diff --git a/Cargo.lock b/Cargo.lock
index 9c00e25178..b99a00db04 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -973,7 +973,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 
 [[package]]
 name = "plane-split"
-version = "0.12.1"
+version = "0.13.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 dependencies = [
  "binary-space-partition 0.1.2 (registry+https://github.com/rust-lang/crates.io-index)",
@@ -1069,7 +1069,7 @@ dependencies = [
  "lazy_static 1.0.0 (registry+https://github.com/rust-lang/crates.io-index)",
  "libc 0.2.42 (registry+https://github.com/rust-lang/crates.io-index)",
  "num_cpus 1.8.0 (registry+https://github.com/rust-lang/crates.io-index)",
- "rand 0.3.22 (registry+https://github.com/rust-lang/crates.io-index)",
+ "rand 0.4.2 (registry+https://github.com/rust-lang/crates.io-index)",
 ]
 
 [[package]]
@@ -1496,7 +1496,7 @@ dependencies = [
  "pathfinder_gfx_utils 0.2.0 (git+https://github.com/pcwalton/pathfinder)",
  "pathfinder_partitioner 0.2.0 (git+https://github.com/pcwalton/pathfinder)",
  "pathfinder_path_utils 0.2.0 (git+https://github.com/pcwalton/pathfinder)",
- "plane-split 0.12.1 (registry+https://github.com/rust-lang/crates.io-index)",
+ "plane-split 0.13.0 (registry+https://github.com/rust-lang/crates.io-index)",
  "png 0.12.0 (registry+https://github.com/rust-lang/crates.io-index)",
  "rayon 1.0.1 (registry+https://github.com/rust-lang/crates.io-index)",
  "ron 0.1.7 (registry+https://github.com/rust-lang/crates.io-index)",
@@ -1803,7 +1803,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 "checksum pathfinder_path_utils 0.2.0 (git+https://github.com/pcwalton/pathfinder)" = "<none>"
 "checksum percent-encoding 1.0.1 (registry+https://github.com/rust-lang/crates.io-index)" = "31010dd2e1ac33d5b46a5b413495239882813e0369f8ed8a5e266f173602f831"
 "checksum pkg-config 0.3.11 (registry+https://github.com/rust-lang/crates.io-index)" = "110d5ee3593dbb73f56294327fe5668bcc997897097cbc76b51e7aed3f52452f"
-"checksum plane-split 0.12.1 (registry+https://github.com/rust-lang/crates.io-index)" = "ff3a4fc9e31d70eb6828e9a2d7a401a824d9f281686a39a8fc06f08796edb1bb"
+"checksum plane-split 0.13.0 (registry+https://github.com/rust-lang/crates.io-index)" = "64d766f38b15fe1337bdddfc869ef5c50437323f857aaaadc6490197db80a1b8"
 "checksum png 0.12.0 (registry+https://github.com/rust-lang/crates.io-index)" = "f54b9600d584d3b8a739e1662a595fab051329eff43f20e7d8cc22872962145b"
 "checksum proc-macro2 0.4.6 (registry+https://github.com/rust-lang/crates.io-index)" = "effdb53b25cdad54f8f48843d67398f7ef2e14f12c1b4cb4effc549a6462a4d6"
 "checksum quick-error 1.2.1 (registry+https://github.com/rust-lang/crates.io-index)" = "eda5fe9b71976e62bc81b781206aaa076401769b2143379d3eb2118388babac4"
diff --git a/webrender/Cargo.toml b/webrender/Cargo.toml
index 7c74c9ed0c..037ce18da8 100644
--- a/webrender/Cargo.toml
+++ b/webrender/Cargo.toml
@@ -32,7 +32,7 @@ image = { optional = true, version = "0.19" }
 lazy_static = "1"
 log = "0.4"
 num-traits = "0.2"
-plane-split = "0.12.1"
+plane-split = "0.13"
 png = { optional = true, version = "0.12" }
 rayon = "1"
 ron = { optional = true, version = "0.1.7" }
diff --git a/webrender/src/batch.rs b/webrender/src/batch.rs
index 00bd69e215..b9cc949f22 100644
--- a/webrender/src/batch.rs
+++ b/webrender/src/batch.rs
@@ -660,8 +660,10 @@ impl AlphaBatchBuilder {
                                         &matrix,
                                         Some(bounding_rect.to_f64()),
                                     );
-                                    for poly in results {
-                                        splitter.add(poly);
+                                    if let Ok(results) = results {
+                                        for poly in results {
+                                            splitter.add(poly);
+                                        }
                                     }
                                 }
                             }
diff --git a/webrender/src/util.rs b/webrender/src/util.rs
index 2b2189a188..846895497a 100644
--- a/webrender/src/util.rs
+++ b/webrender/src/util.rs
@@ -461,12 +461,20 @@ pub fn project_rect<F, T>(
     // Otherwise, it will be clamped to the screen bounds anyway.
     if homogens.iter().any(|h| h.w <= 0.0) {
         let mut clipper = Clipper::new();
-        clipper.add_frustum(
+        let polygon = Polygon::from_rect(*rect, 1);
+
+        let planes = match Clipper::frustum_planes(
             transform,
             Some(*bounds),
-        );
+        ) {
+            Ok(planes) => planes,
+            Err(..) => return None,
+        };
+
+        for plane in planes {
+            clipper.add(plane);
+        }
 
-        let polygon = Polygon::from_rect(*rect, 1);
         let results = clipper.clip(polygon);
         if results.is_empty() {
             return None