diff --git a/crates/pathops/src/boolean.rs b/crates/pathops/src/boolean.rs
index dc3a5cf47..2e7b1b793 100644
--- a/crates/pathops/src/boolean.rs
+++ b/crates/pathops/src/boolean.rs
@@ -656,8 +656,10 @@ pub(crate) fn normalize_bez(bp: &BezPath, rule: FillRule) -> Result<Contours, Pa
     if !crate::budget::sweep_fits([&bp]) {
         return Err(PathOpsError::TooComplex);
     }
-    let top = Topology::<i32>::from_path(&bp, eps).map_err(|_| PathOpsError::OpenPath)?;
-    Ok(top.contours(|w| inside(rule, *w)))
+    // As in `Sweep::new`, a panic in the sweep on near-degenerate input becomes an error.
+    let swept =
+        std::panic::catch_unwind(std::panic::AssertUnwindSafe(|| Topology::<i32>::from_path(&bp, eps).map(|top| top.contours(|w| inside(rule, *w)))));
+    swept.map_err(|_| PathOpsError::Degenerate)?.map_err(|_| PathOpsError::OpenPath)
 }
 
 /// Boolean operation between two filled paths. Returns an empty path on invalid (non-finite) input.
diff --git a/crates/pathops/tests/it/hostile_params.rs b/crates/pathops/tests/it/hostile_params.rs
new file mode 100644
index 000000000..108fe2b48
--- /dev/null
+++ b/crates/pathops/tests/it/hostile_params.rs
@@ -0,0 +1,49 @@
+//! Absurd but finite or non-finite numeric parameters: no panic, hang or runaway allocation.
+
+use vectorcraft_geom::{PathData, Point, SubPath};
+use vectorcraft_pathops::*;
+
+const HOSTILE: [f64; 9] = [f64::NAN, f64::INFINITY, f64::NEG_INFINITY, 0.0, -0.0, 1e-300, 1e300, -1e300, f64::MAX];
+
+fn square() -> PathData {
+    PathData::single(SubPath::polyline(&[Point::new(0.0, 0.0), Point::new(10.0, 0.0), Point::new(10.0, 10.0), Point::new(0.0, 10.0)], true))
+}
+
+fn zigzag() -> PathData {
+    let pts: Vec<Point> = (0..40).map(|i| Point::new(i as f64 * 3.0, if i % 2 == 0 { 0.0 } else { 7.0 })).collect();
+    PathData::single(SubPath::polyline(&pts, false))
+}
+
+#[test]
+fn edit_functions_survive_hostile_numbers() {
+    for paths in [square(), zigzag()] {
+        for &v in &HOSTILE {
+            let _ = simplify(&paths, v);
+            let _ = simplify_with(&paths, &SimplifyOptions { tolerance: v, corner_angle_deg: v, straight_lines: false });
+            let _ = simplify_with(&paths, &SimplifyOptions { tolerance: 0.5, corner_angle_deg: v, straight_lines: true });
+            let _ = smooth(&paths, v);
+            let _ = smooth_level(&paths, v);
+            let _ = remove_redundant_points(&paths, v);
+            let _ = join(&[paths.clone(), zigzag()], v);
+            let _ = simplify_level_tolerance(v);
+            let _ = auto_simplify_level(v);
+        }
+    }
+}
+
+/// A stroke width of 1e200 or more with round joins used to panic inside the sweep (`Left == Ish`).
+#[test]
+fn stroke_and_offset_survive_hostile_numbers() {
+    for paths in [square(), zigzag()] {
+        for &w in &HOSTILE {
+            for &m in &[f64::NAN, 0.0, 1.0, 1e300] {
+                for join in [Join::Miter, Join::Round, Join::Bevel] {
+                    for cap in [Cap::Butt, Cap::Round] {
+                        let _ = outline_stroke(&paths, w, cap, join, m);
+                    }
+                    let _ = offset_path(&paths, w, join, m);
+                }
+            }
+        }
+    }
+}
diff --git a/crates/pathops/tests/it/main.rs b/crates/pathops/tests/it/main.rs
index 3f565e040..552620c0c 100644
--- a/crates/pathops/tests/it/main.rs
+++ b/crates/pathops/tests/it/main.rs
@@ -5,6 +5,7 @@
 #[path = "../common/mod.rs"]
 mod common;
 
+mod hostile_params;
 mod ops;
 mod pathfinder_pinned;
 mod prop_pathops;