diff --git a/src/image/geom.go b/src/image/geom.go
index 7c56010653..70e3ff0288 100644
--- a/src/image/geom.go
+++ b/src/image/geom.go
@@ -62,7 +62,7 @@ func (p Point) Mod(r Rectangle) Point {
 
 // Eq reports whether p and q are equal.
 func (p Point) Eq(q Point) bool {
-	return p.X == q.X && p.Y == q.Y
+	return p == q
 }
 
 // ZP is the zero Point.
@@ -190,10 +190,10 @@ func (r Rectangle) Empty() bool {
 	return r.Min.X >= r.Max.X || r.Min.Y >= r.Max.Y
 }
 
-// Eq reports whether r and s are equal.
+// Eq reports whether r and s contain the same set of points. All empty
+// rectangles are considered equal.
 func (r Rectangle) Eq(s Rectangle) bool {
-	return r.Min.X == s.Min.X && r.Min.Y == s.Min.Y &&
-		r.Max.X == s.Max.X && r.Max.Y == s.Max.Y
+	return r == s || r.Empty() && s.Empty()
 }
 
 // Overlaps reports whether r and s have a non-empty intersection.
@@ -229,7 +229,9 @@ func (r Rectangle) Canon() Rectangle {
 // ZR is the zero Rectangle.
 var ZR Rectangle
 
-// Rect is shorthand for Rectangle{Pt(x0, y0), Pt(x1, y1)}.
+// Rect is shorthand for Rectangle{Pt(x0, y0), Pt(x1, y1)}. The returned
+// rectangle has minimum and maximum coordinates swapped if necessary so that
+// it is well-formed.
 func Rect(x0, y0, x1, y1 int) Rectangle {
 	if x0 > x1 {
 		x0, x1 = x1, x0
diff --git a/src/image/geom_test.go b/src/image/geom_test.go
index 5bbd8a9492..6e9c6a13c2 100644
--- a/src/image/geom_test.go
+++ b/src/image/geom_test.go
@@ -39,6 +39,18 @@ func TestRectangle(t *testing.T) {
 		Rect(6, 5, 4, 3),
 	}
 
+	// r.Eq(s) should be equivalent to every point in r being in s, and every
+	// point in s being in r.
+	for _, r := range rects {
+		for _, s := range rects {
+			got := r.Eq(s)
+			want := in(r, s) == nil && in(s, r) == nil
+			if got != want {
+				t.Errorf("Eq: r=%s, s=%s: got %t, want %t", r, s, got, want)
+			}
+		}
+	}
+
 	// The intersection should be the largest rectangle a such that every point
 	// in a is both in r and in s.
 	for _, r := range rects {