diff --git a/include/wlr/types/wlr_output_layout.h b/include/wlr/types/wlr_output_layout.h
index 9094f02f..144c2d5a 100644
--- a/include/wlr/types/wlr_output_layout.h
+++ b/include/wlr/types/wlr_output_layout.h
@@ -47,9 +47,12 @@ bool wlr_output_layout_intersects(struct wlr_output_layout *layout,
 		struct wlr_output *reference, int x1, int y1, int x2, int y2);
 
 /**
- * Get the closest boundary point of this layout from the given point.
+ * Get the closest boundary point of this layout from the given point from the
+ * reference output. If reference is NULL, gets the closest boundary point from
+ * the entire layout.
  */
 void wlr_output_layout_closest_boundary(struct wlr_output_layout *layout,
-		int x, int y, int *dest_x, int *dest_y);
+		struct wlr_output *reference, double x, double y, double *dest_x,
+		double *dest_y);
 
 #endif
diff --git a/types/wlr_cursor.c b/types/wlr_cursor.c
index c9937c73..affdcdeb 100644
--- a/types/wlr_cursor.c
+++ b/types/wlr_cursor.c
@@ -22,6 +22,7 @@ struct wlr_cursor_state {
 	struct wl_list devices;
 	struct wlr_output_layout *layout;
 	struct wlr_xcursor *xcursor;
+	struct wlr_output *mapped_output;
 };
 
 struct wlr_cursor *wlr_cursor_init() {
@@ -37,6 +38,8 @@ struct wlr_cursor *wlr_cursor_init() {
 		return NULL;
 	}
 
+	cur->state->mapped_output = NULL;
+
 	wl_list_init(&cur->state->devices);
 
 	wl_signal_init(&cur->events.motion);
@@ -66,7 +69,16 @@ void wlr_cursor_set_xcursor(struct wlr_cursor *cur, struct wlr_xcursor *xcur) {
 
 bool wlr_cursor_warp(struct wlr_cursor *cur, double x, double y) {
 	assert(cur->state->layout);
-	if (!wlr_output_layout_output_at(cur->state->layout, x, y)) {
+	struct wlr_output *output;
+	output = wlr_output_layout_output_at(cur->state->layout, x, y);
+
+	if (!output) {
+		return false;
+	}
+
+	if (cur->state->mapped_output &&
+			!wlr_output_layout_contains_point(cur->state->layout,
+				cur->state->mapped_output, x, y)) {
 		return false;
 	}
 
@@ -97,13 +109,16 @@ bool wlr_cursor_warp(struct wlr_cursor *cur, double x, double y) {
 void wlr_cursor_move(struct wlr_cursor *cur, double delta_x, double delta_y) {
 	assert(cur->state->layout);
 
-	int x = cur->x + delta_x;
-	int y = cur->y + delta_y;
+	double x = cur->x + delta_x;
+	double y = cur->y + delta_y;
+
+	struct wlr_output *output;
+	output = wlr_output_layout_output_at(cur->state->layout, x, y);
 
-	if (!wlr_output_layout_output_at(cur->state->layout, x, y)) {
-		int closest_x, closest_y;
-		wlr_output_layout_closest_boundary(cur->state->layout, x, y, &closest_x,
-			&closest_y);
+	if (!output || (cur->state->mapped_output && cur->state->mapped_output != output)) {
+		double closest_x, closest_y;
+		wlr_output_layout_closest_boundary(cur->state->layout,
+			cur->state->mapped_output, x, y, &closest_x, &closest_y);
 		x = closest_x;
 		y = closest_y;
 	}
@@ -210,7 +225,7 @@ void wlr_cursor_attach_output_layout(struct wlr_cursor *cur,
 
 void wlr_cursor_map_to_output(struct wlr_cursor *cur,
 		struct wlr_output *output) {
-	wlr_log(L_DEBUG, "TODO: map to output");
+	cur->state->mapped_output = output;
 }
 
 void wlr_cursor_map_input_to_output(struct wlr_cursor *cur,
diff --git a/types/wlr_output_layout.c b/types/wlr_output_layout.c
index a26a4794..5e2067da 100644
--- a/types/wlr_output_layout.c
+++ b/types/wlr_output_layout.c
@@ -135,11 +135,17 @@ static double get_distance(double x1, double y1, double x2, double y2) {
 }
 
 void wlr_output_layout_closest_boundary(struct wlr_output_layout *layout,
-		int x, int y, int *dest_x, int *dest_y) {
-	int min_x = INT_MAX, min_y = INT_MAX, min_distance = INT_MAX;
+		struct wlr_output *reference, double x, double y, double *dest_x,
+		double *dest_y) {
+	double min_x = INT_MAX, min_y = INT_MAX, min_distance = INT_MAX;
 	struct wlr_output_layout_output *l_output;
 	wl_list_for_each(l_output, &layout->outputs, link) {
-		int width, height, output_x, output_y, output_distance;
+		if (reference != NULL && reference != l_output->output) {
+			continue;
+		}
+
+		int width, height;
+		double output_x, output_y, output_distance;
 		wlr_output_effective_resolution(l_output->output, &width, &height);
 
 		// find the closest x point