Spherical mercator transformation should handle properly out of bounds latitudes (#81145)

Handle properly latitudes close to -90.

Author: iverase

server/src/main/java/org/elasticsearch/common/geo/SphericalMercatorUtils.java

@@ -17,6 +17,8 @@ public class SphericalMercatorUtils {
 
     public static final double MERCATOR_BOUNDS = 20037508.34;
     private static final double MERCATOR_FACTOR = MERCATOR_BOUNDS / 180.0;
+    // latitude lower limit. Below this limit the transformation might result in -Infinity
+    private static final double LAT_LOWER_LIMIT = Math.nextUp(-90.0);
 
     /**
      * Transforms WGS84 longitude to a Spherical mercator longitude
@@ -29,7 +31,7 @@ public static double lonToSphericalMercator(double lon) {
      * Transforms WGS84 latitude to a Spherical mercator latitude
      */
     public static double latToSphericalMercator(double lat) {
-        double y = Math.log(Math.tan((90 + lat) * Math.PI / 360)) / (Math.PI / 180);
+        double y = Math.log(Math.tan((90 + Math.max(lat, LAT_LOWER_LIMIT)) * Math.PI / 360)) / (Math.PI / 180);
         return y * MERCATOR_FACTOR;
     }
 

server/src/test/java/org/elasticsearch/common/geo/SphericalMercatorUtilTests.java

@@ -34,11 +34,28 @@ public void testLat() {
         assertThat(latToSphericalMercator(GeoTileUtils.LATITUDE_MASK), Matchers.closeTo(MERCATOR_BOUNDS, 1e-7));
         assertThat(latToSphericalMercator(-GeoTileUtils.LATITUDE_MASK), Matchers.closeTo(-MERCATOR_BOUNDS, 1e-7));
         assertThat(latToSphericalMercator(0.0), Matchers.closeTo(0, 1e-7));
-        final double lat = latToSphericalMercator(
-            randomValueOtherThanMany(l -> l >= GeoTileUtils.LATITUDE_MASK || l <= -GeoTileUtils.LATITUDE_MASK, GeometryTestUtils::randomLat)
-        );
-        assertThat(lat, Matchers.greaterThanOrEqualTo(-MERCATOR_BOUNDS));
-        assertThat(lat, Matchers.lessThanOrEqualTo(MERCATOR_BOUNDS));
+        {
+            final double lat = latToSphericalMercator(
+                randomValueOtherThanMany(
+                    l -> l >= GeoTileUtils.LATITUDE_MASK || l <= -GeoTileUtils.LATITUDE_MASK,
+                    GeometryTestUtils::randomLat
+                )
+            );
+            assertThat(lat, Matchers.greaterThanOrEqualTo(-MERCATOR_BOUNDS));
+            assertThat(lat, Matchers.lessThanOrEqualTo(MERCATOR_BOUNDS));
+        }
+        {
+            // out of bounds values
+            final double lat = latToSphericalMercator(randomDoubleBetween(GeoTileUtils.LATITUDE_MASK, 90, false));
+            assertThat(lat, Matchers.greaterThan(MERCATOR_BOUNDS));
+            assertTrue(Double.isFinite(latToSphericalMercator(90)));
+        }
+        {
+            // out of bounds values
+            final double lat = latToSphericalMercator(-randomDoubleBetween(GeoTileUtils.LATITUDE_MASK, 90, false));
+            assertThat(lat, Matchers.lessThan(-MERCATOR_BOUNDS));
+            assertTrue(Double.isFinite(latToSphericalMercator(-90)));
+        }
     }
 
     public void testRectangle() {