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diff --git a/src/main/java/org/apache/commons/math3/geometry/spherical/twod/Vertex.java b/src/main/java/org/apache/commons/math3/geometry/spherical/twod/Vertex.java
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@@ -0,0 +1,124 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math3.geometry.spherical.twod;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/** Spherical polygons boundary vertex.
+ * @see SphericalPolygonsSet#getBoundaryLoops()
+ * @see Edge
+ * @since 3.3
+ */
+public class Vertex {
+
+    /** Vertex location. */
+    private final S2Point location;
+
+    /** Incoming edge. */
+    private Edge incoming;
+
+    /** Outgoing edge. */
+    private Edge outgoing;
+
+    /** Circles bound with this vertex. */
+    private final List<Circle> circles;
+
+    /** Build a non-processed vertex not owned by any node yet.
+     * @param location vertex location
+     */
+    Vertex(final S2Point location) {
+        this.location = location;
+        this.incoming = null;
+        this.outgoing = null;
+        this.circles  = new ArrayList<Circle>();
+    }
+
+    /** Get Vertex location.
+     * @return vertex location
+     */
+    public S2Point getLocation() {
+        return location;
+    }
+
+    /** Bind a circle considered to contain this vertex.
+     * @param circle circle to bind with this vertex
+     */
+    void bindWith(final Circle circle) {
+        circles.add(circle);
+    }
+
+    /** Get the common circle bound with both the instance and another vertex, if any.
+     * <p>
+     * When two vertices are both bound to the same circle, this means they are
+     * already handled by node associated with this circle, so there is no need
+     * to create a cut hyperplane for them.
+     * </p>
+     * @param vertex other vertex to check instance against
+     * @return circle bound with both the instance and another vertex, or null if the
+     * two vertices do not share a circle yet
+     */
+    Circle sharedCircleWith(final Vertex vertex) {
+        for (final Circle circle1 : circles) {
+            for (final Circle circle2 : vertex.circles) {
+                if (circle1 == circle2) {
+                    return circle1;
+                }
+            }
+        }
+        return null;
+    }
+
+    /** Set incoming edge.
+     * <p>
+     * The circle supporting the incoming edge is automatically bound
+     * with the instance.
+     * </p>
+     * @param incoming incoming edge
+     */
+    void setIncoming(final Edge incoming) {
+        this.incoming = incoming;
+        bindWith(incoming.getCircle());
+    }
+
+    /** Get incoming edge.
+     * @return incoming edge
+     */
+    public Edge getIncoming() {
+        return incoming;
+    }
+
+    /** Set outgoing edge.
+     * <p>
+     * The circle supporting the outgoing edge is automatically bound
+     * with the instance.
+     * </p>
+     * @param outgoing outgoing edge
+     */
+    void setOutgoing(final Edge outgoing) {
+        this.outgoing = outgoing;
+        bindWith(outgoing.getCircle());
+    }
+
+    /** Get outgoing edge.
+     * @return outgoing edge
+     */
+    public Edge getOutgoing() {
+        return outgoing;
+    }
+
+}