diff --git a/ChangeLog b/ChangeLog
index 71917fca0..74253d627 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,21 @@
+2005-08-21  Billy Biggs  <vektor@dumbterm.net>
+
+	Fix for bug #4165:
+
+	* src/cairo-hull.c: (_cairo_hull_vertex_compare): Use pointer
+	comparison for coincident points to ensure a well-defined
+	ordering, and avoid setting discard on both points.  This fixes
+	problems with my Mac's implementation of qsort.  Final patch by
+	Bertram Felgenhauer.
+
+	* test/clip-operator-ref.png:
+	* test/linear-gradient-ref.png:
+	* test/operator-clear-ref.png:
+	* test/operator-source-ref.png:
+	* test/unantialiased-shapes-ref.png:
+	* test/unbounded-operator-ref.png: Update reference images after
+	the change.
+
 2005-08-21  Owen Taylor  <otaylor@redhat.com>
 
 	* autogen.sh: Check automake-<ver> if automake isn't sufficiently
diff --git a/src/cairo-hull.c b/src/cairo-hull.c
index c93d70625..34e0588af 100644
--- a/src/cairo-hull.c
+++ b/src/cairo-hull.c
@@ -97,7 +97,12 @@ _cairo_hull_vertex_compare (const void *av, const void *bv)
 		  (cairo_fixed_48_16_t) a->slope.dy * a->slope.dy);
 	b_dist = ((cairo_fixed_48_16_t) b->slope.dx * b->slope.dx +
 		  (cairo_fixed_48_16_t) b->slope.dy * b->slope.dy);
-	if (a_dist < b_dist) {
+	/*
+	 * Use pointer comparison for coincident points to ensure
+	 * a well-defined ordering, and avoid setting discard on
+	 * both points.
+	 */
+	if (a_dist < b_dist || (a_dist == b_dist && a < b)) {
 	    a->discard = 1;
 	    ret = -1;
 	} else {
diff --git a/test/clip-operator-ref.png b/test/clip-operator-ref.png
index 1cd0e5be1..d1be82b3d 100644
Binary files a/test/clip-operator-ref.png and b/test/clip-operator-ref.png differ
diff --git a/test/linear-gradient-ref.png b/test/linear-gradient-ref.png
index 77904144d..021b50173 100644
Binary files a/test/linear-gradient-ref.png and b/test/linear-gradient-ref.png differ
diff --git a/test/operator-clear-ref.png b/test/operator-clear-ref.png
index 538024a26..4ee43f1cc 100644
Binary files a/test/operator-clear-ref.png and b/test/operator-clear-ref.png differ
diff --git a/test/operator-source-ref.png b/test/operator-source-ref.png
index 77b6abab8..a0102139d 100644
Binary files a/test/operator-source-ref.png and b/test/operator-source-ref.png differ
diff --git a/test/unantialiased-shapes-ref.png b/test/unantialiased-shapes-ref.png
index b94859224..ad7999327 100644
Binary files a/test/unantialiased-shapes-ref.png and b/test/unantialiased-shapes-ref.png differ
diff --git a/test/unbounded-operator-ref.png b/test/unbounded-operator-ref.png
index b197c00ce..ff7a9624a 100644
Binary files a/test/unbounded-operator-ref.png and b/test/unbounded-operator-ref.png differ