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new 9566eb7 Add skeleton base class for meridional distance calculation
on ellipsoid. Add formulas to be used as reference in the test class (the
formula actually used by implementation may differ).
https://issues.apache.org/jira/browse/SIS-450
9566eb7 is described below
commit 9566eb7e7894483da943682782124e19f9895d1c
Author: Martin Desruisseaux <[email protected]>
AuthorDate: Mon Apr 22 17:54:28 2019 +0200
Add skeleton base class for meridional distance calculation on ellipsoid.
Add formulas to be used as reference in the test class (the formula
actually used by implementation may differ).
https://issues.apache.org/jira/browse/SIS-450
---
.../projection/MeridionalDistanceBased.java | 95 ++++++++++++++++
.../operation/projection/Sinusoidal.java | 2 +-
.../projection/MeridionalDistanceTest.java | 125 +++++++++++++++++++++
.../operation/projection/SinusoidalTest.java | 2 +-
.../sis/test/suite/ReferencingTestSuite.java | 1 +
5 files changed, 223 insertions(+), 2 deletions(-)
diff --git
a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/MeridionalDistanceBased.java
b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/MeridionalDistanceBased.java
new file mode 100644
index 0000000..0d2b2ed
--- /dev/null
+++
b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/MeridionalDistanceBased.java
@@ -0,0 +1,95 @@
+/*
+ * 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 java.io.IOException;
+import java.io.ObjectInputStream;
+
+
+/**
+ * Base class of map projections based on distance along the meridian from
equator to latitude φ.
+ *
+ * @author Martin Desruisseaux (MPO, IRD, Geomatys)
+ * @author Rémi Maréchal (Geomatys)
+ * @version 1.0
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Meridian_arc";>Meridian arc on
Wikipedia</a>
+ *
+ * @since 1.0
+ * @module
+ */
+abstract class MeridionalDistanceBased extends NormalizedProjection {
+ /**
+ * {@code false} for using the original formulas as published by EPSG, or
{@code true} for using formulas
+ * modified using trigonometric identities. Use of trigonometric
identities reduces the amount of calls to
+ * {@link Math#sin(double)} and similar methods. Snyder 3-34 to 3-39 give
the following identities:
+ *
+ * <pre>
+ * If: f(φ) = A⋅sin(2φ) + B⋅sin(4φ) + C⋅sin(6φ) + D⋅sin(8φ)
+ * Then: f(φ) = sin(2φ)⋅(A′ + cos(2φ)⋅(B′ + cos(2φ)⋅(C′ +
D′⋅cos(2φ))))
+ * Where: A′ = A - C
+ * B′ = 2B - 4D
+ * C′ = 4C
+ * D′ = 8D
+ * </pre>
+ *
+ * Similar, but with cosine instead than sin and the addition of a
constant:
+ *
+ * <pre>
+ * If: f(φ) = A + B⋅cos(2φ) + C⋅cos(4φ) + D⋅cos(6φ) + E⋅cos(8φ)
+ * Then: f(φ) = A′ + cos(2φ)⋅(B′ + cos(2φ)⋅(C′ + cos(2φ)⋅(D′ +
E′⋅cos(2φ))))
+ * Where: A′ = A - C + E
+ * B′ = B - 3D
+ * C′ = 2C - 8E
+ * D′ = 4D
+ * E′ = 8E
+ * </pre>
+ */
+ private static final boolean ALLOW_TRIGONOMETRIC_IDENTITIES = true;
+
+ /**
+ * Creates a new normalized projection from the parameters computed by the
given initializer.
+ */
+ MeridionalDistanceBased(final Initializer initializer) {
+ super(initializer);
+ computeCoefficients();
+ }
+
+ /**
+ * Creates a new projection initialized to the same parameters than the
given one.
+ */
+ MeridionalDistanceBased(final MeridionalDistanceBased other) {
+ super(other);
+ }
+
+ /**
+ * Restores transient fields after deserialization.
+ */
+ private void readObject(final ObjectInputStream in) throws IOException,
ClassNotFoundException {
+ in.defaultReadObject();
+ computeCoefficients();
+ }
+
+ /**
+ * Computes the coefficients in the series expansions from the {@link
#eccentricitySquared} value.
+ * This method shall be invoked after {@code MeridionalDistanceBased}
construction or deserialization.
+ */
+ private void computeCoefficients() {
+ final double e2 = eccentricitySquared;
+ // TODO
+ }
+}
diff --git
a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/Sinusoidal.java
b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/Sinusoidal.java
index fc94ef6..64b5fac 100644
---
a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/Sinusoidal.java
+++
b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/Sinusoidal.java
@@ -42,7 +42,7 @@ import static
org.apache.sis.internal.referencing.provider.Sinusoidal.*;
* @since 1.0
* @module
*/
-public class Sinusoidal extends NormalizedProjection {
+public class Sinusoidal extends MeridionalDistanceBased {
/**
* For cross-version compatibility.
*/
diff --git
a/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/MeridionalDistanceTest.java
b/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/MeridionalDistanceTest.java
new file mode 100644
index 0000000..35ee297
--- /dev/null
+++
b/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/MeridionalDistanceTest.java
@@ -0,0 +1,125 @@
+/*
+ * 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 java.util.Random;
+import org.apache.sis.referencing.operation.DefaultOperationMethod;
+import org.apache.sis.test.TestUtilities;
+import org.apache.sis.test.DependsOn;
+import org.junit.Test;
+
+import static java.lang.StrictMath.*;
+import static org.junit.Assert.assertEquals;
+
+
+/**
+ * Tests the meridional distances computed by {@link MeridionalDistanceBased}.
+ *
+ * @author Martin Desruisseaux (Geomatys)
+ * @version 1.0
+ * @since 1.0
+ * @module
+ */
+@DependsOn(NormalizedProjectionTest.class)
+public final strictfp class MeridionalDistanceTest extends
MapProjectionTestCase {
+ /**
+ * Creates a new test case.
+ */
+ public MeridionalDistanceTest() {
+ final DefaultOperationMethod provider = new
org.apache.sis.internal.referencing.provider.Sinusoidal();
+ transform = new Sinusoidal(provider, parameters(provider, true));
+ tolerance = NormalizedProjection.ANGULAR_TOLERANCE; // = linear
tolerance on a sphere of radius 1.
+ }
+
+ /**
+ * Computes the meridional distance using equation given in EPSG guidance
notes, which is also from Snyder book.
+ * The equation is given in Snyder 3-21. We use this equation as a
reference for testing validity of other forms.
+ * The equation is:
+ *
+ * {@preformat math
+ * M = a[(1 – e²/4 – 3e⁴/64 – 5e⁶/256 – …)⋅φ
+ * – (3e²/8 + 3e⁴/32 + 45e⁶/1024 + …)⋅sin2φ
+ * + (15e⁴/256 + 45e⁶/1024 + …)⋅sin4φ
+ * – (35e⁶/3072 + …)⋅sin6φ
+ * + …]
+ * }
+ *
+ * @param φ latitude in radians.
+ * @return meridional distance from equator to the given latitude on an
ellipsoid with semi-major axis of 1.
+ */
+ private double reference(final double φ) {
+ final MeridionalDistanceBased projection = (MeridionalDistanceBased)
transform;
+ final double e2 = projection.eccentricitySquared;
+ final double e4 = e2*e2;
+ final double e6 = e2*e4;
+ /*
+ * Smallest terms of the series should be added first for better
accuracy.
+ * The final multiplication by (1 - e2) is already included in all
terms.
+ */
+ return - (35./3072*e6) * sin(6*φ)
+ + (45./1024*e6 + 15./256*e4) * sin(4*φ)
+ - (45./1024*e6 + 3./32 *e4 + 3./8*e2) * sin(2*φ)
+ + (-5./256 *e6 - 3./64 *e4 - 1./4*e2 + 1) * φ;
+ }
+
+ /**
+ * Series expansion with more terms. We use this formulas as a reference
for testing accuracy of the formula
+ * implemented by {@link MeridionalDistanceBased} after making sure that
+ * this value is in agreement with {@link #reference(double)}.
+ *
+ * <p>References:</p>
+ * <ul>
+ * <li>Kawase, Kazushige (2011). A General Formula for Calculating
Meridian Arc Length and its Application to Coordinate
+ * Conversion in the Gauss-Krüger Projection. Bulletin of the
Geospatial Information Authority of Japan, Vol.59.
+ * <a
href="http://www.gsi.go.jp/common/000062452.pdf";>(download)</a></li>
+ * <li><a
href="https://en.wikipedia.org/wiki/Meridian_arc#Series_expansions";>Meridian
arc — series expansions</a>
+ * on Wikipedia.</li>
+ * </ul>
+ */
+ private double referenceMoreAccurate(final double φ) {
+ final MeridionalDistanceBased projection = (MeridionalDistanceBased)
transform;
+ final double e2 = projection.eccentricitySquared;
+ final double e4 = e2*e2;
+ final double e6 = e2*e4;
+ final double e8 = e4*e4;
+ final double e10 = e2*e8;
+ final double C1 = 43659./ 65536*e10 + 11025./16384*e8 + 175./256*e6 +
45./64*e4 + 3./4*e2 + 1;
+ final double C2 = 72765./ 65536*e10 + 2205./ 2048*e8 + 525./512*e6 +
15./16*e4 + 3./4*e2;
+ final double C3 = 10395./ 16384*e10 + 2205./ 4096*e8 + 105./256*e6 +
15./64*e4;
+ final double C4 = 31185./131072*e10 + 315./ 2048*e8 + 35./512*e6;
+ final double C5 = 3465./ 65536*e10 + 315./16384*e8;
+ final double C6 = 693./131072*e10;
+ final double v = -C6*sin(10*φ)/10 + C5*sin(8*φ)/8 - C4*sin(6*φ)/6 +
C3*sin(4*φ)/4 - C2*sin(2*φ)/2 + C1*φ;
+ return v * (1 - e2);
+ }
+
+ /**
+ * Compares {@link MeridionalDistanceBased} calculation with formulas
taken as references.
+ */
+ @Test
+ public void compareWithReference() {
+ final MeridionalDistanceBased projection = (MeridionalDistanceBased)
transform;
+ final Random random = TestUtilities.createRandomNumberGenerator();
+ for (int i=0; i<100; i++) {
+ final double φ = random.nextDouble() * PI - PI/2;
+ final double reference = reference(φ);
+ final double accurate = referenceMoreAccurate(φ);
+ assertEquals("Accurate formula disagree with reference.",
reference, accurate, 2E-10);
+ // TODO: invoke MeridionalDistanceBased method.
+ }
+ }
+}
diff --git
a/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/SinusoidalTest.java
b/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/SinusoidalTest.java
index acd8869..a51ebcb 100644
---
a/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/SinusoidalTest.java
+++
b/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/SinusoidalTest.java
@@ -34,7 +34,7 @@ import static org.junit.Assert.*;
* @since 1.0
* @module
*/
-@DependsOn(NormalizedProjectionTest.class)
+@DependsOn(MeridionalDistanceTest.class)
public final strictfp class SinusoidalTest extends MapProjectionTestCase {
/**
* Creates a new instance of {@link Sinusoidal} concatenated with the
(de)normalization matrices.
diff --git
a/core/sis-referencing/src/test/java/org/apache/sis/test/suite/ReferencingTestSuite.java
b/core/sis-referencing/src/test/java/org/apache/sis/test/suite/ReferencingTestSuite.java
index 972fcdb..e72ed1f 100644
---
a/core/sis-referencing/src/test/java/org/apache/sis/test/suite/ReferencingTestSuite.java
+++
b/core/sis-referencing/src/test/java/org/apache/sis/test/suite/ReferencingTestSuite.java
@@ -175,6 +175,7 @@ import org.junit.BeforeClass;
org.apache.sis.referencing.operation.projection.ObliqueMercatorTest.class,
org.apache.sis.referencing.operation.projection.CylindricalEqualAreaTest.class,
org.apache.sis.referencing.operation.projection.AlbersEqualAreaTest.class,
+
org.apache.sis.referencing.operation.projection.MeridionalDistanceTest.class,
org.apache.sis.referencing.operation.projection.SinusoidalTest.class,
org.apache.sis.referencing.operation.projection.MollweideTest.class,
