diff --git a/src/lib.rs b/src/lib.rs
index b82a941..a5ab04c 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -256,4 +256,16 @@ mod tests {
         let path = BezPath::from_svg(path).unwrap();
         Topology::from_path(&path, 0.001).unwrap();
     }
+
+    #[test]
+    fn empty_paths() {
+        let contours = binary_op(
+            &BezPath::new(),
+            &BezPath::new(),
+            FillRule::EvenOdd,
+            BinaryOp::Xor,
+        )
+        .unwrap();
+        assert!(contours.contours().next().is_none());
+    }
 }
diff --git a/src/sweep/sweep_line.rs b/src/sweep/sweep_line.rs
index 60d2a6b..ac7baa7 100644
--- a/src/sweep/sweep_line.rs
+++ b/src/sweep/sweep_line.rs
@@ -317,7 +317,7 @@ impl<'segs> Sweeper<'segs> {
         Sweeper {
             eps,
             line: SegmentOrder::default(),
-            y: events.next_y(segments).unwrap(),
+            y: events.next_y(segments).unwrap_or(f64::INFINITY),
             events,
             segments,
             segs_needing_positions: Vec::new(),
@@ -1932,6 +1932,14 @@ mod tests {
         insta::assert_ron_snapshot!(snapshot_outputs(segs, 0.25));
     }
 
+    #[test]
+    fn empty_sweep_line() {
+        let segs = Segments::default();
+        let mut sweep = Sweeper::new(&segs, 1.0);
+        let mut bufs = SweepLineBuffers::default();
+        assert!(sweep.next_line(&mut bufs).is_none());
+    }
+
     proptest! {
     #[test]
     fn perturbation_test_f64(perturbations in prop::collection::vec(perturbation(f64_perturbation(0.1)), 1..5)) {