diff --git a/crates/prc-render/src/render.rs b/crates/prc-render/src/render.rs
index d9072a3055..3670878e17 100644
--- a/crates/prc-render/src/render.rs
+++ b/crates/prc-render/src/render.rs
@@ -5,7 +5,7 @@
 
 use crate::WorldMesh;
 use crate::raster::{Corner, Target, View, ViewCorner, at};
-use crate::vec3::{cross, dot, length, normalize, scale, sub};
+use crate::vec3::{cross, dot, length, normalize, scale, sub, unit_cross};
 use pdfcraft_prc::TriangleMesh;
 
 /// The largest image [`render`] draws, in pixels (width × height).
@@ -318,7 +318,7 @@ impl Scene {
         let Some(world) = mesh.triangles.get(t).and_then(|tri| corners(mesh, tri)) else {
             return;
         };
-        let Some(face) = normalize(cross(sub(at3(&world, 1), at3(&world, 0)), sub(at3(&world, 2), at3(&world, 0)))) else {
+        let Some(face) = unit_cross(sub(at3(&world, 1), at3(&world, 0)), sub(at3(&world, 2), at3(&world, 0))) else {
             return;
         };
         let stored = stored_normals(mesh, t);
diff --git a/crates/prc-render/src/render/tests.rs b/crates/prc-render/src/render/tests.rs
index 8d0764315d..ec8104a260 100644
--- a/crates/prc-render/src/render/tests.rs
+++ b/crates/prc-render/src/render/tests.rs
@@ -268,3 +268,11 @@ fn unlit_draws_the_plain_colour_and_the_headlight_shades_by_angle() {
     assert_eq!(lit(Lighting::Headlight, 1.0), [151, 153, 159, 255]);
     assert_eq!(lit(Lighting::Unlit, 1.0), [190, 192, 200, 255]);
 }
+
+#[test]
+fn a_huge_square_is_drawn() {
+    // Its edges' cross product (about 1e320) overflows unless they are scaled first.
+    let image = render(&[quad(0.0, 1e160, 0.0)], &ortho(4e160), &small()).unwrap();
+    assert_eq!(pixel(&image, 20, 20), [190, 192, 200, 255]);
+    assert_eq!(pixel(&image, 1, 1), [255, 255, 255, 255]);
+}
diff --git a/crates/prc-render/src/vec3.rs b/crates/prc-render/src/vec3.rs
index 8ebf844087..7a673e0055 100644
--- a/crates/prc-render/src/vec3.rs
+++ b/crates/prc-render/src/vec3.rs
@@ -40,6 +40,17 @@ pub(crate) fn normalize(a: Vec3) -> Option<Vec3> {
     (l.is_finite() && l > 0.0).then(|| scale(a, 1.0 / l))
 }
 
+/// The unit normal of the plane spanned by `a` and `b` (`a × b`, normalized); `None` when they are
+/// parallel, zero or not finite. Both are first divided by their largest component, so the cross
+/// product of two huge edges cannot overflow before it is normalized.
+pub(crate) fn unit_cross(a: Vec3, b: Vec3) -> Option<Vec3> {
+    let big = a.iter().chain(b.iter()).fold(0.0_f64, |m, c| m.max(c.abs()));
+    if !(big.is_finite() && big > 0.0) {
+        return None;
+    }
+    normalize(cross(a.map(|c| c / big), b.map(|c| c / big)))
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
@@ -63,4 +74,12 @@ mod tests {
         assert_eq!(normalize([1e200, 0.0, 0.0]), Some([1.0, 0.0, 0.0]));
         assert_eq!(normalize([0.0, -3e-320, 0.0]), Some([0.0, -1.0, 0.0]));
     }
+
+    #[test]
+    fn unit_cross_survives_edges_whose_product_overflows() {
+        assert_eq!(unit_cross([1e160, 0.0, 0.0], [0.0, 1e160, 0.0]), Some([0.0, 0.0, 1.0]));
+        assert_eq!(unit_cross([1e-170, 0.0, 0.0], [0.0, 1e-170, 0.0]), Some([0.0, 0.0, 1.0]));
+        assert_eq!(unit_cross([2.0, 0.0, 0.0], [4.0, 0.0, 0.0]), None);
+        assert_eq!(unit_cross([f64::INFINITY, 0.0, 0.0], [0.0, 1.0, 0.0]), None);
+    }
 }