diff --git a/crates/specialized/rtx-cfd/src/mesh/patch_mesh.rs b/crates/specialized/rtx-cfd/src/mesh/patch_mesh.rs
index 235ae29..80fe1b0 100644
--- a/crates/specialized/rtx-cfd/src/mesh/patch_mesh.rs
+++ b/crates/specialized/rtx-cfd/src/mesh/patch_mesh.rs
@@ -173,6 +173,23 @@ impl PatchMesh {
         k * (self.ns + 1) + i
     }
     /// Node coordinates.
+    /// `[x_min, x_max, y_min, y_max]` over the nodes.
+    pub fn bounding_box(&self) -> [f64; 4] {
+        let (mut b, mut first) = ([0.0; 4], true);
+        for (&x, &y) in self.x.iter().zip(&self.y) {
+            if first {
+                b = [x, x, y, y];
+                first = false;
+            } else {
+                b[0] = b[0].min(x);
+                b[1] = b[1].max(x);
+                b[2] = b[2].min(y);
+                b[3] = b[3].max(y);
+            }
+        }
+        b
+    }
+
     pub fn node_xy(&self, n: usize) -> [f64; 2] {
         [self.x[n], self.y[n]]
     }
diff --git a/crates/specialized/rtx-cfd/src/solvers/incompressible/overset/overlap.rs b/crates/specialized/rtx-cfd/src/solvers/incompressible/overset/overlap.rs
index 2e208c6..a20ca16 100644
--- a/crates/specialized/rtx-cfd/src/solvers/incompressible/overset/overlap.rs
+++ b/crates/specialized/rtx-cfd/src/solvers/incompressible/overset/overlap.rs
@@ -162,13 +162,20 @@ impl OverlapMap {
         let primal = QuadIndex::primal(patch);
         let body = body_polygon(patch);
 
-        // 1. Cells.
+        // 1. Cells. A centre outside the patch's node bounding box lies in
+        //    no patch cell and outside the body (which the patch encloses):
+        //    Active without a point location (PERF-2 P1.2, the same class
+        //    the search would return).
+        let bbox = patch.bounding_box();
         let mut class = vec![CellClass::Active; nx * ny];
         let mut hole_cells = 0;
         for j in 0..ny {
             for i in 0..nx {
                 let x = (i as f64 + 0.5) * dx;
                 let y = (j as f64 + 0.5) * dy;
+                if x < bbox[0] || x > bbox[1] || y < bbox[2] || y > bbox[3] {
+                    continue;
+                }
                 let in_hole = match primal.locate(patch, x, y) {
                     Some(c) => patch.cell_ki(c).0 <= hole_row_max,
                     None => body