diff --git a/binaries/data/mods/public/maps/random/alpine_valley.js b/binaries/data/mods/public/maps/random/alpine_valley.js
index 0af400a986..9b1b7f5dca 100644
--- a/binaries/data/mods/public/maps/random/alpine_valley.js
+++ b/binaries/data/mods/public/maps/random/alpine_valley.js
@@ -33,7 +33,7 @@ function MountainRangeBuilder(args)
 	/**
 	 * Array of Vector2D locations where a mountainrange can start or end.
 	 */
-	this.vertices = args.points;
+	this.vertices = args.getPoints();
 
 	/**
 	 * Number of mountainranges starting or ending at the given point.
diff --git a/binaries/data/mods/public/maps/random/ardennes_forest.js b/binaries/data/mods/public/maps/random/ardennes_forest.js
index 360974db59..aa5e928ef7 100644
--- a/binaries/data/mods/public/maps/random/ardennes_forest.js
+++ b/binaries/data/mods/public/maps/random/ardennes_forest.js
@@ -79,7 +79,7 @@ createArea(
 	]);
 Engine.SetProgress(5);
 
-// Find all hills
+g_Map.log("Finding hills");
 var noise0 = new Noise2D(20);
 for (var ix = 0; ix < mapSize; ix++)
 	for (var iz = 0; iz < mapSize; iz++)
@@ -253,17 +253,12 @@ for (let size of [scaleByMapSize(50, 800), scaleByMapSize(50, 400), scaleByMapSi
 
 Engine.SetProgress(50);
 
-var explorablePoints = [];
-
 for (var ix = 0; ix < mapSize; ix++)
 	for (var iz = 0; iz < mapSize; iz++)
 	{
 		let position = new Vector2D(ix, iz);
 		let h = g_Map.getHeight(position);
 
-		if (h > 15 && h < 45 && clPlayer.countMembersInRadius(position, 1) == 0)
-			explorablePoints.push(position);
-
 		if (h > 35 && randBool(0.1) ||
 		    h < 15 && randBool(0.05) && clHillDeco.countMembersInRadius(position, 1) == 0)
 			g_Map.placeEntityAnywhere(
@@ -273,7 +268,13 @@ for (var ix = 0; ix < mapSize; ix++)
 				randomAngle());
 	}
 
-var explorableArea = g_Map.createArea(explorablePoints);
+var explorableArea = createArea(
+	new MapBoundsPlacer(),
+	undefined,
+	[
+		new HeightConstraint(15, 45),
+		avoidClasses(clPlayer, 1)
+	]);
 
 Engine.SetProgress(55);
 
diff --git a/binaries/data/mods/public/maps/random/dodecanese.js b/binaries/data/mods/public/maps/random/dodecanese.js
index 802c50d908..d6e9ef67bc 100644
--- a/binaries/data/mods/public/maps/random/dodecanese.js
+++ b/binaries/data/mods/public/maps/random/dodecanese.js
@@ -333,7 +333,7 @@ createDecoration(
 
 g_Map.log("Placing bridges");
 var bridges = 0;
-for (let bridgeStart of shuffleArray(areaShoreline.points))
+for (let bridgeStart of shuffleArray(areaShoreline.getPoints()))
 {
 	if (new NearTileClassConstraint(clBridge, bridgeLength * 8).allows(bridgeStart))
 		continue;
diff --git a/binaries/data/mods/public/maps/random/hellas.js b/binaries/data/mods/public/maps/random/hellas.js
index 5124a159fe..2382a8ab44 100644
--- a/binaries/data/mods/public/maps/random/hellas.js
+++ b/binaries/data/mods/public/maps/random/hellas.js
@@ -119,7 +119,7 @@ while (true)
 	if (!passableLandArea)
 		continue;
 
-	landRatio = passableLandArea.points.length / diskArea(fractionToTiles(0.5));
+	landRatio = passableLandArea.getPoints().length / diskArea(fractionToTiles(0.5));
 	g_Map.log("Land ratio: " + landRatio.toFixed(3));
 	if (landRatio < minLandRatio || landRatio > maxLandRatio)
 		continue;
@@ -153,7 +153,7 @@ while (true)
 				new SlopeConstraint(2, Infinity)
 			]);
 
-		cliffsRatio = cliffsArea.points.length / Math.square(g_Map.getSize());
+		cliffsRatio = cliffsArea.getPoints().length / Math.square(g_Map.getSize());
 		g_Map.log("Smoothing heightmap, cliff ratio: " + cliffsRatio.toFixed(3));
 		if (cliffsRatio < maxCliffRatio)
 			break;
@@ -295,11 +295,11 @@ var areaWater = createArea(
 	stayClasses(clWater, 2));
 
 g_Map.log("Creating docks");
-if (areaWater && areaWater.points.length)
+if (areaWater && areaWater.getPoints().length)
 	for (let i = 0; i < scaleByMapSize(1, 2); ++i)
 		for (let tryNr = 0; tryNr < 60; ++tryNr)
 		{
-			let positionLand = pickRandom(areaLand.points);
+			let positionLand = pickRandom(areaLand.getPoints());
 			let positionDock = areaWater.getClosestPointTo(positionLand);
 
 			if (!g_Map.inMapBounds(positionDock) || !avoidClasses(clDock, 50, clPlayer, 30).allows(positionDock))
diff --git a/binaries/data/mods/public/maps/random/pompeii.js b/binaries/data/mods/public/maps/random/pompeii.js
index 91b60098b8..0f1e35131d 100644
--- a/binaries/data/mods/public/maps/random/pompeii.js
+++ b/binaries/data/mods/public/maps/random/pompeii.js
@@ -177,7 +177,7 @@ createObjectGroupsByAreas(
 g_Map.log("Creating docks");
 for (let i = 0; i < scaleByMapSize(2, 4); ++i)
 {
-	let positionLand = pickRandom(areaDockStart.points);
+	let positionLand = pickRandom(areaDockStart.getPoints());
 	let dockPosition = areaShoreline.getClosestPointTo(positionLand);
 
 	if (!avoidClasses(g_TileClasses.mountain, scaleByMapSize(4, 6), g_TileClasses.dock, 10).allows(dockPosition))
diff --git a/binaries/data/mods/public/maps/random/rmgen-common/player.js b/binaries/data/mods/public/maps/random/rmgen-common/player.js
index 4ec1209d9b..4011ac7848 100644
--- a/binaries/data/mods/public/maps/random/rmgen-common/player.js
+++ b/binaries/data/mods/public/maps/random/rmgen-common/player.js
@@ -633,7 +633,7 @@ function playerPlacementRandom(playerIDs, constraints = undefined)
 
 	for (let i = 0; i < getNumPlayers(); ++i)
 	{
-		let position = pickRandom(area.points);
+		let position = pickRandom(area.getPoints());
 
 		// Minimum distance between initial bases must be a quarter of the map diameter
 		if (locations.some(loc => loc.distanceTo(position) < playerMinDist) ||
diff --git a/binaries/data/mods/public/maps/random/rmgen/Area.js b/binaries/data/mods/public/maps/random/rmgen/Area.js
index 1ed78179f2..13e293a261 100644
--- a/binaries/data/mods/public/maps/random/rmgen/Area.js
+++ b/binaries/data/mods/public/maps/random/rmgen/Area.js
@@ -1,16 +1,27 @@
 /**
- * @file An Area is a set of points identified by an ID that was registered with the RandomMap.
+ * @file An Area is a set of Vector2D points and a cache to lookup membership quickly.
  */
 
 function Area(points, id)
 {
-	this.points = points;
-	this.id = id;
+	this.points = deepfreeze(points);
+
+	this.cache = [];
+	for (let x = 0; x < g_Map.getSize(); ++x)
+		this.cache[x] = new Uint8Array(g_Map.getSize());
+
+	for (let point of points)
+		this.cache[point.x][point.y] = 1;
 }
 
-Area.prototype.getID = function()
+Area.prototype.getPoints = function()
 {
-	return this.id;
+	return this.points;
+};
+
+Area.prototype.contains = function(point)
+{
+	return g_Map.inMapBounds(point) && this.cache[point.x][point.y] == 1;
 };
 
 Area.prototype.getClosestPointTo = function(position)
diff --git a/binaries/data/mods/public/maps/random/rmgen/Constraint.js b/binaries/data/mods/public/maps/random/rmgen/Constraint.js
index 5c9b51cd48..e9272af77c 100644
--- a/binaries/data/mods/public/maps/random/rmgen/Constraint.js
+++ b/binaries/data/mods/public/maps/random/rmgen/Constraint.js
@@ -31,16 +31,29 @@ AndConstraint.prototype.allows = function(position)
 };
 
 /**
- * The AvoidAreaConstraint is met if the tile is not part of the given Area.
- */
-function AvoidAreaConstraint(area)
+ * The StayAreasConstraint is met if some of the given Areas contains the point.
+  */
+function StayAreasConstraint(areas)
 {
-	this.area = area;
+	this.areas = areas;
 }
 
-AvoidAreaConstraint.prototype.allows = function(position)
+StayAreasConstraint.prototype.allows = function(position)
 {
-	return g_Map.area[position.x][position.y] != this.area.getID();
+	return this.areas.some(area => area.contains(position));
+};
+
+/**
+ * The AvoidAreasConstraint is met if none of the given Areas contain the point.
+ */
+function AvoidAreasConstraint(areas)
+{
+	this.areas = areas;
+}
+
+AvoidAreasConstraint.prototype.allows = function(position)
+{
+	return this.areas.every(area => !area.contains(position))
 };
 
 /**
diff --git a/binaries/data/mods/public/maps/random/rmgen/RandomMap.js b/binaries/data/mods/public/maps/random/rmgen/RandomMap.js
index 4b66a8754b..9e799a7804 100644
--- a/binaries/data/mods/public/maps/random/rmgen/RandomMap.js
+++ b/binaries/data/mods/public/maps/random/rmgen/RandomMap.js
@@ -28,12 +28,9 @@ function RandomMap(baseHeight, baseTerrain)
 
 	// Create 2D arrays for terrain objects and areas
 	this.terrainEntities = [];
-	this.area = [];
 
 	for (let i = 0; i < this.size; ++i)
 	{
-		this.area[i] = new Uint16Array(this.size);
-
 		this.terrainEntities[i] = [];
 		for (let j = 0; j < this.size; ++j)
 			this.terrainEntities[i][j] = undefined;
@@ -55,8 +52,6 @@ function RandomMap(baseHeight, baseTerrain)
 
 	this.entities = [];
 
-	this.areaID = 0;
-
 	// Starting entity ID, arbitrary number to leave some space for player entities
 	this.entityCount = 150;
 }
@@ -315,17 +310,6 @@ RandomMap.prototype.setTerrainEntity = function(templateName, playerID, position
 		new Entity(this.getEntityID(), templateName, playerID, position, orientation);
 };
 
-/**
- * Constructs a new Area object and informs the Map which points correspond to this area.
- */
-RandomMap.prototype.createArea = function(points)
-{
-	let areaID = ++this.areaID;
-	for (let p of points)
-		this.area[p.x][p.y] = areaID;
-	return new Area(points, areaID);
-};
-
 RandomMap.prototype.createTileClass = function()
 {
 	return new TileClass(this.size);
diff --git a/binaries/data/mods/public/maps/random/rmgen/library.js b/binaries/data/mods/public/maps/random/rmgen/library.js
index e64bce373f..e2d8eb1bbb 100644
--- a/binaries/data/mods/public/maps/random/rmgen/library.js
+++ b/binaries/data/mods/public/maps/random/rmgen/library.js
@@ -141,7 +141,7 @@ function createAreas(centeredPlacer, painter, constraint, amount, retryFactor =
 function createAreasInAreas(centeredPlacer, painter, constraint, amount, retryFactor, areas)
 {
 	let placeFunc = function() {
-		centeredPlacer.setCenterPosition(pickRandom(pickRandom(areas).points));
+		centeredPlacer.setCenterPosition(pickRandom(pickRandom(areas).getPoints()));
 		return createArea(centeredPlacer, painter, constraint);
 	};
 
@@ -169,7 +169,7 @@ function createObjectGroups(group, player, constraint, amount, retryFactor = 10,
 function createObjectGroupsByAreas(group, player, constraint, amount, retryFactor, areas, behaveDeprecated = false)
 {
 	let placeFunc = function() {
-		group.setCenterPosition(pickRandom(pickRandom(areas).points));
+		group.setCenterPosition(pickRandom(pickRandom(areas).getPoints()));
 		return createObjectGroup(group, player, constraint);
 	};
 
@@ -193,7 +193,7 @@ function createArea(placer, painters, constraints)
 	if (!points)
 		return undefined;
 
-	let area = g_Map.createArea(points);
+	let area = new Area(points);
 
 	new MultiPainter(painters).paint(area);
 
diff --git a/binaries/data/mods/public/maps/random/rmgen/painter/ElevationBlendingPainter.js b/binaries/data/mods/public/maps/random/rmgen/painter/ElevationBlendingPainter.js
index 49865c745b..a42b309f01 100644
--- a/binaries/data/mods/public/maps/random/rmgen/painter/ElevationBlendingPainter.js
+++ b/binaries/data/mods/public/maps/random/rmgen/painter/ElevationBlendingPainter.js
@@ -9,6 +9,6 @@ function ElevationBlendingPainter(targetHeight, strength)
 
 ElevationBlendingPainter.prototype.paint = function(area)
 {
-	for (let point of area.points)
+	for (let point of area.getPoints())
 		g_Map.setHeight(point, this.strength * this.targetHeight + (1 - this.strength) * g_Map.getHeight(point));
 };
diff --git a/binaries/data/mods/public/maps/random/rmgen/painter/ElevationPainter.js b/binaries/data/mods/public/maps/random/rmgen/painter/ElevationPainter.js
index 938f45c60f..3d9ab515ff 100644
--- a/binaries/data/mods/public/maps/random/rmgen/painter/ElevationPainter.js
+++ b/binaries/data/mods/public/maps/random/rmgen/painter/ElevationPainter.js
@@ -8,7 +8,7 @@ function ElevationPainter(elevation)
 
 ElevationPainter.prototype.paint = function(area)
 {
-	for (let point of area.points)
+	for (let point of area.getPoints())
 		for (let vertex of g_TileVertices)
 		{
 			let position = Vector2D.add(point, vertex);
diff --git a/binaries/data/mods/public/maps/random/rmgen/painter/HeightmapPainter.js b/binaries/data/mods/public/maps/random/rmgen/painter/HeightmapPainter.js
index 0975e75777..5802709017 100644
--- a/binaries/data/mods/public/maps/random/rmgen/painter/HeightmapPainter.js
+++ b/binaries/data/mods/public/maps/random/rmgen/painter/HeightmapPainter.js
@@ -43,7 +43,7 @@ HeightmapPainter.prototype.paint = function(area)
 	// Additional complexity to process all 4 vertices of each tile, i.e the last row too
 	let seen = new Array(g_Map.height.length).fill(0).map(zero => new Uint8Array(g_Map.height.length).fill(0));
 
-	for (let point of area.points)
+	for (let point of area.getPoints())
 		for (let vertex of g_TileVertices)
 		{
 			let vertexPos = Vector2D.add(point, vertex);
diff --git a/binaries/data/mods/public/maps/random/rmgen/painter/LayeredPainter.js b/binaries/data/mods/public/maps/random/rmgen/painter/LayeredPainter.js
index 2edc589e7f..8cb5da4a7a 100644
--- a/binaries/data/mods/public/maps/random/rmgen/painter/LayeredPainter.js
+++ b/binaries/data/mods/public/maps/random/rmgen/painter/LayeredPainter.js
@@ -22,7 +22,7 @@ LayeredPainter.prototype.paint = function(area)
 		"area": area,
 		"brushSize": 1,
 		"gridSize": g_Map.getSize(),
-		"withinArea": (areaID, position) => g_Map.area[position.x][position.y] == areaID,
+		"withinArea": (area, position) => area.contains(position),
 		"paintTile": (point, distance) => {
 			let width = 0;
 			let i = 0;
diff --git a/binaries/data/mods/public/maps/random/rmgen/painter/RandomElevationPainter.js b/binaries/data/mods/public/maps/random/rmgen/painter/RandomElevationPainter.js
index 04e977f64d..827b160642 100644
--- a/binaries/data/mods/public/maps/random/rmgen/painter/RandomElevationPainter.js
+++ b/binaries/data/mods/public/maps/random/rmgen/painter/RandomElevationPainter.js
@@ -9,7 +9,7 @@ function RandomElevationPainter(minHeight, maxHeight)
 
 RandomElevationPainter.prototype.paint = function(area)
 {
-	for (let point of area.points)
+	for (let point of area.getPoints())
 		for (let vertex of g_TileVertices)
 		{
 			let position = Vector2D.add(point, vertex);
diff --git a/binaries/data/mods/public/maps/random/rmgen/painter/SmoothElevationPainter.js b/binaries/data/mods/public/maps/random/rmgen/painter/SmoothElevationPainter.js
index 49433d266b..8d9dbdbd0b 100644
--- a/binaries/data/mods/public/maps/random/rmgen/painter/SmoothElevationPainter.js
+++ b/binaries/data/mods/public/maps/random/rmgen/painter/SmoothElevationPainter.js
@@ -45,7 +45,7 @@ SmoothElevationPainter.prototype.paint = function(area)
 	// Get heightmap grid vertices within or adjacent to the area
 	let brushSize = 2;
 	let heightPoints = [];
-	for (let point of area.points)
+	for (let point of area.getPoints())
 		for (let dx = -1; dx < 1 + brushSize; ++dx)
 		{
 			let nx = point.x + dx;
@@ -64,11 +64,11 @@ SmoothElevationPainter.prototype.paint = function(area)
 		}
 
 	// Every vertex of a tile is considered within the area
-	let withinArea = (areaID, position) => {
+	let withinArea = (area, position) => {
 		for (let vertex of g_TileVertices)
 		{
 			let vertexPos = Vector2D.sub(position, vertex);
-			if (g_Map.inMapBounds(vertexPos) && g_Map.area[vertexPos.x][vertexPos.y] == areaID)
+			if (g_Map.inMapBounds(vertexPos) && area.contains(vertexPos))
 				return true;
 		}
 
@@ -94,10 +94,9 @@ SmoothElevationPainter.prototype.paint = function(area)
 	});
 
 	// Smooth everything out
-	let areaID = area.getID();
 	for (let point of heightPoints)
 	{
-		if (!withinArea(areaID, point))
+		if (!withinArea(area, point))
 			continue;
 
 		let count = 0;
@@ -149,8 +148,7 @@ function breadthFirstSearchPaint(args)
 
 	// Find all points outside of the area, mark them as seen and set zero distance
 	let pointQueue = [];
-	let areaID = args.area.getID();
-	for (let point of args.area.points)
+	for (let point of args.area.getPoints())
 		// The brushSize is added because the entire brushSize is by definition part of the area
 		for (let dx = -1; dx < 1 + args.brushSize; ++dx)
 		{
@@ -160,7 +158,7 @@ function breadthFirstSearchPaint(args)
 				let nz = point.y + dz;
 				let position = new Vector2D(nx, nz);
 
-				if (!withinGrid(nx, nz) || args.withinArea(areaID, position) || saw[nx][nz])
+				if (!withinGrid(nx, nz) || args.withinArea(args.area, position) || saw[nx][nz])
 					continue;
 
 				saw[nx][nz] = 1;
@@ -176,7 +174,7 @@ function breadthFirstSearchPaint(args)
 		let point = pointQueue.shift();
 		let distance = dist[point.x][point.y];
 
-		if (args.withinArea(areaID, point))
+		if (args.withinArea(args.area, point))
 			args.paintTile(point, distance);
 
 		// Enqueue neighboring points
@@ -188,7 +186,7 @@ function breadthFirstSearchPaint(args)
 				let nz = point.y + dz;
 				let position = new Vector2D(nx, nz);
 
-				if (!withinGrid(nx, nz) || !args.withinArea(areaID, position) || saw[nx][nz])
+				if (!withinGrid(nx, nz) || !args.withinArea(args.area, position) || saw[nx][nz])
 					continue;
 
 				saw[nx][nz] = 1;
diff --git a/binaries/data/mods/public/maps/random/rmgen/painter/SmoothingPainter.js b/binaries/data/mods/public/maps/random/rmgen/painter/SmoothingPainter.js
index 2915ad408f..503c2f4762 100644
--- a/binaries/data/mods/public/maps/random/rmgen/painter/SmoothingPainter.js
+++ b/binaries/data/mods/public/maps/random/rmgen/painter/SmoothingPainter.js
@@ -33,7 +33,7 @@ SmoothingPainter.prototype.paint = function(area)
 		// Additional complexity to process all 4 vertices of each tile, i.e the last row too
 		let seen = new Array(heightmap.length).fill(0).map(zero => new Uint8Array(heightmap.length).fill(0));
 
-		for (let point of area.points)
+		for (let point of area.getPoints())
 			for (let tileVertex of g_TileVertices)
 			{
 				let vertex = Vector2D.add(point, tileVertex);
diff --git a/binaries/data/mods/public/maps/random/rmgen/painter/TerrainPainter.js b/binaries/data/mods/public/maps/random/rmgen/painter/TerrainPainter.js
index 2480ed8f16..3e63e53ed6 100644
--- a/binaries/data/mods/public/maps/random/rmgen/painter/TerrainPainter.js
+++ b/binaries/data/mods/public/maps/random/rmgen/painter/TerrainPainter.js
@@ -9,6 +9,6 @@ function TerrainPainter(terrain)
 
 TerrainPainter.prototype.paint = function(area)
 {
-	for (let point of area.points)
+	for (let point of area.getPoints())
 		this.terrain.place(point);
 };
diff --git a/binaries/data/mods/public/maps/random/rmgen/painter/TerrainTextureArrayPainter.js b/binaries/data/mods/public/maps/random/rmgen/painter/TerrainTextureArrayPainter.js
index 96d640139e..2da99cef24 100644
--- a/binaries/data/mods/public/maps/random/rmgen/painter/TerrainTextureArrayPainter.js
+++ b/binaries/data/mods/public/maps/random/rmgen/painter/TerrainTextureArrayPainter.js
@@ -16,7 +16,7 @@ TerrainTextureArrayPainter.prototype.paint = function(area)
 	let sourceSize = Math.sqrt(this.textureIDs.length);
 	let scale = sourceSize / g_Map.getSize();
 
-	for (let point of area.points)
+	for (let point of area.getPoints())
 	{
 		let sourcePos = Vector2D.mult(point, scale).floor();
 		g_Map.setTexture(point, this.textureNames[this.textureIDs[sourcePos.x * sourceSize + sourcePos.y]]);
diff --git a/binaries/data/mods/public/maps/random/rmgen/painter/TileClassPainter.js b/binaries/data/mods/public/maps/random/rmgen/painter/TileClassPainter.js
index dfd88211df..e1631833c1 100644
--- a/binaries/data/mods/public/maps/random/rmgen/painter/TileClassPainter.js
+++ b/binaries/data/mods/public/maps/random/rmgen/painter/TileClassPainter.js
@@ -8,6 +8,6 @@ function TileClassPainter(tileClass)
 
 TileClassPainter.prototype.paint = function(area)
 {
-	for (let point of area.points)
+	for (let point of area.getPoints())
 		this.tileClass.add(point);
 };
diff --git a/binaries/data/mods/public/maps/random/rmgen/painter/TileClassUnPainter.js b/binaries/data/mods/public/maps/random/rmgen/painter/TileClassUnPainter.js
index 7cd8004e03..b368c565e7 100644
--- a/binaries/data/mods/public/maps/random/rmgen/painter/TileClassUnPainter.js
+++ b/binaries/data/mods/public/maps/random/rmgen/painter/TileClassUnPainter.js
@@ -8,6 +8,6 @@ function TileClassUnPainter(tileClass)
 
 TileClassUnPainter.prototype.paint = function(area)
 {
-	for (let point of area.points)
+	for (let point of area.getPoints())
 		this.tileClass.remove(point);
 };
diff --git a/binaries/data/mods/public/maps/random/rmgen2/gaia.js b/binaries/data/mods/public/maps/random/rmgen2/gaia.js
index 61e441a66e..55be48adae 100644
--- a/binaries/data/mods/public/maps/random/rmgen2/gaia.js
+++ b/binaries/data/mods/public/maps/random/rmgen2/gaia.js
@@ -52,7 +52,7 @@ function addBluffs(constraint, size, deviation, fill, baseHeight)
 		if (rendered[0] === undefined)
 			continue;
 
-		var points = rendered[0].points;
+		var points = rendered[0].getPoints();
 
 		var corners = findCorners(points);