diff --git a/src/cartographerFlatXY.js b/src/cartographerFlatXY.js
index 661d9a4..4a8e8f3 100644
--- a/src/cartographerFlatXY.js
+++ b/src/cartographerFlatXY.js
@@ -8,7 +8,9 @@ import Square from './square.js';
 
 const tilePointToSquare = ({tilePoint, mapPoint, pixelPoint}) => ({
 	tile: tilePoint instanceof Square ? tilePoint : new Square(tilePoint),
-	mapTile: mapPoint instanceof Square ? mapPoint : new Square(mapPoint),
+	mapTile: mapPoint instanceof Square ? mapPoint :
+		mapPoint ? new Square(mapPoint) :
+		mapPoint,
 	pixelPoint,
 });
 
diff --git a/src/cartographerFlatXYZ.js b/src/cartographerFlatXYZ.js
index 23bbdb1..bdba7af 100644
--- a/src/cartographerFlatXYZ.js
+++ b/src/cartographerFlatXYZ.js
@@ -8,7 +8,9 @@ import Point from './point.js';
 
 const tilePointToHex = ({tilePoint, mapPoint, pixelPoint}) => ({
 	tile: tilePoint instanceof Hex ? tilePoint : new Hex(tilePoint),
-	mapTile: mapPoint instanceof Hex ? mapPoint : new Hex(mapPoint),
+	mapTile: mapPoint instanceof Hex ? mapPoint :
+		mapPoint ? new Hex(mapPoint) :
+		mapPoint,
 	pixelPoint,
 });
 
diff --git a/src/cartographerPointyXY.js b/src/cartographerPointyXY.js
index 5215fed..be2f686 100644
--- a/src/cartographerPointyXY.js
+++ b/src/cartographerPointyXY.js
@@ -8,7 +8,9 @@ import Point from './point.js';
 
 const tilePointToSquare = ({tilePoint, mapPoint, pixelPoint}) => ({
 	tile: tilePoint instanceof Square ? tilePoint : new Square(tilePoint),
-	mapTile: mapPoint instanceof Square ? mapPoint : new Square(mapPoint),
+	mapTile: mapPoint instanceof Square ? mapPoint :
+		mapPoint ? new Square(mapPoint) :
+		mapPoint,
 	pixelPoint,
 });
 
diff --git a/src/cartographerPointyXYZ.js b/src/cartographerPointyXYZ.js
index 6a7a2f1..d6f26e0 100644
--- a/src/cartographerPointyXYZ.js
+++ b/src/cartographerPointyXYZ.js
@@ -8,7 +8,9 @@ import Point from './point.js';
 
 const tilePointToHex = ({tilePoint, mapPoint, pixelPoint}) => ({
 	tile: tilePoint instanceof Hex ? tilePoint : new Hex(tilePoint),
-	mapTile: mapPoint instanceof Hex ? mapPoint : new Hex(mapPoint),
+	mapTile: mapPoint instanceof Hex ? mapPoint :
+		mapPoint ? new Hex(mapPoint) :
+		mapPoint,
 	pixelPoint,
 });