diff --git a/binaries/data/mods/public/maps/random/belgian_uplands.js b/binaries/data/mods/public/maps/random/belgian_uplands.js
index 1f4a463cfc..2744055a86 100644
--- a/binaries/data/mods/public/maps/random/belgian_uplands.js
+++ b/binaries/data/mods/public/maps/random/belgian_uplands.js
@@ -101,7 +101,7 @@ while (true)
 	g_Map.log("Mark valid heightrange for player starting positions");
 	let tHeightRange = g_Map.createTileClass();
 	let area = createArea(
-		new ClumpPlacer(diskArea(fractionToTiles(0.5) - MAP_BORDER_WIDTH), 1, 1, Infinity, mapCenter),
+		new DiskPlacer(fractionToTiles(0.5) - MAP_BORDER_WIDTH, mapCenter),
 		new TileClassPainter(tHeightRange),
 		new HeightConstraint(lowerHeightLimit, upperHeightLimit));
 
diff --git a/binaries/data/mods/public/maps/random/caledonian_meadows.js b/binaries/data/mods/public/maps/random/caledonian_meadows.js
index 14bd8937fb..dad28b845c 100644
--- a/binaries/data/mods/public/maps/random/caledonian_meadows.js
+++ b/binaries/data/mods/public/maps/random/caledonian_meadows.js
@@ -297,7 +297,7 @@ Engine.SetProgress(30);
 g_Map.log("Smoothing player locations");
 for (let position of playerPosition)
 	createArea(
-		new ClumpPlacer(diskArea(35), 1, 1, Infinity, position),
+		new DiskPlacer(35, position),
 		new SmoothElevationPainter(ELEVATION_SET, g_Map.getHeight(position), 35));
 
 g_Map.log("Creating paths between players");
diff --git a/binaries/data/mods/public/maps/random/gear.js b/binaries/data/mods/public/maps/random/gear.js
index b2daf8fe60..aae3bb5076 100644
--- a/binaries/data/mods/public/maps/random/gear.js
+++ b/binaries/data/mods/public/maps/random/gear.js
@@ -116,7 +116,7 @@ else if (mapSize == 448)
 
 g_Map.log("Creating big circular lake");
 createArea(
-	new ClumpPlacer(diskArea(radiusCentralLake), 1, 1, Infinity, mapCenter),
+	new DiskPlacer(radiusCentralLake, mapCenter),
 	new SmoothElevationPainter(ELEVATION_SET, heightSeaGround, 4));
 
 g_Map.log("Creating rivers between players");
@@ -144,22 +144,22 @@ for (let m = 0; m < numPlayers * split; ++m)
 
 g_Map.log("Creating ring of land connecting players");
 createArea(
-	new ClumpPlacer(diskArea(radiusCentralRingLand), 1, 1, Infinity, mapCenter),
+	new DiskPlacer(radiusCentralRingLand, mapCenter),
 	new SmoothElevationPainter(ELEVATION_SET, heightRing, 4));
 
 g_Map.log("Creating inner ring of water");
 createArea(
-	new ClumpPlacer(diskArea(radiusCentralWaterRing), 1, 1, Infinity, mapCenter),
+	new DiskPlacer(radiusCentralWaterRing, mapCenter),
 	new SmoothElevationPainter(ELEVATION_SET, heightShallow, 3));
 
 g_Map.log("Creating central island");
 createArea(
-	new ClumpPlacer(diskArea(radiusCentralIsland), 1, 1, Infinity, mapCenter),
+	new DiskPlacer(radiusCentralIsland, mapCenter),
 	new SmoothElevationPainter(ELEVATION_SET, heightRing, 3));
 
 g_Map.log("Creating hill on the central island");
 createArea(
-	new ClumpPlacer(diskArea(radiusCentralHill), 1, 1, Infinity, mapCenter),
+	new DiskPlacer(radiusCentralHill, mapCenter),
 	new SmoothElevationPainter(ELEVATION_SET, heightHill, 8));
 
 paintTerrainBasedOnHeight(-6, 1, 1, tWater);
diff --git a/binaries/data/mods/public/maps/random/lions_den.js b/binaries/data/mods/public/maps/random/lions_den.js
index 11e7d7977f..daf2a78934 100644
--- a/binaries/data/mods/public/maps/random/lions_den.js
+++ b/binaries/data/mods/public/maps/random/lions_den.js
@@ -482,7 +482,7 @@ function createSunkenTerrain()
 
 	g_Map.log("Creating central valley");
 	createArea(
-		new ClumpPlacer(diskArea(fractionToTiles(0.29)), 1, 1, Infinity, mapCenter),
+		new DiskPlacer(fractionToTiles(0.29), mapCenter),
 		[
 			new LayeredPainter([g_Terrains.cliff, lower], [3]),
 			new SmoothElevationPainter(ELEVATION_SET, heightValley, 3),
@@ -491,7 +491,7 @@ function createSunkenTerrain()
 
 	g_Map.log("Creating central hill");
 	createArea(
-		new ClumpPlacer(diskArea(fractionToTiles(0.21)), 1, 1, Infinity, mapCenter),
+		new DiskPlacer(fractionToTiles(0.21), mapCenter),
 		[
 			new LayeredPainter([g_Terrains.cliff, topTerrain], [3]),
 			new SmoothElevationPainter(ELEVATION_SET, heightHill, 3),
diff --git a/binaries/data/mods/public/maps/random/mediterranean.js b/binaries/data/mods/public/maps/random/mediterranean.js
index 169c9ba3ea..9ee83321d1 100644
--- a/binaries/data/mods/public/maps/random/mediterranean.js
+++ b/binaries/data/mods/public/maps/random/mediterranean.js
@@ -107,7 +107,7 @@ Engine.SetProgress(30);
 
 g_Map.log("Marking land");
 createArea(
-	new ClumpPlacer(diskArea(fractionToTiles(0.5)), 1, 1, Infinity, mapCenter),
+	new DiskPlacer(fractionToTiles(0.5), mapCenter),
 	new TileClassPainter(g_TileClasses.land),
 	avoidClasses(g_TileClasses.water, 0));
 Engine.SetProgress(35);
diff --git a/binaries/data/mods/public/maps/random/ngorongoro.js b/binaries/data/mods/public/maps/random/ngorongoro.js
index 17227194ad..f72e64999e 100644
--- a/binaries/data/mods/public/maps/random/ngorongoro.js
+++ b/binaries/data/mods/public/maps/random/ngorongoro.js
@@ -106,7 +106,7 @@ Engine.SetProgress(40);
 
 g_Map.log("Marking eden");
 createArea(
-	new ClumpPlacer(diskArea(fractionToTiles(0.14)), 1, 1, Infinity, mapCenter),
+	new DiskPlacer(fractionToTiles(0.14), mapCenter),
 	new TileClassPainter(g_TileClasses.eden),
 	new HeightConstraint(-Infinity, heightEden));
 Engine.SetProgress(45);
diff --git a/binaries/data/mods/public/maps/random/pompeii.js b/binaries/data/mods/public/maps/random/pompeii.js
index 4aad3bb381..ebaa540e4d 100644
--- a/binaries/data/mods/public/maps/random/pompeii.js
+++ b/binaries/data/mods/public/maps/random/pompeii.js
@@ -132,7 +132,7 @@ Engine.SetProgress(40);
 
 g_Map.log("Marking dock search location");
 var areaDockStart = createArea(
-	new ClumpPlacer(diskArea(fractionToTiles(0.5)) - 10, 1, 1, Infinity, mapCenter),
+	new DiskPlacer(fractionToTiles(0.5) - 10, mapCenter),
 	undefined,
 	stayClasses(g_TileClasses.land, 6));
 
diff --git a/binaries/data/mods/public/maps/random/red_sea.js b/binaries/data/mods/public/maps/random/red_sea.js
index e291d1dd91..8d016bbc30 100644
--- a/binaries/data/mods/public/maps/random/red_sea.js
+++ b/binaries/data/mods/public/maps/random/red_sea.js
@@ -88,7 +88,7 @@ Engine.SetProgress(30);
 
 g_Map.log("Marking land");
 createArea(
-	new ClumpPlacer(diskArea(fractionToTiles(0.5)), 1, 1, Infinity, mapCenter),
+	new DiskPlacer(fractionToTiles(0.5), mapCenter),
 	new TileClassPainter(g_TileClasses.land),
 	avoidClasses(g_TileClasses.water, 0));
 Engine.SetProgress(35);
diff --git a/binaries/data/mods/public/maps/random/rmgen/placer_centered.js b/binaries/data/mods/public/maps/random/rmgen/placer_centered.js
index e78469b050..e123ed11b2 100644
--- a/binaries/data/mods/public/maps/random/rmgen/placer_centered.js
+++ b/binaries/data/mods/public/maps/random/rmgen/placer_centered.js
@@ -3,6 +3,38 @@
  * The center can be modified externally using setCenterPosition, typically called by createAreas.
  */
 
+/**
+ * Returns all points on a disk at the given location that meet the constraint.
+ */
+function DiskPlacer(radius, centerPosition = undefined)
+{
+	this.radius = radius;
+	this.centerPosition = undefined;
+
+	if (centerPosition)
+		this.setCenterPosition(centerPosition);
+}
+
+DiskPlacer.prototype.setCenterPosition = function(position)
+{
+	this.centerPosition = deepfreeze(position.clone().round());
+};
+
+DiskPlacer.prototype.place = function(constraint)
+{
+	let points = [];
+
+	for (let x = 0; x < g_Map.getSize(); ++x)
+		for (let y = 0; y < g_Map.getSize(); ++y)
+		{
+			let point = new Vector2D(x, y);
+			if (this.centerPosition.distanceTo(point) <= this.radius && constraint.allows(point))
+				points.push(point);
+		}
+
+	return points;
+};
+
 /**
  * Generates a roughly circular clump of points.
  *
diff --git a/binaries/data/mods/public/maps/random/rmgen/placer_noncentered.js b/binaries/data/mods/public/maps/random/rmgen/placer_noncentered.js
index 7fa8822fd9..39bcae592d 100644
--- a/binaries/data/mods/public/maps/random/rmgen/placer_noncentered.js
+++ b/binaries/data/mods/public/maps/random/rmgen/placer_noncentered.js
@@ -186,7 +186,7 @@ function RandomPathPlacer(pathStart, pathEnd, pathWidth, offset, blended)
 	this.pathEnd = pathEnd;
 	this.offset = offset;
 	this.blended = blended;
-	this.clumpPlacer = new ClumpPlacer(diskArea(pathWidth), 1, 1, Infinity);
+	this.diskPlacer = new DiskPlacer(pathWidth);
 	this.maxPathLength = fractionToTiles(2);
 }
 
@@ -203,10 +203,10 @@ RandomPathPlacer.prototype.place = function(constraint)
 				-getAngle(this.pathStart.x, this.pathStart.y, this.pathEnd.x, this.pathEnd.y) +
 				-Math.PI / 2 * (randFloat(-1, 1) + (this.blended ? 0.5 : 0)))).round();
 
-		this.clumpPlacer.setCenterPosition(position);
+		this.diskPlacer.setCenterPosition(position);
 
-		for (let point of this.clumpPlacer.place(constraint) || [])
-			if (points.every(p => p.x != point.x || p.y != point.y))
+		for (let point of this.diskPlacer.place(constraint))
+			if (points.every(p => !Vector2D.isEqualTo(p, point)))
 				points.push(point);
 	}
 
diff --git a/binaries/data/mods/public/maps/random/wild_lake.js b/binaries/data/mods/public/maps/random/wild_lake.js
index 8ff5e63ccd..9329c0b899 100644
--- a/binaries/data/mods/public/maps/random/wild_lake.js
+++ b/binaries/data/mods/public/maps/random/wild_lake.js
@@ -635,7 +635,7 @@ for (let i = 0; i < resourceSpots.length; ++i)
 
 	if (radius)
 		createArea(
-			new ClumpPlacer(diskArea(radius), 1, 1, Infinity, resourceSpots[i]),
+			new DiskPlacer(radius, resourceSpots[i]),
 			new SmoothElevationPainter(ELEVATION_SET, g_Map.getHeight(resourceSpots[i]), radius / 3));
 }