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diff --git a/src/main/java/org/apache/commons/math3/geometry/spherical/oned/S1Point.java b/src/main/java/org/apache/commons/math3/geometry/spherical/oned/S1Point.java
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+/*
+ * 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.oned;
+
+import org.apache.commons.math3.geometry.Point;
+import org.apache.commons.math3.geometry.Space;
+import org.apache.commons.math3.geometry.euclidean.twod.Vector2D;
+import org.apache.commons.math3.util.FastMath;
+import org.apache.commons.math3.util.MathUtils;
+
+/** This class represents a point on the 1-sphere.
+ * <p>Instances of this class are guaranteed to be immutable.</p>
+ * @since 3.3
+ */
+public class S1Point implements Point<Sphere1D> {
+
+   // CHECKSTYLE: stop ConstantName
+    /** A vector with all coordinates set to NaN. */
+    public static final S1Point NaN = new S1Point(Double.NaN, Vector2D.NaN);
+    // CHECKSTYLE: resume ConstantName
+
+    /** Serializable UID. */
+    private static final long serialVersionUID = 20131218L;
+
+    /** Azimuthal angle \( \alpha \). */
+    private final double alpha;
+
+    /** Corresponding 2D normalized vector. */
+    private final Vector2D vector;
+
+    /** Simple constructor.
+     * Build a vector from its coordinates
+     * @param alpha azimuthal angle \( \alpha \)
+     * @see #getAlpha()
+     */
+    public S1Point(final double alpha) {
+        this(MathUtils.normalizeAngle(alpha, FastMath.PI),
+             new Vector2D(FastMath.cos(alpha), FastMath.sin(alpha)));
+    }
+
+    /** Build a point from its internal components.
+     * @param alpha azimuthal angle \( \alpha \)
+     * @param vector corresponding vector
+     */
+    private S1Point(final double alpha, final Vector2D vector) {
+        this.alpha  = alpha;
+        this.vector = vector;
+    }
+
+    /** Get the azimuthal angle \( \alpha \).
+     * @return azimuthal angle \( \alpha \)
+     * @see #S1Point(double)
+     */
+    public double getAlpha() {
+        return alpha;
+    }
+
+    /** Get the corresponding normalized vector in the 2D euclidean space.
+     * @return normalized vector
+     */
+    public Vector2D getVector() {
+        return vector;
+    }
+
+    /** {@inheritDoc} */
+    public Space getSpace() {
+        return Sphere1D.getInstance();
+    }
+
+    /** {@inheritDoc} */
+    public boolean isNaN() {
+        return Double.isNaN(alpha);
+    }
+
+    /** {@inheritDoc} */
+    public double distance(final Point<Sphere1D> point) {
+        return distance(this, (S1Point) point);
+    }
+
+    /** Compute the distance (angular separation) between two points.
+     * @param p1 first vector
+     * @param p2 second vector
+     * @return the angular separation between p1 and p2
+     */
+    public static double distance(S1Point p1, S1Point p2) {
+        return Vector2D.angle(p1.vector, p2.vector);
+    }
+
+    /**
+     * Test for the equality of two points on the 2-sphere.
+     * <p>
+     * If all coordinates of two points are exactly the same, and none are
+     * <code>Double.NaN</code>, the two points are considered to be equal.
+     * </p>
+     * <p>
+     * <code>NaN</code> coordinates are considered to affect globally the vector
+     * and be equals to each other - i.e, if either (or all) coordinates of the
+     * 2D vector are equal to <code>Double.NaN</code>, the 2D vector is equal to
+     * {@link #NaN}.
+     * </p>
+     *
+     * @param other Object to test for equality to this
+     * @return true if two points on the 2-sphere objects are equal, false if
+     *         object is null, not an instance of S2Point, or
+     *         not equal to this S2Point instance
+     *
+     */
+    @Override
+    public boolean equals(Object other) {
+
+        if (this == other) {
+            return true;
+        }
+
+        if (other instanceof S1Point) {
+            final S1Point rhs = (S1Point) other;
+            if (rhs.isNaN()) {
+                return this.isNaN();
+            }
+
+            return alpha == rhs.alpha;
+        }
+
+        return false;
+
+    }
+
+    /**
+     * Get a hashCode for the 2D vector.
+     * <p>
+     * All NaN values have the same hash code.</p>
+     *
+     * @return a hash code value for this object
+     */
+    @Override
+    public int hashCode() {
+        if (isNaN()) {
+            return 542;
+        }
+        return 1759 * MathUtils.hash(alpha);
+    }
+
+}