diff --git a/util/box.c b/util/box.c
index bc2c60dd..73a42633 100644
--- a/util/box.c
+++ b/util/box.c
@@ -1,4 +1,3 @@
-#include <limits.h>
 #include <math.h>
 #include <stdbool.h>
 #include <stdlib.h>
@@ -14,10 +13,29 @@ void wlr_box_closest_point(const struct wlr_box *box, double x, double y,
 		return;
 	}
 
+	// Note: the width and height of the box are exclusive; that is,
+	// for a 100x100 box at (0,0), the point (99,99) is inside it
+	// while the point (100,100) is outside it.
+	//
+	// Mathematically, there exists no single closest point to the
+	// bottom-right corner of the box while remaining inside it. You
+	// can construct an infinite series approaching the limit, such
+	// as {(99,99), (99.9,99.9), (99.99,99.99)...}, but since the
+	// intervals are half-open, there is no "last" point.
+	//
+	// This function must therefore define an arbitrary "closest"
+	// point. For simplicity and consistency, this is defined to be
+	// (box.x + width - 1, box.y + height - 1).
+	//
+	// (The previous implementation was non-linear: with the example
+	// 100x100 box, it would return an input point of (99.9,99.9)
+	// unchanged, but for an input point (100.1,100.1) the returned
+	// point would jump back to (99.0,99.0). This is now fixed.)
+
 	// find the closest x point
 	if (x < box->x) {
 		*dest_x = box->x;
-	} else if (x >= box->x + box->width) {
+	} else if (x > box->x + box->width - 1) {
 		*dest_x = box->x + box->width - 1;
 	} else {
 		*dest_x = x;
@@ -26,7 +44,7 @@ void wlr_box_closest_point(const struct wlr_box *box, double x, double y,
 	// find closest y point
 	if (y < box->y) {
 		*dest_y = box->y;
-	} else if (y >= box->y + box->height) {
+	} else if (y > box->y + box->height - 1) {
 		*dest_y = box->y + box->height - 1;
 	} else {
 		*dest_y = y;