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new 27a08d6 Finer determination of Transverse Mercator domain of validity.
27a08d6 is described below
commit 27a08d6d693d3bbd87b7e92f8cb714da6f5bd258
Author: Martin Desruisseaux <[email protected]>
AuthorDate: Wed Feb 24 16:12:51 2021 +0100
Finer determination of Transverse Mercator domain of validity.
---
.../operation/projection/TransverseMercator.java | 39 +++++++++++++++------
.../projection/TransverseMercatorTest.java | 22 ++++++++----
.../doc-files/TransverseMercatorErrors.png | Bin 0 -> 7954 bytes
3 files changed, 44 insertions(+), 17 deletions(-)
diff --git
a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/TransverseMercator.java
b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/TransverseMercator.java
index 837c488..fb00694 100644
---
a/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/TransverseMercator.java
+++
b/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/TransverseMercator.java
@@ -59,7 +59,7 @@ import static
org.apache.sis.internal.referencing.provider.TransverseMercator.*;
*
* @author Martin Desruisseaux (Geomatys)
* @author Rémi Maréchal (Geomatys)
- * @version 1.0
+ * @version 1.1
*
* @see Mercator
* @see ObliqueMercator
@@ -77,7 +77,7 @@ public class TransverseMercator extends NormalizedProjection {
* Distance from central meridian, in degrees, at which errors are
considered too important.
* This threshold is determined by comparisons of computed values against
values provided by
* <cite>Karney (2009) Test data for the transverse Mercator
projection</cite> data file.
- * On the WGS84 ellipsoid we observed:
+ * On the WGS84 ellipsoid we observed at equator:
*
* <ul>
* <li>For ∆λ below 60°, errors below 1 centimetre.</li>
@@ -89,8 +89,24 @@ public class TransverseMercator extends NormalizedProjection
{
* <li>For ∆λ between 76° and 78°, errors up to 1 kilometre.</li>
* <li>For ∆λ greater than 85°, results are chaotic.</li>
* </ul>
+ *
+ * For latitudes greater than 20°, errors are less than 0.5 meters for all
∆λ < 83°.
+ * Errors become suddenly much higher at ∆λ > 82.6° no matter the
latitude.
+ */
+ static final double DOMAIN_OF_VALIDITY = 82.5;
+
+ /**
+ * The domain of validity at equator. We keep using the limit at all
latitudes up to
+ * {@value #LATITUDE_OF_REDUCED_DOMAIN} degrees, even if actually the
limit could be
+ * progressively relaxed until it reaches {@value #DOMAIN_OF_VALIDITY}
degrees.
*/
- static final double DOMAIN_OF_VALIDITY = 70;
+ static final double DOMAIN_OF_VALIDITY_AT_EQUATOR = 70;
+
+ /**
+ * The maximal latitude (exclusive) where to use {@link
#DOMAIN_OF_VALIDITY_AT_EQUATOR}
+ * instead of {@link #DOMAIN_OF_VALIDITY}.
+ */
+ static final double LATITUDE_OF_REDUCED_DOMAIN = 20;
/**
* {@code false} for using the original formulas as published by EPSG, or
{@code true} for using formulas
@@ -376,7 +392,8 @@ public class TransverseMercator extends
NormalizedProjection {
final boolean derivate) throws ProjectionException
{
final double λ = srcPts[srcOff];
- if (abs(λ) >= DOMAIN_OF_VALIDITY * (PI/180)) {
+ final double φ = srcPts[srcOff+1];
+ if (abs(λ) >= DOMAIN_OF_VALIDITY_AT_EQUATOR * (PI/180)) {
/*
* The Transverse Mercator projection is conceptually a Mercator
projection rotated by 90°.
* In Mercator projection, y values tend toward infinity for
latitudes close to ±90°.
@@ -395,11 +412,13 @@ public class TransverseMercator extends
NormalizedProjection {
* using WGS84 ellipsoid. We do not need to reduce the limit for
the spherical formulas,
* because the mathematic are simpler and the function still
smooth until 90°.
*/
- if (Math.abs(IEEEremainder(λ, 2*PI)) >= DOMAIN_OF_VALIDITY *
(PI/180)) { // More costly check.
+ final double limit = (abs(φ) < LATITUDE_OF_REDUCED_DOMAIN *
(PI/180))
+ ? (PI/180) * DOMAIN_OF_VALIDITY_AT_EQUATOR
+ : (PI/180) * DOMAIN_OF_VALIDITY;
+ if (Math.abs(IEEEremainder(λ, 2*PI)) >= limit) {
throw new
ProjectionException(Errors.format(Errors.Keys.OutsideDomainOfValidity));
}
}
- final double φ = srcPts[srcOff+1];
final double sinλ = sin(λ);
final double ℯsinφ = sin(φ) * eccentricity;
final double Q = asinh(tan(φ)) - atanh(ℯsinφ) * eccentricity;
@@ -681,6 +700,9 @@ public class TransverseMercator extends
NormalizedProjection {
final boolean derivate) throws
ProjectionException
{
final double λ = srcPts[srcOff];
+ final double φ = srcPts[srcOff + 1];
+ final double sinλ = sin(λ);
+ final double cosλ = cos(λ);
/*
* The Transverse Mercator projection is conceptually a Mercator
projection rotated by 90°.
* In Mercator projection, y values tend toward infinity for
latitudes close to ±90° while
@@ -700,12 +722,9 @@ public class TransverseMercator extends
NormalizedProjection {
* the limit for the spherical formulas, because the mathematic
are simpler and the function
* still smooth until 90°.
*/
- if (abs(λ) > PI/2) {
+ if (cosλ < 0) { // Implies
Math.abs(IEEEremainder(λ, 2*PI)) > PI/2
throw new
ProjectionException(Errors.format(Errors.Keys.OutsideDomainOfValidity));
}
- final double φ = srcPts[srcOff+1];
- final double sinλ = sin(λ);
- final double cosλ = cos(λ);
final double sinφ = sin(φ);
final double cosφ = cos(φ);
final double tanφ = sinφ / cosφ;
diff --git
a/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/TransverseMercatorTest.java
b/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/TransverseMercatorTest.java
index 164d1ac..e526e3f 100644
---
a/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/TransverseMercatorTest.java
+++
b/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/TransverseMercatorTest.java
@@ -16,7 +16,6 @@
*/
package org.apache.sis.referencing.operation.projection;
-import java.util.Arrays;
import java.util.Random;
import java.io.IOException;
import java.io.LineNumberReader;
@@ -33,7 +32,7 @@ import org.apache.sis.test.DependsOn;
import org.junit.Test;
import static java.lang.Double.NaN;
-import static java.lang.StrictMath.min;
+import static java.lang.StrictMath.abs;
import static java.lang.StrictMath.toRadians;
import static org.apache.sis.test.Assert.*;
import static
org.apache.sis.internal.referencing.provider.TransverseMercator.LATITUDE_OF_ORIGIN;
@@ -183,6 +182,12 @@ public final strictfp class TransverseMercatorTest extends
MapProjectionTestCase
/**
* Compares with <cite>Karney (2009) Test data for the transverse Mercator
projection</cite>.
* This is an optional test executed only if the {@code
$SIS_DATA/Tests/TMcoords.dat} file is found.
+ * The errors observed as of February 2021 are illustrated below. In this
image of size 91×91 pixels,
+ * pixels coordinates are longitude and latitude coordinates with (0,0) in
the upper-left corner.
+ * Black pixels are errors less than 0.5 meters. Yellow pixels are errors
between 0.5 and 1.5 meters.
+ * Red pixels are errors of 254.5 meters or more.
+ *
+ * <img src="doc-files/TransverseMercatorErrors.png" alt="Errors of
Transverse Mercator projection">
*
* @throws IOException if an error occurred while reading the test file.
* @throws FactoryException if an error occurred while creating the map
projection.
@@ -205,17 +210,20 @@ public final strictfp class TransverseMercatorTest
extends MapProjectionTestCase
final double[] target = new double[2];
String line;
while ((line = reader.readLine()) != null) {
- Arrays.fill(source, Double.NaN);
final CharSequence[] split = CharSequences.split(line, ' ');
- for (int i=min(split.length, 4); --i >= 0;) {
+ for (int i=4; --i >= 0;) {
final double value =
Double.parseDouble(split[i].toString());
if (i <= 1) source[i ^ 1] = value;
// Swap axis order.
else target[i - 2] = value;
}
// Relax tolerance for longitudes very far from central
meridian.
- final double longitude = StrictMath.abs(source[0]);
- if (longitude < TransverseMercator.DOMAIN_OF_VALIDITY) {
- if (StrictMath.abs(source[1]) >= 89.9) tolerance = 0.1;
+ final double longitude = abs(source[0]);
+ final double latitude = abs(source[1]);
+ final double limit = (latitude <
TransverseMercator.LATITUDE_OF_REDUCED_DOMAIN
+ ?
TransverseMercator.DOMAIN_OF_VALIDITY_AT_EQUATOR
+ :
TransverseMercator.DOMAIN_OF_VALIDITY);
+ if (longitude < limit) {
+ if (latitude >= 89.9) tolerance = 0.1;
else if (longitude <= 60) tolerance =
Formulas.LINEAR_TOLERANCE;
else if (longitude <= 66) tolerance = 0.1;
else if (longitude <= 70) tolerance = 1;
diff --git
a/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/doc-files/TransverseMercatorErrors.png
b/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/doc-files/TransverseMercatorErrors.png
new file mode 100644
index 0000000..47a76b7
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b/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/doc-files/TransverseMercatorErrors.png
differ
