diff --git a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix1.java b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix1.java
index 8504238..ff93401 100644
--- a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix1.java
+++ b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix1.java
@@ -30,7 +30,7 @@
  * └     ┘</pre></blockquote>
  *
  * @author  Martin Desruisseaux (IRD, Geomatys)
- * @version 0.4
+ * @version 1.1
  *
  * @see Matrix2
  * @see Matrix3
@@ -39,8 +39,7 @@
  * @since 0.4
  * @module
  */
-@SuppressWarnings("CloneableClassWithoutClone")             // No field in this class needs clone.
-public final class Matrix1 extends MatrixSIS {
+public class Matrix1 extends MatrixSIS {
     /**
      * Serial number for inter-operability with different versions.
      */
@@ -260,6 +259,14 @@
     }
 
     /**
+     * {@inheritDoc}
+     */
+    @Override
+    public Matrix1 clone() {
+        return (Matrix1) super.clone();
+    }
+
+    /**
      * Returns {@code true} if the specified object is of type {@code Matrix1} and
      * all of the data members are equal to the corresponding data members in this matrix.
      *
@@ -268,7 +275,7 @@
      */
     @Override
     public boolean equals(final Object object) {
-        if (object instanceof Matrix1) {
+        if (object != null && object.getClass() == getClass()) {
             final Matrix1 that = (Matrix1) object;
             return Numerics.equals(m00, that.m00);
         }
diff --git a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix2.java b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix2.java
index 04e0f51..c3f455a 100644
--- a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix2.java
+++ b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix2.java
@@ -31,7 +31,7 @@
  * └         ┘</pre></blockquote>
  *
  * @author  Martin Desruisseaux (IRD, Geomatys)
- * @version 0.4
+ * @version 1.1
  *
  * @see Matrix1
  * @see Matrix3
@@ -40,8 +40,7 @@
  * @since 0.4
  * @module
  */
-@SuppressWarnings("CloneableClassWithoutClone")             // No field in this class needs clone.
-public final class Matrix2 extends MatrixSIS {
+public class Matrix2 extends MatrixSIS {
     /**
      * Serial number for inter-operability with different versions.
      */
@@ -284,6 +283,14 @@
     }
 
     /**
+     * {@inheritDoc}
+     */
+    @Override
+    public Matrix2 clone() {
+        return (Matrix2) super.clone();
+    }
+
+    /**
      * Returns {@code true} if the specified object is of type {@code Matrix2} and
      * all of the data members are equal to the corresponding data members in this matrix.
      *
@@ -292,7 +299,7 @@
      */
     @Override
     public boolean equals(final Object object) {
-        if (object instanceof Matrix2) {
+        if (object != null && object.getClass() == getClass()) {
             final Matrix2 that = (Matrix2) object;
             return Numerics.equals(this.m00, that.m00) &&
                    Numerics.equals(this.m01, that.m01) &&
diff --git a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix3.java b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix3.java
index 6edfb8f..d246bc0 100644
--- a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix3.java
+++ b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix3.java
@@ -30,7 +30,7 @@
  * └             ┘</pre></blockquote>
  *
  * @author  Martin Desruisseaux (IRD, Geomatys)
- * @version 0.6
+ * @version 1.1
  *
  * @see Matrix1
  * @see Matrix2
@@ -39,8 +39,7 @@
  * @since 0.4
  * @module
  */
-@SuppressWarnings("CloneableClassWithoutClone")             // No field in this class needs clone.
-public final class Matrix3 extends MatrixSIS {
+public class Matrix3 extends MatrixSIS {
     /**
      * Serial number for inter-operability with different versions.
      */
@@ -298,4 +297,12 @@
         swap = m02; m02 = m20; m20 = swap;
         swap = m12; m12 = m21; m21 = swap;
     }
+
+    /**
+     * {@inheritDoc}
+     */
+    @Override
+    public Matrix3 clone() {
+        return (Matrix3) super.clone();
+    }
 }
diff --git a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix4.java b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix4.java
index 8093b87..2f14f39 100644
--- a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix4.java
+++ b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/Matrix4.java
@@ -31,7 +31,7 @@
  * └                 ┘</pre></blockquote>
  *
  * @author  Martin Desruisseaux (IRD, Geomatys)
- * @version 0.6
+ * @version 1.1
  *
  * @see Matrix1
  * @see Matrix2
@@ -40,8 +40,7 @@
  * @since 0.4
  * @module
  */
-@SuppressWarnings("CloneableClassWithoutClone")             // No field in this class needs clone.
-public final class Matrix4 extends MatrixSIS {
+public class Matrix4 extends MatrixSIS {
     /**
      * Serial number for inter-operability with different versions.
      */
@@ -336,4 +335,12 @@
         swap = m13; m13 = m31; m31 = swap;
         swap = m23; m23 = m32; m32 = swap;
     }
+
+    /**
+     * {@inheritDoc}
+     */
+    @Override
+    public Matrix4 clone() {
+        return (Matrix4) super.clone();
+    }
 }
diff --git a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/package-info.java b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/package-info.java
index 0005bb1..db87112 100644
--- a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/package-info.java
+++ b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/matrix/package-info.java
@@ -69,7 +69,7 @@
  * Like SIS, Vecmath is optimized for small matrices of interest for 2D and 3D graphics.</p>
  *
  * @author  Martin Desruisseaux (IRD, Geomatys)
- * @version 0.8
+ * @version 1.1
  * @since   0.4
  * @module
  */
diff --git a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/Inverter.java b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/Inverter.java
new file mode 100644
index 0000000..d928119
--- /dev/null
+++ b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/Inverter.java
@@ -0,0 +1,105 @@
+/*
+ * 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.sis.referencing.operation.projection;
+
+import org.apache.sis.internal.referencing.Resources;
+import org.apache.sis.referencing.operation.matrix.Matrix2;
+
+import static java.lang.Math.abs;
+
+
+/**
+ * A temporary Jacobian matrix where to write the derivative of a forward projection.
+ * This Jacobian matrix is used for calculation of inverse projection when no inverse
+ * formulas is available, or when the inverse formula is too approximate (for example
+ * because eccentricity is too high). This class processes as below:
+ *
+ * <ol>
+ *   <li>Given a first estimation of (λ,φ), compute the forward projection (x′,y′)
+ *       for that estimation together with the Jacobian matrix at that position.</li>
+ *   <li>Compute the errors compared to the specified (x,y) values.</li>
+ *   <li>Convert that (Δx,Δy) error into a (Δλ,Δφ) error using the inverse of the Jacobian matrix.</li>
+ *   <li>Correct (λ,φ) and continue iteratively until the error is small enough.</li>
+ * </ol>
+ *
+ * This algorithm described in EPSG guidance note for {@link Orthographic} projection
+ * but can be applied to any map projection, not only orthographic.
+ *
+ * <p>This algorithm is defined in a {@link Matrix2} subclass for allowing map projection
+ * implementations to use {@code if (derivative instanceof Inverter)} check for detecting
+ * when a {@code transform} method is invoked for the purpose of an inverse projection.</p>
+ *
+ * @author  Martin Desruisseaux (Geomatys)
+ * @version 1.1
+ *
+ * @ee <a href="https://issues.apache.org/jira/browse/SIS-478">SIS-478</a>
+ *
+ * @since 1.1
+ * @module
+ */
+@SuppressWarnings({"CloneableClassWithoutClone", "serial"})
+final class Inverter extends Matrix2 {
+    /**
+     * Creates a new matrix initialized to identity.
+     */
+    Inverter() {
+    }
+
+    /**
+     * Computes the inverse of the given projection. Before this method is invoked,
+     * the {@code dstPts[dstOff]} and {@code dstPts[dstOff+1]} array elements must
+     * contain the initial λ and φ estimations respectively. After method returns,
+     * the same array elements contain the refined λ and φ values.
+     *
+     * <p>Note: restricted to {@link Orthographic} projection for now,
+     * but may be generalized to any projection in a future version.</p>
+     *
+     * @param  projection  the forward projection for which to compute an inverse projection.
+     * @param  x           the  easting value from {@code srcPts[srcOff]}.
+     * @param  y           the northing value from {@code srcPts[srcOff+1]}.
+     * @param  dstPts      the array where to refine the (λ,φ) values.
+     * @param  dstOff      index of the λ element in the {@code dstPts} array.
+     * @throws ProjectionException if the iterative algorithm does not converge.
+     */
+    final void inverseTransform(final Orthographic projection, final double x, final double y,
+            final double[] dstPts, final int dstOff) throws ProjectionException
+    {
+        double λ = dstPts[dstOff  ];
+        double φ = dstPts[dstOff+1];
+        for (int it=NormalizedProjection.MAXIMUM_ITERATIONS; --it >= 0;) {
+            final double cosφ = projection.transform(dstPts, dstOff, dstPts, dstOff, this);
+            final double ΔE   = x - dstPts[dstOff  ];
+            final double ΔN   = y - dstPts[dstOff+1];
+            final double D    = (m01 * m10) - (m00 * m11);    // Determinant.
+            final double Δλ   = (m01*ΔN - m11*ΔE) / D;
+            final double Δφ   = (m10*ΔE - m00*ΔN) / D;
+            dstPts[dstOff  ]  = λ += Δλ;
+            dstPts[dstOff+1]  = φ += Δφ;
+            /*
+             * Following condition uses ! for stopping iteration on NaN values.
+             * We do not use Math.max(…) because we want to check NaN separately
+             * for φ and λ.
+             */
+            if (!(abs(Δφ)      > NormalizedProjection.ANGULAR_TOLERANCE ||
+                  abs(Δλ*cosφ) > NormalizedProjection.ANGULAR_TOLERANCE))
+            {
+                return;
+            }
+        }
+        throw new ProjectionException(Resources.format(Resources.Keys.NoConvergence));
+    }
+}
diff --git a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/Orthographic.java b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/Orthographic.java
index 9e3d024..87b9705 100644
--- a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/Orthographic.java
+++ b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/Orthographic.java
@@ -25,7 +25,6 @@
 import org.apache.sis.referencing.operation.matrix.Matrix2;
 import org.apache.sis.referencing.operation.matrix.MatrixSIS;
 import org.apache.sis.referencing.operation.transform.ContextualParameters;
-import org.apache.sis.internal.referencing.Resources;
 import org.apache.sis.util.ComparisonMode;
 import org.apache.sis.util.Workaround;
 
@@ -150,13 +149,16 @@
      * <div class="note"><b>Implementation note:</b>
      * in other map projections, we use a different class for ellipsoidal formulas.
      * But the orthographic projection is a bit different; for this one it is more
-     * convenient to use a flag.</div>
+     * convenient to use {@code if} statements.</div>
      *
+     * @param  derivative  where to store the Jacobian matrix, or {@code null} if none.
+     *         If this matrix is an {@link Inverter} instance, we take that as a flag
+     *         meaning to not set out-of-range results to NaN.
      * @return {@code cos(φ)}, useful for error tolerance check.
      */
-    private double transform(final double[] srcPts, final int srcOff,
-                             final double[] dstPts, final int dstOff,
-                             final Matrix2 derivative)
+    final double transform(final double[] srcPts, final int srcOff,
+                           final double[] dstPts, final int dstOff,
+                           final Matrix2 derivative)
     {
         final double λ    = srcPts[srcOff  ];
         final double φ    = srcPts[srcOff+1];
@@ -174,7 +176,7 @@
          * then the point is on the opposite hemisphere and should be clipped.
          */
         double rν;
-        if (cosc >= 0) {
+        if (cosc >= 0 || derivative instanceof Inverter) {
             x  = cosφ * sinλ;                           // Snyder (20-3)
             y  = mℯ2_cosφ0*sinφ - sinφ0*cosφ_cosλ;      // Snyder (20-4) × (1 – ℯ²)
             rν = 1;
@@ -203,7 +205,7 @@
             derivative.m00 =  cosφ_cosλ / rν;                           // ∂E/∂λ
             derivative.m01 = -sinφ*sinλ * ρ;                            // ∂E/∂φ
             derivative.m10 =  sinφ0 * x;                                // ∂N/∂λ
-            derivative.m11 = (cosφ0 * cosφ + sinφ0_sinφ*cosλ) * ρ;      // ∂N/∂φ
+            derivative.m11 = (cosφ0*cosφ + sinφ0_sinφ*cosλ) * ρ;        // ∂N/∂φ
         }
         return cosφ;
     }
@@ -238,29 +240,9 @@
              *
              * See https://issues.apache.org/jira/browse/SIS-478
              */
-            final Matrix2 J = new Matrix2();                    // Jacobian matrix.
-            double λ = dstPts[dstOff  ];
-            double φ = dstPts[dstOff+1];
-            for (int it=0; it<MAXIMUM_ITERATIONS; it++) {
-                final double cosφ = transform(dstPts, dstOff, dstPts, dstOff, J);
-                final double ΔE   = x - dstPts[dstOff  ];
-                final double ΔN   = y - dstPts[dstOff+1];
-                final double D    = (J.m01 * J.m10) - (J.m00 * J.m11);    // Determinant.
-                final double Δλ   = (J.m01*ΔN - J.m11*ΔE) / D;
-                final double Δφ   = (J.m10*ΔE - J.m00*ΔN) / D;
-                dstPts[dstOff  ]  = λ += Δλ;
-                dstPts[dstOff+1]  = φ += Δφ;
-                /*
-                 * Following condition uses ! for stopping iteration on NaN values.
-                 * We do not use Math.max(…) because we want to check NaN separately
-                 * for φ and λ.
-                 */
-                if (!(abs(Δφ) > ANGULAR_TOLERANCE || abs(cosφ*abs(Δλ)) > ANGULAR_TOLERANCE)) {
-                    dstPts[dstOff] = IEEEremainder(dstPts[dstOff], PI);
-                    return;
-                }
-            }
-            throw new ProjectionException(Resources.format(Resources.Keys.NoConvergence));
+            final Inverter j = new Inverter();                      // Jacobian matrix.
+            j.inverseTransform(this, x, y, dstPts, dstOff);
+            dstPts[dstOff] = IEEEremainder(dstPts[dstOff], PI);
         }
     }
 
diff --git a/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/OrthographicTest.java b/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/OrthographicTest.java
index 42fc7c5..434d55b 100644
--- a/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/OrthographicTest.java
+++ b/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/OrthographicTest.java
@@ -16,6 +16,7 @@
  */
 package org.apache.sis.referencing.operation.projection;
 
+import org.opengis.util.FactoryException;
 import org.opengis.referencing.operation.TransformException;
 import org.apache.sis.referencing.operation.transform.CoordinateDomain;
 import org.apache.sis.internal.referencing.provider.MapProjection;
@@ -144,4 +145,18 @@
         verifyInDomain(CoordinateDomain.GEOGRAPHIC_RADIANS_SOUTH, 753524735);
         verifyDerivative(toRadians(5), toRadians(-85));
     }
+
+    /**
+     * Tests the <cite>"Orthographic"</cite> (EPSG:9840) projection method.
+     * This test is defined in GeoAPI conformance test suite.
+     *
+     * @throws FactoryException if an error occurred while creating the map projection.
+     * @throws TransformException if an error occurred while projecting a coordinate.
+     *
+     * @see org.opengis.test.referencing.ParameterizedTransformTest#testOrthographic()
+     */
+    @Test
+    public void runGeoapiTest() throws FactoryException, TransformException {
+        createGeoApiTest(new org.apache.sis.internal.referencing.provider.Orthographic()).testOrthographic();
+    }
 }