fix: Apply correction to distanceToLine() measurements (#767)

* Testing new distance to line formula

* Add links to theory for initial implementation

* Add lonCorrection

From #720 (comment)

* chore: addded tests for different latitudes and magnitude

* chore: added javadoc

Co-authored-by: Enrique López Mañas <eenriquelopez@gmail.com>

Author: barbeau

library/src/main/java/com/google/maps/android/PolyUtil.java

@@ -22,9 +22,25 @@
 import java.util.List;
 import java.util.Stack;
 
-import static com.google.maps.android.SphericalUtil.*;
-import static java.lang.Math.*;
-import static com.google.maps.android.MathUtil.*;
+import static com.google.maps.android.MathUtil.EARTH_RADIUS;
+import static com.google.maps.android.MathUtil.clamp;
+import static com.google.maps.android.MathUtil.hav;
+import static com.google.maps.android.MathUtil.havDistance;
+import static com.google.maps.android.MathUtil.havFromSin;
+import static com.google.maps.android.MathUtil.inverseMercator;
+import static com.google.maps.android.MathUtil.mercator;
+import static com.google.maps.android.MathUtil.sinFromHav;
+import static com.google.maps.android.MathUtil.sinSumFromHav;
+import static com.google.maps.android.MathUtil.wrap;
+import static com.google.maps.android.SphericalUtil.computeDistanceBetween;
+import static java.lang.Math.PI;
+import static java.lang.Math.cos;
+import static java.lang.Math.max;
+import static java.lang.Math.min;
+import static java.lang.Math.sin;
+import static java.lang.Math.sqrt;
+import static java.lang.Math.tan;
+import static java.lang.Math.toRadians;
 
 public class PolyUtil {
 
@@ -466,16 +482,18 @@ public static double distanceToLine(final LatLng p, final LatLng start, final La
             return computeDistanceBetween(end, p);
         }
 
+        // Implementation of http://paulbourke.net/geometry/pointlineplane/ or http://geomalgorithms.com/a02-_lines.html
         final double s0lat = toRadians(p.latitude);
         final double s0lng = toRadians(p.longitude);
         final double s1lat = toRadians(start.latitude);
         final double s1lng = toRadians(start.longitude);
         final double s2lat = toRadians(end.latitude);
         final double s2lng = toRadians(end.longitude);
 
+        double lonCorrection = Math.cos(s1lat);
         double s2s1lat = s2lat - s1lat;
-        double s2s1lng = s2lng - s1lng;
-        final double u = ((s0lat - s1lat) * s2s1lat + (s0lng - s1lng) * s2s1lng)
+        double s2s1lng = (s2lng - s1lng) * lonCorrection;
+        final double u = ((s0lat - s1lat) * s2s1lat + (s0lng - s1lng) * lonCorrection * s2s1lng)
                 / (s2s1lat * s2s1lat + s2s1lng * s2s1lng);
         if (u <= 0) {
             return computeDistanceBetween(p, start);

library/src/test/java/com/google/maps/android/PolyUtilTest.java

@@ -23,7 +23,10 @@
 import java.util.ArrayList;
 import java.util.List;
 
-import static org.junit.Assert.*;
+import static org.junit.Assert.assertEquals;
+import static org.junit.Assert.assertFalse;
+import static org.junit.Assert.assertSame;
+import static org.junit.Assert.assertTrue;
 
 public class PolyUtilTest {
     private static final String TEST_LINE =
@@ -469,14 +472,60 @@ public void testIsClosedPolygon() {
         assertTrue(PolyUtil.isClosedPolygon(poly));
     }
 
+    /**
+     * The following method checks whether {@link PolyUtil#distanceToLine(LatLng, LatLng, LatLng)  distanceToLine()} }
+     * is determining the distance between a point and a segment accurately.
+     *
+     * Currently there are tests for different orders of magnitude (i.e., 1X, 10X, 100X, 1000X), as well as a test
+     * where the segment and the point lie in different hemispheres.
+     *
+     * If further tests need to be added here, make sure that the distance has been verified with <a href="https://www.qgis.org/">QGIS</a>.
+     *
+     * @see <a href="https://www.qgis.org/">QGIS</a>
+     */
     @Test
     public void testDistanceToLine() {
         LatLng startLine = new LatLng(28.05359, -82.41632);
         LatLng endLine = new LatLng(28.05310, -82.41634);
         LatLng p = new LatLng(28.05342, -82.41594);
 
         double distance = PolyUtil.distanceToLine(p, startLine, endLine);
-        assertEquals(37.947946, distance, 1e-6);
+        assertEquals(37.94596795917082, distance, 1e-6);
+
+        startLine = new LatLng(49.321045, 12.097749);
+        endLine = new LatLng(49.321016, 12.097795);
+        p = new LatLng(49.3210674, 12.0978238);
+
+        distance = PolyUtil.distanceToLine(p, startLine, endLine);
+        assertEquals(5.559443879999753, distance, 1e-6);
+
+        startLine = new LatLng(48.125961, 11.548998);
+        endLine = new LatLng(48.125918, 11.549005);
+        p = new LatLng(48.125941, 11.549028);
+
+        distance = PolyUtil.distanceToLine(p, startLine, endLine);
+        assertEquals(1.9733966358947437, distance, 1e-6);
+
+        startLine = new LatLng(78.924669, 11.925521);
+        endLine = new LatLng(78.924707, 11.929060);
+        p = new LatLng(78.923164, 11.924029);
+
+        distance = PolyUtil.distanceToLine(p, startLine, endLine);
+        assertEquals(170.35662670453187, distance, 1e-6);
+
+        startLine = new LatLng(69.664036, 18.957124);
+        endLine = new LatLng(69.664029, 18.957109);
+        p = new LatLng(69.672901, 18.967911);
+
+        distance = PolyUtil.distanceToLine(p, startLine, endLine);
+        assertEquals(1070.222749990837, distance, 1e-6);
+
+        startLine = new LatLng(-0.018200, 109.343282);
+        endLine = new LatLng(-0.017877, 109.343537);
+        p = new LatLng(0.058299, 109.408054);
+
+        distance = PolyUtil.distanceToLine(p, startLine, endLine);
+        assertEquals(11100.157563150981, distance, 1e-6);
     }
 
     @Test