diff --git a/crates/fj-kernel/src/algorithms/mod.rs b/crates/fj-kernel/src/algorithms/mod.rs
index 01928fca2c..5f4a319934 100644
--- a/crates/fj-kernel/src/algorithms/mod.rs
+++ b/crates/fj-kernel/src/algorithms/mod.rs
@@ -6,13 +6,13 @@
 mod approx;
 mod sweep;
 mod transform;
-mod triangulation;
+mod triangulate;
 
 pub mod intersection;
 
 pub use self::{
     approx::{CycleApprox, FaceApprox, InvalidTolerance, Tolerance},
     sweep::sweep,
-    transform::transform,
-    triangulation::triangulate,
+    transform::transform_shape,
+    triangulate::triangulate,
 };
diff --git a/crates/fj-kernel/src/algorithms/sweep.rs b/crates/fj-kernel/src/algorithms/sweep.rs
index 0645b2a85f..33ab653fcc 100644
--- a/crates/fj-kernel/src/algorithms/sweep.rs
+++ b/crates/fj-kernel/src/algorithms/sweep.rs
@@ -8,7 +8,7 @@ use crate::{
     shape::LocalForm,
 };
 
-use super::{transform::transform_cycles, CycleApprox, Tolerance};
+use super::{transform::transform_face, CycleApprox, Tolerance};
 
 /// Create a solid by sweeping a sketch
 pub fn sweep(
@@ -88,18 +88,14 @@ fn create_top_face(
     is_sweep_along_negative_direction: bool,
     target: &mut Vec<Face>,
 ) {
+    let translation = Transform::translation(path);
+    let face = transform_face(face, &translation);
+
     let mut surface = face.surface();
 
     let mut exteriors = face.brep().exteriors.clone();
     let mut interiors = face.brep().interiors.clone();
 
-    let translation = Transform::translation(path);
-
-    surface = surface.transform(&translation);
-
-    exteriors = transform_cycles(&exteriors, &translation);
-    interiors = transform_cycles(&interiors, &translation);
-
     if is_sweep_along_negative_direction {
         surface = surface.reverse();
 
diff --git a/crates/fj-kernel/src/algorithms/transform.rs b/crates/fj-kernel/src/algorithms/transform.rs
index 11e88e4f3e..066a48e53c 100644
--- a/crates/fj-kernel/src/algorithms/transform.rs
+++ b/crates/fj-kernel/src/algorithms/transform.rs
@@ -6,41 +6,40 @@ use crate::{
 };
 
 /// Transform a shape
-pub fn transform(faces: &[Face], transform: &Transform) -> Vec<Face> {
-    let mut target = Vec::new();
-
+pub fn transform_shape(faces: &mut Vec<Face>, transform: &Transform) {
     for face in faces {
-        let face = match face {
-            Face::Face(face) => {
-                let surface = face.surface.transform(transform);
+        *face = transform_face(face, transform);
+    }
+}
 
-                let exteriors = transform_cycles(&face.exteriors, transform);
-                let interiors = transform_cycles(&face.interiors, transform);
+pub fn transform_face(face: &Face, transform: &Transform) -> Face {
+    match face {
+        Face::Face(face) => {
+            let surface = face.surface.transform(transform);
 
-                let color = face.color;
+            let exteriors = transform_cycles(&face.exteriors, transform);
+            let interiors = transform_cycles(&face.interiors, transform);
 
-                Face::Face(FaceBRep {
-                    surface,
-                    exteriors,
-                    interiors,
-                    color,
-                })
-            }
-            Face::Triangles(triangles) => {
-                let mut target = Vec::new();
+            let color = face.color;
 
-                for &(triangle, color) in triangles {
-                    let triangle = transform.transform_triangle(&triangle);
-                    target.push((triangle, color));
-                }
+            Face::Face(FaceBRep {
+                surface,
+                exteriors,
+                interiors,
+                color,
+            })
+        }
+        Face::Triangles(triangles) => {
+            let mut target = Vec::new();
 
-                Face::Triangles(target)
+            for &(triangle, color) in triangles {
+                let triangle = transform.transform_triangle(&triangle);
+                target.push((triangle, color));
             }
-        };
-        target.push(face);
-    }
 
-    target
+            Face::Triangles(target)
+        }
+    }
 }
 
 pub fn transform_cycles(
diff --git a/crates/fj-kernel/src/algorithms/triangulation/delaunay.rs b/crates/fj-kernel/src/algorithms/triangulate/delaunay.rs
similarity index 100%
rename from crates/fj-kernel/src/algorithms/triangulation/delaunay.rs
rename to crates/fj-kernel/src/algorithms/triangulate/delaunay.rs
diff --git a/crates/fj-kernel/src/algorithms/triangulation/mod.rs b/crates/fj-kernel/src/algorithms/triangulate/mod.rs
similarity index 100%
rename from crates/fj-kernel/src/algorithms/triangulation/mod.rs
rename to crates/fj-kernel/src/algorithms/triangulate/mod.rs
diff --git a/crates/fj-kernel/src/algorithms/triangulation/polygon.rs b/crates/fj-kernel/src/algorithms/triangulate/polygon.rs
similarity index 100%
rename from crates/fj-kernel/src/algorithms/triangulation/polygon.rs
rename to crates/fj-kernel/src/algorithms/triangulate/polygon.rs
diff --git a/crates/fj-kernel/src/algorithms/triangulation/ray.rs b/crates/fj-kernel/src/algorithms/triangulate/ray.rs
similarity index 100%
rename from crates/fj-kernel/src/algorithms/triangulation/ray.rs
rename to crates/fj-kernel/src/algorithms/triangulate/ray.rs
diff --git a/crates/fj-operations/src/transform.rs b/crates/fj-operations/src/transform.rs
index 07f4868e79..6fbe0d0110 100644
--- a/crates/fj-operations/src/transform.rs
+++ b/crates/fj-operations/src/transform.rs
@@ -1,6 +1,6 @@
 use fj_interop::debug::DebugInfo;
 use fj_kernel::{
-    algorithms::{transform, Tolerance},
+    algorithms::{transform_shape, Tolerance},
     objects::Face,
     validation::{validate, Validated, ValidationConfig, ValidationError},
 };
@@ -15,9 +15,14 @@ impl ToShape for fj::Transform {
         tolerance: Tolerance,
         debug_info: &mut DebugInfo,
     ) -> Result<Validated<Vec<Face>>, ValidationError> {
-        let shape = self.shape.to_shape(config, tolerance, debug_info)?;
-        let faces = transform(&shape.into_inner(), &make_transform(self));
-        validate(faces, config)
+        let mut shape = self
+            .shape
+            .to_shape(config, tolerance, debug_info)?
+            .into_inner();
+
+        transform_shape(&mut shape, &make_transform(self));
+
+        validate(shape, config)
     }
 
     fn bounding_volume(&self) -> Aabb<3> {