final IMesh<P, E, F> mesh,
-			final double minX,
-			final double minY,
-			final double width,
-			final double height,
+			final VRectangle bound,
 			final Predicate<E> illegalPredicate) {
-		this.mesh = mesh;
 		this.points = new HashSet<>();
 		this.illegalPredicate = illegalPredicate;
-		this.p_max = mesh.createVertex(minX + width, minY + height);
-		this.p_min = mesh.createVertex(minX, minY);
-		init(p_max, p_min);
+		this.bound = bound;
 	}
 
-	public IncrementalTriangulation(
-			final IMesh<P, E, F> mesh,
-			final double minX,
-			final double minY,
-			final double width,
-			final double height) {
-		this(mesh, minX, minY, width, height, halfEdge -> true);
+	public IncrementalTriangulation(final VRectangle bound) {
+		this(bound, halfEdge -> true);
+	}
+
+	public void setPointLocator(final IPointLocator<P, E, F> pointLocator) {
+		this.pointLocator = pointLocator;
+	}
+
+	public void setMesh(final IMesh<P, E, F> mesh) {
+		this.mesh = mesh;
 	}
 
-	private void init(final P p_max, final P p_min) {
-		VRectangle bound = new VRectangle(p_min.getX(), p_min.getY(), p_max.getX()-p_min.getX(), p_max.getY()- p_min.getY());
+	public F getSuperTriangle() {
+		return superTriangle;
+	}
 
+	@Override
+	public void init() {
 		double gap = 1.0;
 		double max = Math.max(bound.getWidth(), bound.getHeight())*2;
 		p0 = mesh.insertVertex(bound.getX() - max - gap, bound.getY() - gap);
@@ -120,14 +117,15 @@ public class IncrementalTriangulation<P extends IPoint, E extends IHalfEdge<P>,
 		he1 = borderEdges.get(1);
 		he2 = borderEdges.get(2);
 
-	//	this.pointLocator = IPointLocator.createDelaunayTree(this, superTriangle);
-		this.pointLocator = IPointLocator.createBaseLocator(this);
 		this.finalized = false;
+		this.initialized = true;
 	}
 
 
 	@Override
 	public void compute() {
+		init();
+
 		// 1. insert points
 		for(P p : points) {
 			insert(p);
@@ -155,14 +153,16 @@ public class IncrementalTriangulation<P extends IPoint, E extends IHalfEdge<P>,
 			F face = faces.iterator().next();
 			splitTriangle(face, point,  true);
 			insertedEdge = mesh.getEdge(point);
+			insertEvent(insertedEdge);
 
 		} // point lies on an edge of 2 triangles
 		else if(faces.size() == 2) {
 			Iterator<F> it = faces.iterator();
 			log.info("splitEdge:" + point);
 			E halfEdge = findTwins(it.next(), it.next()).get();
-			splitEdge(point, halfEdge, true);
-			insertedEdge = mesh.getEdge(point);
+			List<E> newEdges = splitEdge(point, halfEdge, true);
+			insertedEdge = newEdges.stream().filter(he -> getMesh().getVertex(he).equals(point)).findAny().get();
+			insertEvent(insertedEdge);
 		}
 		else if(faces.size() == 0) {
 			log.warn("ignore insertion point, since the point " + point + " already exists or it is too close to another point!");
@@ -174,6 +174,18 @@ public class IncrementalTriangulation<P extends IPoint, E extends IHalfEdge<P>,
 		return insertedEdge;
 	}
 
+	@Override
+	public void insert(final Set<P> points) {
+		if(!initialized) {
+			init();
+		}
+
+		// 1. insert points
+		for(P p : points) {
+			insert(p);
+		}
+	}
+
 	/**
 	 * Removes the super triangle from the mesh data structure.
 	 */
@@ -282,7 +294,7 @@ public class IncrementalTriangulation<P extends IPoint, E extends IHalfEdge<P>,
 	}
 
 	@Override
-	public Optional<F> locate(final IPoint point) {
+	public Optional<F> locate(final P point) {
 		return pointLocator.locate(point);
 	}
 
@@ -296,6 +308,11 @@ public class IncrementalTriangulation<P extends IPoint, E extends IHalfEdge<P>,
 		return stream();
 	}
 
+	@Override
+	public Stream<VTriangle> streamTriangles() {
+		return stream().map(f -> getMesh().toTriangle(f));
+	}
+
 	@Override
 	public void remove(P point) {
 		throw new UnsupportedOperationException("not jet implemented.");
@@ -341,9 +358,7 @@ public class IncrementalTriangulation<P extends IPoint, E extends IHalfEdge<P>,
 			P x = mesh.getVertex(t0);
 			P y = mesh.getVertex(t1);
 			P z = mesh.getVertex(t2);
-			if(x.equals(y)) {
-				System.out.print("error");
-			}
+
 			VTriangle triangle = new VTriangle(new VPoint(x), new VPoint(y), new VPoint(z));
 			return triangle.isInCircumscribedCycle(p);
 		}
@@ -374,8 +389,8 @@ public class IncrementalTriangulation<P extends IPoint, E extends IHalfEdge<P>,
 	}
 
 	@Override
-	public void insertEvent(final P vertex) {
-		pointLocator.insertEvent(vertex);
+	public void insertEvent(final E halfEdge) {
+		pointLocator.insertEvent(halfEdge);
 	}
 
 	@Override
@@ -408,8 +423,13 @@ public class IncrementalTriangulation<P extends IPoint, E extends IHalfEdge<P>,
 
 		IPointConstructor<VPoint> pointConstructor =  (x, y) -> new VPoint(x, y);
 		long ms = System.currentTimeMillis();
-		IncrementalTriangulation<VPoint, PHalfEdge<VPoint>, PFace<VPoint>> bw = new IncrementalTriangulation<>(new PMesh<>(pointConstructor), points);
+
+		PMesh<VPoint> mesh = new PMesh<>(pointConstructor);
+		IncrementalTriangulation<VPoint, PHalfEdge<VPoint>, PFace<VPoint>> bw = new IncrementalTriangulation<>(points);
+		bw.setMesh(mesh);
+		bw.setPointLocator(new DelaunayTree<>(bw));
 		bw.compute();
+
 		Set<VLine> edges = bw.getEdges();
 		edges.addAll(bw.getTriangles().stream().map(triangle -> new VLine(triangle.getIncenter(), triangle.p1)).collect(Collectors.toList()));
 		System.out.println(System.currentTimeMillis() - ms);
@@ -433,9 +453,13 @@ public class IncrementalTriangulation<P extends IPoint, E extends IHalfEdge<P>,
 		window2.getContentPane().add(new Lines(edges2, points, max));
 		window2.setVisible(true);
 
-		UniformTriangulation<VPoint, PHalfEdge<VPoint>, PFace<VPoint>> uniformTriangulation = new UniformTriangulation<>(new PMesh<>(pointConstructor),0, 0, width, height, 10.0);
+		UniformTriangulation<VPoint, PHalfEdge<VPoint>, PFace<VPoint>> uniformTriangulation = ITriangulation.createUnifirmTriangulation(
+				IPointLocator.Type.DELAUNAY_TREE,
+				new VRectangle(0, 0, width, height),
+				10.0,
+				(x, y) -> new VPoint(x, y));
+
 		uniformTriangulation.compute();
-		uniformTriangulation.finalize();
 		Set<VLine> edges3 = uniformTriangulation.getEdges();
 
 		JFrame window3 = new JFrame();
@@ -444,7 +468,12 @@ public class IncrementalTriangulation<P extends IPoint, E extends IHalfEdge<P>,
 		window3.getContentPane().add(new Lines(edges3, edges3.stream().flatMap(edge -> edge.streamPoints()).collect(Collectors.toSet()), max));
 		window3.setVisible(true);
 
-		UniformRefinementTriangulation<VPoint, PHalfEdge<VPoint>, PFace<VPoint>> uniformRefinement = new UniformRefinementTriangulation<>(new PMesh<>(pointConstructor), 0, 0, width, height, Arrays.asList(new VRectangle(200, 200, 100, 200)), p -> 10.0);
+		UniformRefinementTriangulation<VPoint> uniformRefinement = new UniformRefinementTriangulation<>(
+				new VRectangle(0, 0, width, height),
+				Arrays.asList(new VRectangle(200, 200, 100, 200)),
+				p -> 10.0,
+				(x, y) -> new VPoint(x, y));
+
 		uniformRefinement.compute();
 		Set<VLine> edges4 = uniformRefinement.getEdges();
 

VadereUtils/src/org/vadere/util/geometry/mesh/triangulations/UniformRefinementTriangulation.java

@@ -2,9 +2,11 @@ package org.vadere.util.geometry.mesh.triangulations;
 
 import org.apache.log4j.LogManager;
 import org.apache.log4j.Logger;
-import org.vadere.util.geometry.mesh.inter.IFace;
-import org.vadere.util.geometry.mesh.inter.IHalfEdge;
+import org.vadere.util.geometry.mesh.impl.PFace;
+import org.vadere.util.geometry.mesh.impl.PHalfEdge;
 import org.vadere.util.geometry.mesh.inter.IMesh;
+import org.vadere.util.geometry.mesh.inter.IPointLocator;
+import org.vadere.util.geometry.mesh.inter.ITriangulation;
 import org.vadere.util.geometry.shapes.IPoint;