diff --git a/crates/geom/src/corners.rs b/crates/geom/src/corners.rs
index fe64d9e64..6fe68e576 100644
--- a/crates/geom/src/corners.rs
+++ b/crates/geom/src/corners.rs
@@ -39,7 +39,11 @@ impl Side {
 
     /// The side's length.
     fn length(&self) -> f64 {
-        if self.straight() { self.curve.p0.distance(self.curve.p3) } else { crate::path::measured_arclen(&kurbo::PathSeg::Cubic(self.curve), ARCLEN_ACCURACY) }
+        if self.straight() {
+            self.curve.p0.distance(self.curve.p3)
+        } else {
+            crate::path::measured_arclen(&kurbo::PathSeg::Cubic(self.curve), ARCLEN_ACCURACY)
+        }
     }
 
     /// The parameter `s` along the side from the corner, the point there and the direction the
diff --git a/crates/tools/src/distort/liquify.rs b/crates/tools/src/distort/liquify.rs
index de40eef35..1e917ffc4 100644
--- a/crates/tools/src/distort/liquify.rs
+++ b/crates/tools/src/distort/liquify.rs
@@ -388,7 +388,8 @@ fn subdivide(sp: &mut SubPath, prm: &LiquifyParams, c: Point, spacing: f64) {
             continue;
         }
         let len = cub.arclen(1e-3);
-        let k = (len / spacing).ceil() as usize;
+        // (No more pieces than the anchors left under the ceiling.)
+        let k = ((len / spacing).ceil() as usize).min(MAX_ANCHORS.saturating_sub(sp.anchors.len()) + 1);
         if k <= 1 {
             seg += 1;
             continue;
diff --git a/crates/tools/src/distort/perspective.rs b/crates/tools/src/distort/perspective.rs
index 4f172760b..3d3042d6d 100644
--- a/crates/tools/src/distort/perspective.rs
+++ b/crates/tools/src/distort/perspective.rs
@@ -549,6 +549,11 @@ impl PerspectiveGrid {
         let Some(h) = self.homography(plane) else { return vec![] };
         let d = self.domain(plane);
         let mut out = vec![];
+        // A stored grid is not checked: no spacing, or an extent that isn't a number, has no lines.
+        let (w, h_len) = (d.width(), d.height());
+        if !(self.cell.is_finite() && self.cell > 0.0 && w.is_finite() && h_len.is_finite()) {
+            return out;
+        }
         let step = |len: f64| {
             let mut s = self.cell;
             while len / s > 120.0 {
@@ -556,20 +561,19 @@ impl PerspectiveGrid {
             }
             s
         };
-        let (su, sv) = (step(d.width()), step(d.height()));
-        let mut u = 0.0;
-        while u <= d.width() + 1e-9 {
-            if let (Some(a), Some(b)) = (h.apply(Point::new(u, 0.0)), h.apply(Point::new(u, d.height()))) {
+        let (su, sv) = (step(w), step(h_len));
+        // Counted, not summed: a count in whole lines (at most 121 a way).
+        for i in 0..=((w + 1e-9) / su).floor() as usize {
+            let u = i as f64 * su;
+            if let (Some(a), Some(b)) = (h.apply(Point::new(u, 0.0)), h.apply(Point::new(u, h_len))) {
                 out.push((a, b));
             }
-            u += su;
         }
-        let mut v = 0.0;
-        while v <= d.height() + 1e-9 {
-            if let (Some(a), Some(b)) = (h.apply(Point::new(0.0, v)), h.apply(Point::new(d.width(), v))) {
+        for i in 0..=((h_len + 1e-9) / sv).floor() as usize {
+            let v = i as f64 * sv;
+            if let (Some(a), Some(b)) = (h.apply(Point::new(0.0, v)), h.apply(Point::new(w, v))) {
                 out.push((a, b));
             }
-            v += sv;
         }
         out
     }