proof-of-concept for TileCoord hilbert curve sequence supporting up t…

…o zoom 15 [onthegomap#98, onthegomap#128]
bdon · Jul 11, 2022 · 6726e6d · 6726e6d
1 parent 52432b8
commit 6726e6d
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Showing 2 changed files with 74 additions and 65 deletions.
diff --git a/planetiler-core/src/main/java/com/onthegomap/planetiler/geo/TileCoord.java b/planetiler-core/src/main/java/com/onthegomap/planetiler/geo/TileCoord.java
@@ -1,6 +1,5 @@
 package com.onthegomap.planetiler.geo;
 
-import com.onthegomap.planetiler.mbtiles.Mbtiles;
 import com.onthegomap.planetiler.util.Format;
 import javax.annotation.concurrent.Immutable;
 import org.locationtech.jts.geom.Coordinate;
@@ -9,40 +8,69 @@
 /**
  * The coordinate of a <a href="https://wiki.openstreetmap.org/wiki/Slippy_map_tilenames">slippy map tile</a>.
  * <p>
- * In order to encode into a 32-bit integer, only zoom levels {@code <= 14} are supported since we need 4 bits for the
- * zoom-level, and 14 bits each for the x/y coordinates.
+ * In order to encode into a 32-bit integer, we define a sequence of Hilbert curves for each zoom level, starting at the
+ * top-left.
  * <p>
- * Tiles are ordered by z ascending, x ascending, y descending to match index ordering of {@link Mbtiles} sqlite
- * database.
  *
  * @param encoded the tile ID encoded as a 32-bit integer
  * @param x       x coordinate of the tile where 0 is the western-most tile just to the east the international date line
  *                and 2^z-1 is the eastern-most tile
  * @param y       y coordinate of the tile where 0 is the northern-most tile and 2^z-1 is the southern-most tile
- * @param z       zoom level ({@code <= 14})
+ * @param z       zoom level ({@code <= 15})
  */
 @Immutable
 public record TileCoord(int encoded, int x, int y, int z) implements Comparable<TileCoord> {
-  // TODO: support higher than z14
-  // z15 could theoretically fit into a 32-bit integer but needs a different packing strategy
   // z16+ would need more space
-  // also need to remove hardcoded z14 limits
 
   private static final int XY_MASK = (1 << 14) - 1;
 
   public TileCoord {
-    assert z <= 14;
+    assert z <= 15;
   }
 
   public static TileCoord ofXYZ(int x, int y, int z) {
     return new TileCoord(encode(x, y, z), x, y, z);
   }
 
   public static TileCoord decode(int encoded) {
-    int z = (encoded >> 28) + 8;
-    int x = (encoded >> 14) & XY_MASK;
-    int y = ((1 << z) - 1) - ((encoded) & XY_MASK);
-    return new TileCoord(encoded, x, y, z);
+    int acc = 0;
+    int tmp_z = 0;
+    while (true) {
+      int num_tiles = (1 << tmp_z) * (1 << tmp_z);
+      if (acc + num_tiles > encoded) {
+        int position = encoded - acc;
+        return decodeOnLevel(tmp_z, position, encoded);
+      }
+      acc += num_tiles;
+      tmp_z++;
+    }
+  }
+
+  private static void rotate(int n, int[] xy, int rx, int ry) {
+    if (ry == 0) {
+      if (rx == 1) {
+        xy[0] = n - 1 - xy[0];
+        xy[1] = n - 1 - xy[1];
+      }
+      int t = xy[0];
+      xy[0] = xy[1];
+      xy[1] = t;
+    }
+  }
+
+  private static TileCoord decodeOnLevel(int z, int position, int encoded) {
+    int n = 1 << z;
+    int rx, ry, t = position;
+    int[] xy = {0, 0};
+    for (int s = 1; s < n; s *= 2) {
+      rx = 1 & Integer.divideUnsigned(t, 2);
+      ry = 1 & (t ^ rx);
+      rotate(s, xy, rx, ry);
+      xy[0] += s * rx;
+      xy[1] += s * ry;
+      t = Integer.divideUnsigned(t, 4);
+    }
+    return new TileCoord(encoded, xy[0], xy[1], z);
   }
 
   /** Returns the tile containing a latitude/longitude coordinate at a given zoom level. */
@@ -54,30 +82,20 @@ public static TileCoord aroundLngLat(double lng, double lat, int zoom) {
   }
 
   private static int encode(int x, int y, int z) {
-    int max = 1 << z;
-    if (x >= max) {
-      x %= max;
-    }
-    if (x < 0) {
-      x += max;
-    }
-    if (y < 0) {
-      y = 0;
-    }
-    if (y >= max) {
-      y = max - 1;
+    int acc = 0;
+    for (int tmp_z = 0; tmp_z < z; tmp_z++) {
+      acc += (1 << tmp_z) * (1 << tmp_z);
     }
-    // since most significant bit is treated as the sign bit, make:
-    // z0-7 get encoded from 8 (0b1000) to 15 (0b1111)
-    // z8-14 get encoded from 0 (0b0000) to 6 (0b0110)
-    // so that encoded tile coordinates are ordered by zoom level
-    if (z < 8) {
-      z += 8;
-    } else {
-      z -= 8;
+    int n = 1 << z;
+    int rx, ry, d = 0;
+    int[] xy = {x, y};
+    for (int s = Integer.divideUnsigned(n, 2); s > 0; s = Integer.divideUnsigned(s, 2)) {
+      rx = (xy[0] & s) > 0 ? 1 : 0;
+      ry = (xy[1] & s) > 0 ? 1 : 0;
+      d += s * s * ((3 * rx) ^ ry);
+      rotate(s, xy, rx, ry);
     }
-    y = max - 1 - y;
-    return (z << 28) | (x << 14) | y;
+    return acc + d;
   }
 
   @Override

diff --git a/planetiler-core/src/test/java/com/onthegomap/planetiler/geo/TileCoordTest.java b/planetiler-core/src/test/java/com/onthegomap/planetiler/geo/TileCoordTest.java
@@ -1,10 +1,7 @@
 package com.onthegomap.planetiler.geo;
 
 import static org.junit.jupiter.api.Assertions.assertEquals;
-import static org.junit.jupiter.api.Assertions.assertThrows;
-import static org.junit.jupiter.api.Assertions.fail;
 
-import org.junit.jupiter.api.Test;
 import org.junit.jupiter.params.ParameterizedTest;
 import org.junit.jupiter.params.provider.CsvSource;
 
@@ -17,6 +14,14 @@ class TileCoordTest {
     "0,1,1",
     "1,1,1",
     "100,100,14",
+    "0,0,14",
+    "16383,0,14",
+    "0,16383,14",
+    "16363,16363,14",
+    "0,0,15",
+    "32767,0,15",
+    "0,32767,15",
+    "32767,32767,15"
   })
   void testTileCoord(int x, int y, int z) {
     TileCoord coord1 = TileCoord.ofXYZ(x, y, z);
@@ -27,31 +32,17 @@ void testTileCoord(int x, int y, int z) {
     assertEquals(coord1, coord2);
   }
 
-  @Test
-  void testTileSortOrderRespectZ() {
-    int last = Integer.MIN_VALUE;
-    for (int z = 0; z <= 14; z++) {
-      int encoded = TileCoord.ofXYZ(0, 0, z).encoded();
-      if (encoded < last) {
-        fail("encoded value for z" + (z - 1) + " (" + last + ") is not less than z" + z + " (" + encoded + ")");
-      }
-      last = encoded;
-    }
-  }
-
-  @Test
-  void testTileSortOrderFlipY() {
-    for (int z = 1; z <= 14; z++) {
-      int encoded1 = TileCoord.ofXYZ(0, 1, z).encoded();
-      int encoded2 = TileCoord.ofXYZ(0, 0, z).encoded();
-      if (encoded2 < encoded1) {
-        fail("encoded value for y=1 is not less than y=0 at z=" + z);
-      }
-    }
-  }
-
-  @Test
-  void testThrowsPastZ14() {
-    assertThrows(AssertionError.class, () -> TileCoord.ofXYZ(0, 0, 15));
+  @ParameterizedTest
+  @CsvSource({
+    "0,0,0,0",
+    "0,0,1,1",
+    "0,1,1,2",
+    "1,1,1,3",
+    "1,0,1,4",
+    "0,0,2,5",
+  })
+  void testTileOrderHilbert(int x, int y, int z, int i) {
+    int encoded = TileCoord.ofXYZ(x, y, z).encoded();
+    assertEquals(i, encoded);
   }
 }