diff --git a/crates/engine/src/cmd/fileio/affinity/master_copies.rs b/crates/engine/src/cmd/fileio/affinity/master_copies.rs
index 91b0ce53c..f0ab8bd40 100644
--- a/crates/engine/src/cmd/fileio/affinity/master_copies.rs
+++ b/crates/engine/src/cmd/fileio/affinity/master_copies.rs
@@ -1,7 +1,8 @@
 use super::nodes::MAX_DEPTH;
 use super::{Kind, af};
 
-/// What copying a subtree takes: its nodes, characters and table cells (`work`), and its pixels.
+/// What copying a subtree takes: its nodes, characters, table cells and path segments (`work`),
+/// and its pixels.
 #[derive(Clone, Copy, Debug, Default)]
 pub(super) struct CopyCost {
     pub(super) work: u64,
@@ -40,8 +41,58 @@ pub(super) fn copy_cost(n: &af::Node, depth: usize) -> CopyCost {
     let own = match &n.kind {
         Kind::Text(t) => CopyCost { work: 1 + len(&t.runs), pixels: 0 },
         Kind::Table(t) => CopyCost { work: 1 + t.cells.iter().map(|c| 1 + len(&c.runs)).sum::<u64>(), pixels: 0 },
-        Kind::Image(img) => CopyCost { work: 1, pixels: u64::from(img.width) * u64::from(img.height) },
+        Kind::Image(img) => CopyCost { work: 1, pixels: pixels(img) },
+        // Each copy builds its own path: a curve of many segments costs them all.
+        Kind::Shape { path, .. } | Kind::Artboard { path, .. } => CopyCost { work: 1 + segments(path), pixels: 0 },
         _ => CopyCost { work: 1, pixels: 0 },
     };
-    n.children.iter().fold(own, |c, ch| c.plus(copy_cost(ch, depth + 1)))
+    // A vector mask is a path of its own, and a pixel mask an image of its own, in every copy.
+    let mask =
+        CopyCost { work: n.mask.as_ref().map_or(0, segments) + u64::from(n.pixel_mask.is_some()), pixels: n.pixel_mask.as_ref().map_or(0, pixels) };
+    n.children.iter().fold(own.plus(mask), |c, ch| c.plus(copy_cost(ch, depth + 1)))
+}
+
+/// The subpaths and segments of `p`.
+fn segments(p: &af::Path) -> u64 {
+    p.subpaths.iter().map(|s| 1 + s.segments.len() as u64).sum()
+}
+
+fn pixels(img: &af::Image) -> u64 {
+    u64::from(img.width) * u64::from(img.height)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn node(kind: Kind, mask: Option<af::Path>) -> af::Node {
+        af::Node {
+            class: vectorcraft_affinity::stream::Tag::of(b"ShpN"),
+            name: String::new(),
+            visible: true,
+            locked: false,
+            opacity: 1.0,
+            blend: af::Blend::Normal,
+            kind,
+            mask,
+            pixel_mask: None,
+            effects: vec![],
+            children: vec![],
+        }
+    }
+
+    fn path(n: usize) -> af::Path {
+        let p = af::Point { x: 0.0, y: 0.0 };
+        af::Path { subpaths: vec![af::SubPath { start: p, segments: vec![[p; 3]; n], closed: false }] }
+    }
+
+    /// A curve, and a vector mask, cost every segment each copy rebuilds: a shape of a million
+    /// segments shown on many pages can't pass as one object.
+    #[test]
+    fn paths_and_masks_cost_their_segments() {
+        let shape = |n| Kind::Shape { path: path(n), fills: vec![], strokes: vec![], even_odd: false };
+        assert!(copy_cost(&node(shape(1_000_000), None), 0).work > 1_000_000);
+        assert!(copy_cost(&node(Kind::Group, Some(path(1_000_000))), 0).work > 1_000_000);
+        assert!(copy_cost(&node(shape(3), None), 0).work < 10);
+    }
 }
diff --git a/crates/engine/src/cmd/fileio/affinity/nodes.rs b/crates/engine/src/cmd/fileio/affinity/nodes.rs
index 2e9334227..36734dbe3 100644
--- a/crates/engine/src/cmd/fileio/affinity/nodes.rs
+++ b/crates/engine/src/cmd/fileio/affinity/nodes.rs
@@ -11,6 +11,15 @@ pub(super) fn affine(a: af::Affine) -> Affine {
     Affine::new(a.0)
 }
 
+/// Are all of `p`'s points, mapped by `to_doc`, finite and within `MAX_COORD` of the origin?
+pub(super) fn path_in_range(p: &af::Path, to_doc: Affine) -> bool {
+    let ok = |q: &af::Point| {
+        let d = to_doc * kurbo::Point::new(q.x, q.y);
+        [d.x, d.y].iter().all(|v| v.is_finite() && v.abs() <= crate::MAX_COORD)
+    };
+    p.subpaths.iter().all(|s| ok(&s.start) && s.segments.iter().flatten().all(ok))
+}
+
 impl Builder {
     pub(super) fn layer_with(&mut self, name: Option<&str>, children: Vec<Arc<Node>>) -> Arc<Node> {
         let id = self.doc.alloc_id();
@@ -107,6 +116,12 @@ impl Builder {
                 return None;
             }
         }
+        // So must its vector mask, which becomes a clipping path: every control point, not just
+        // the finite ones a bounding box takes.
+        if n.mask.as_ref().is_some_and(|m| !path_in_range(m, to_doc)) {
+            self.warn("objects beyond the document range VectorCraft supports (left out)");
+            return None;
+        }
         let n = &*self.overlaid(n);
         // Register before descending so nested artboards keep their document order. Inside an
         // embedded document an artboard is just its content's frame.
@@ -252,3 +267,25 @@ impl Builder {
         Some(Arc::new(out))
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn path(points: &[(f64, f64)]) -> af::Path {
+        let p = |&(x, y): &(f64, f64)| af::Point { x, y };
+        let start = p(&points[0]);
+        let segments = points[1..].iter().map(|q| [start, p(q), p(q)]).collect();
+        af::Path { subpaths: vec![af::SubPath { start, segments, closed: true }] }
+    }
+
+    /// A mask's control points are checked as mapped into the document, NaN ones included.
+    #[test]
+    fn mask_paths_must_stay_in_the_document_range() {
+        let k = Affine::scale(0.75);
+        assert!(path_in_range(&path(&[(0.0, 0.0), (100.0, 0.0), (100.0, 100.0)]), k));
+        assert!(!path_in_range(&path(&[(0.0, 0.0), (1.0e7, 0.0)]), k));
+        assert!(!path_in_range(&path(&[(0.0, 0.0), (f64::NAN, 0.0)]), k));
+        assert!(!path_in_range(&path(&[(0.0, 0.0), (1.0, 1.0)]), Affine::scale(1.0e9)));
+    }
+}