diff --git a/cameo/area.c b/cameo/area.c
index 953f472..0995e12 100644
--- a/cameo/area.c
+++ b/cameo/area.c
@@ -10,6 +10,11 @@
  * (at your option) any later version.
  */
 
+/*
+ * We use the following requirement to simplify toolpath generation: the
+ * outlines must be designed such that the tool can pass along all the
+ * outlines without cutting into anything it's not supposed to.
+ */
 
 #include <stdio.h>
 #include <stddef.h>
@@ -145,7 +150,8 @@ static int touch(double ax, double ay, double bx, double by,
 
 
 static int hit_segment(double fx, double fy, double tx, double ty,
-    const struct point *a, const struct point *b, double r, double *n)
+    const struct point *a, const struct point *b, double r, int enter,
+    double *n)
 {
 	double dx, dy, d;
 	double px, py;
@@ -158,6 +164,12 @@ printf("      seg (%g,%g)+(%g,%g) -> (%g,%g)-(%g,%g)\n",
 
 	dx = b->x-a->x;
 	dy = b->y-a->y;
+
+	if (enter && dy < 0)
+		return 0;
+	if (!enter && dy > 0)
+		return 0;
+
 	d = hypot(dx, dy);
 
 	px = a->x-dy/d*r;
@@ -194,7 +206,7 @@ static int hit_path(double fx, double fy, double tx, double ty,
 		left = !left;
 	for (p = path->first; p != path->last; p = p->next) {
 		if (hit_segment(fx, fy, tx, ty,
-		    left ? p : p->next, left ? p->next : p, r, &tmp)) {
+		    left ? p : p->next, left ? p->next : p, r, enter, &tmp)) {
 			if (!found || nx > tmp)
 				nx = tmp;
 			found = 1;