diff --git a/shader/fine.wgsl b/shader/fine.wgsl
index 4cb5a8e..5e7a772 100644
--- a/shader/fine.wgsl
+++ b/shader/fine.wgsl
@@ -251,7 +251,7 @@ fn main(
                 for (var i = 0u; i < PIXELS_PER_THREAD; i += 1u) {
                     let my_xy = vec2(xy.x + f32(i), xy.y);
                     // TODO: can hoist y, but for now stick to the GLSL version
-                    let xy_xformed = rad.matrx.xz * my_xy.x + rad.matrx.yw * my_xy.y - rad.xlat;
+                    let xy_xformed = rad.matrx.xy * my_xy.x + rad.matrx.zw * my_xy.y - rad.xlat;
                     let ba = dot(xy_xformed, rad.c1);
                     let ca = rad.ra * dot(xy_xformed, xy_xformed);
                     let t = sqrt(ba * ba + ca) - ba - rad.roff;
diff --git a/src/encoding/encoding.rs b/src/encoding/encoding.rs
index 4d866c2..588015c 100644
--- a/src/encoding/encoding.rs
+++ b/src/encoding/encoding.rs
@@ -120,10 +120,16 @@ impl Encoding {
     }
 
     /// Encodes a transform.
-    pub fn encode_transform(&mut self, transform: Transform) {
+    ///
+    /// If the given transform is different from the current one, encodes it an
+    /// returns true. Otherwise, encodes nothing and returns false.
+    pub fn encode_transform(&mut self, transform: Transform) -> bool {
         if self.transforms.last() != Some(&transform) {
             self.path_tags.push(PathTag::TRANSFORM);
             self.transforms.push(transform);
+            true
+        } else {
+            false
         }
     }
 
diff --git a/src/scene.rs b/src/scene.rs
index 3fb7a96..98d491a 100644
--- a/src/scene.rs
+++ b/src/scene.rs
@@ -140,13 +140,14 @@ impl<'a> SceneBuilder<'a> {
         });
         if self.scene.encode_shape(shape, true) {
             if let Some(brush_transform) = brush_transform {
-                self.scene
-                    .encode_transform(Transform::from_kurbo(&(transform * brush_transform)));
-                self.scene.swap_last_path_tags();
-                self.scene.encode_brush(brush, 1.0);
-            } else {
-                self.scene.encode_brush(brush, 1.0);
+                if self
+                    .scene
+                    .encode_transform(Transform::from_kurbo(&(transform * brush_transform)))
+                {
+                    self.scene.swap_last_path_tags();
+                }
             }
+            self.scene.encode_brush(brush, 1.0);
         }
     }
 
@@ -164,13 +165,14 @@ impl<'a> SceneBuilder<'a> {
         self.scene.encode_linewidth(style.width);
         if self.scene.encode_shape(shape, false) {
             if let Some(brush_transform) = brush_transform {
-                self.scene
-                    .encode_transform(Transform::from_kurbo(&(transform * brush_transform)));
-                self.scene.swap_last_path_tags();
-                self.scene.encode_brush(brush, 1.0);
-            } else {
-                self.scene.encode_brush(brush, 1.0);
+                if self
+                    .scene
+                    .encode_transform(Transform::from_kurbo(&(transform * brush_transform)))
+                {
+                    self.scene.swap_last_path_tags();
+                }
             }
+            self.scene.encode_brush(brush, 1.0);
         }
     }