diff --git a/main/opengeometry-three/tests/node/regions.test.mjs b/main/opengeometry-three/tests/node/regions.test.mjs
index 9b713251..8f1d7619 100644
--- a/main/opengeometry-three/tests/node/regions.test.mjs
+++ b/main/opengeometry-three/tests/node/regions.test.mjs
@@ -126,6 +126,32 @@ test('a boundary that cannot be closed is InvalidTopology with the 2.0 text', ()
   );
 });
 
+test('two wall pieces whose mitre faces cross at a 0.003 degree bend unite to one region', () => {
+  const ring = (points) => points.map(([x, z]) => ({ x, y: 0, z }));
+  const first = {
+    outer: ring([
+      [-7.915506291175921, -2.642064756497319], [-7.840493708824079, -2.575935243502681],
+      [-5.360466317231342, -5.389100659702814], [-5.435482107488363, -5.455226533879618],
+      [-7.915504659116948, -2.642066607788105],
+    ]),
+    holes: [],
+  };
+  const second = {
+    outer: ring([
+      [-8.973504659071258, -1.442066607747827], [-8.898495340928742, -1.375933392252173],
+      [-7.840495340928741, -2.575933392252173], [-7.915504659071259, -2.642066607747827],
+      [-7.915506291221608, -2.642064756537601],
+    ]),
+    holes: [],
+  };
+  const united = OpenGeometry.booleanRegions2D([first], [second], 'union');
+  const overlap = area(OpenGeometry.booleanRegions2D([first], [second], 'intersection'));
+  const apart = Math.abs(signedArea(first.outer)) + Math.abs(signedArea(second.outer));
+  assert.equal(united.length, 1);
+  assert(overlap > 0 && overlap < 1e-7, `overlap ${overlap}`);
+  assert(Math.abs(area(united) + overlap - apart) < 1e-9);
+});
+
 test('the curved boolean keeps an island in the hole of a frame apart in both operand orders', () => {
   const frame = curvedRegion(0, 0, 10, 10, [1, 1, 9, 9]);
   const island = curvedRegion(3, 3, 7, 7, [4, 4, 6, 6]);
diff --git a/main/opengeometry/src/geom2d/poly2d.rs b/main/opengeometry/src/geom2d/poly2d.rs
index ba2cefaa..065c1037 100644
--- a/main/opengeometry/src/geom2d/poly2d.rs
+++ b/main/opengeometry/src/geom2d/poly2d.rs
@@ -127,7 +127,7 @@ pub(super) fn segment_cross_t2(
     let r = Pt2::new(a2.x - a1.x, a2.z - a1.z);
     let s = Pt2::new(b2.x - b1.x, b2.z - b1.z);
     let denom = cross2(r, s);
-    if denom.abs() < eps {
+    if denom.abs() <= eps * r.x.hypot(r.z).min(s.x.hypot(s.z)) {
         return None;
     }
     let qp = Pt2::new(b1.x - a1.x, b1.z - a1.z);
diff --git a/main/opengeometry/src/geom2d/tests/boolean2d.rs b/main/opengeometry/src/geom2d/tests/boolean2d.rs
index 06109028..0bb34cd0 100644
--- a/main/opengeometry/src/geom2d/tests/boolean2d.rs
+++ b/main/opengeometry/src/geom2d/tests/boolean2d.rs
@@ -309,3 +309,28 @@ fn a_hole_that_no_region_contains_is_an_error() {
         Some(RegionBooleanError::OrphanHole)
     );
 }
+
+#[test]
+fn two_near_collinear_wall_pieces_unite_across_their_mitre() {
+    let first = vec![
+        p(-7.915506291175921, -2.642064756497319),
+        p(-7.840493708824079, -2.575935243502681),
+        p(-5.360466317231342, -5.389100659702814),
+        p(-5.435482107488363, -5.455226533879618),
+        p(-7.915504659116948, -2.642066607788105),
+    ];
+    let second = vec![
+        p(-8.973504659071258, -1.442066607747827),
+        p(-8.898495340928742, -1.375933392252173),
+        p(-7.840495340928741, -2.575933392252173),
+        p(-7.915504659071259, -2.642066607747827),
+        p(-7.915506291221608, -2.642064756537601),
+    ];
+    let (a, b) = (vec![first], vec![second]);
+    let [(united, union_area), (_, overlap), (_, remainder)] = areas_of_all_operations(&a, &b);
+    let (first_area, second_area) = (signed_area2(&a[0]).abs(), signed_area2(&b[0]).abs());
+    assert_eq!(united, 1);
+    assert!(overlap > 0.0 && overlap < 1.0e-7, "overlap {overlap}");
+    assert!((union_area + overlap - first_area - second_area).abs() < 1.0e-9);
+    assert!((remainder + overlap - first_area).abs() < 1.0e-9);
+}