diff --git a/crates/fj-kernel/src/algorithms/approx/curves.rs b/crates/fj-kernel/src/algorithms/approx/curves.rs
index 6e3d7e88c..1d76078f9 100644
--- a/crates/fj-kernel/src/algorithms/approx/curves.rs
+++ b/crates/fj-kernel/src/algorithms/approx/curves.rs
@@ -52,7 +52,7 @@ pub fn approx_circle(
 
     for i in 0..n {
         let angle = Scalar::PI * 2. / n as f64 * i as f64;
-        let point = circle.point_curve_to_model(&Point::from([angle]));
+        let point = circle.point_from_circle_coords([angle]);
         out.push(point);
     }
 }
diff --git a/crates/fj-kernel/src/algorithms/triangulation/mod.rs b/crates/fj-kernel/src/algorithms/triangulation/mod.rs
index 54b079612..600d41a64 100644
--- a/crates/fj-kernel/src/algorithms/triangulation/mod.rs
+++ b/crates/fj-kernel/src/algorithms/triangulation/mod.rs
@@ -32,7 +32,7 @@ pub fn triangulate(
                     .map(|vertex| {
                         // Can't panic, unless the approximation wrongfully
                         // generates points that are not in the surface.
-                        surface.convert_point_to_surface_coords(vertex)
+                        surface.point_to_surface_coords(vertex)
                     })
                     .collect();
                 let face_as_polygon = Polygon::new(surface)
@@ -40,9 +40,7 @@ pub fn triangulate(
                         |point| {
                             // Can't panic, unless the approximation wrongfully
                             // generates points that are not in the surface.
-                            surface
-                                .convert_point_to_surface_coords(point)
-                                .native()
+                            surface.point_to_surface_coords(point).native()
                         },
                     ))
                     .with_interiors(approx.interiors.into_iter().map(
@@ -51,9 +49,7 @@ pub fn triangulate(
                                 // Can't panic, unless the approximation
                                 // wrongfully generates points that are not in
                                 // the surface.
-                                surface
-                                    .convert_point_to_surface_coords(point)
-                                    .native()
+                                surface.point_to_surface_coords(point).native()
                             })
                         },
                     ));
diff --git a/crates/fj-kernel/src/algorithms/triangulation/polygon.rs b/crates/fj-kernel/src/algorithms/triangulation/polygon.rs
index 68fce75cb..5630b876f 100644
--- a/crates/fj-kernel/src/algorithms/triangulation/polygon.rs
+++ b/crates/fj-kernel/src/algorithms/triangulation/polygon.rs
@@ -140,7 +140,7 @@ impl Polygon {
         };
 
         let mut check = TriangleEdgeCheck::new(
-            self.surface.convert_point_from_surface_coords(&ray.origin),
+            self.surface.point_from_surface_coords(ray.origin),
         );
 
         let mut num_hits = 0;
@@ -201,8 +201,7 @@ impl Polygon {
 
                     let edge =
                         Segment::from_points(edge.points().map(|point| {
-                            self.surface
-                                .convert_point_from_surface_coords(&point)
+                            self.surface.point_from_surface_coords(point)
                         }));
                     check.hits.push(edge);
                 }
diff --git a/crates/fj-kernel/src/geometry/curves/circle.rs b/crates/fj-kernel/src/geometry/curves/circle.rs
index bb19f0d1d..a82609e94 100644
--- a/crates/fj-kernel/src/geometry/curves/circle.rs
+++ b/crates/fj-kernel/src/geometry/curves/circle.rs
@@ -55,8 +55,11 @@ impl Circle {
     /// Callers are advised to be careful about the points they pass, as the
     /// point not being on the curve, intentional or not, will not result in an
     /// error.
-    pub fn point_model_to_curve(&self, point: &Point<3>) -> Point<1> {
-        let v = point - self.center;
+    pub fn point_to_circle_coords(
+        &self,
+        point: impl Into<Point<3>>,
+    ) -> Point<1> {
+        let v = point.into() - self.center;
         let atan = Scalar::atan2(v.y, v.x);
         let coord = if atan >= Scalar::ZERO {
             atan
@@ -67,13 +70,19 @@ impl Circle {
     }
 
     /// Convert a point on the curve into model coordinates
-    pub fn point_curve_to_model(&self, point: &Point<1>) -> Point<3> {
-        self.center + self.vector_curve_to_model(&point.coords)
+    pub fn point_from_circle_coords(
+        &self,
+        point: impl Into<Point<1>>,
+    ) -> Point<3> {
+        self.center + self.vector_from_circle_coords(point.into().coords)
     }
 
     /// Convert a vector on the curve into model coordinates
-    pub fn vector_curve_to_model(&self, vector: &Vector<1>) -> Vector<3> {
-        let angle = vector.t;
+    pub fn vector_from_circle_coords(
+        &self,
+        vector: impl Into<Vector<1>>,
+    ) -> Vector<3> {
+        let angle = vector.into().t;
         let (sin, cos) = angle.sin_cos();
 
         self.a * cos + self.b * sin
@@ -97,19 +106,19 @@ mod tests {
         };
 
         assert_eq!(
-            circle.point_model_to_curve(&Point::from([2., 2., 3.])),
+            circle.point_to_circle_coords([2., 2., 3.]),
             Point::from([0.]),
         );
         assert_eq!(
-            circle.point_model_to_curve(&Point::from([1., 3., 3.])),
+            circle.point_to_circle_coords([1., 3., 3.]),
             Point::from([FRAC_PI_2]),
         );
         assert_eq!(
-            circle.point_model_to_curve(&Point::from([0., 2., 3.])),
+            circle.point_to_circle_coords([0., 2., 3.]),
             Point::from([PI]),
         );
         assert_eq!(
-            circle.point_model_to_curve(&Point::from([1., 1., 3.])),
+            circle.point_to_circle_coords([1., 1., 3.]),
             Point::from([FRAC_PI_2 * 3.]),
         );
     }
diff --git a/crates/fj-kernel/src/geometry/curves/mod.rs b/crates/fj-kernel/src/geometry/curves/mod.rs
index f2f59ef16..9c7c34d51 100644
--- a/crates/fj-kernel/src/geometry/curves/mod.rs
+++ b/crates/fj-kernel/src/geometry/curves/mod.rs
@@ -82,26 +82,35 @@ impl Curve {
     /// Callers are advised to be careful about the points they pass, as the
     /// point not being on the curve, intentional or not, will never result in
     /// an error.
-    pub fn point_model_to_curve(&self, point: &Point<3>) -> Point<1> {
+    pub fn point_to_curve_coords(
+        &self,
+        point: impl Into<Point<3>>,
+    ) -> Point<1> {
         match self {
-            Self::Circle(curve) => curve.point_model_to_curve(point),
-            Self::Line(curve) => curve.point_to_line_coords(*point),
+            Self::Circle(curve) => curve.point_to_circle_coords(point),
+            Self::Line(curve) => curve.point_to_line_coords(point),
         }
     }
 
     /// Convert a point on the curve into model coordinates
-    pub fn point_curve_to_model(&self, point: &Point<1>) -> Point<3> {
+    pub fn point_from_curve_coords(
+        &self,
+        point: impl Into<Point<1>>,
+    ) -> Point<3> {
         match self {
-            Self::Circle(curve) => curve.point_curve_to_model(point),
-            Self::Line(curve) => curve.point_from_line_coords(*point),
+            Self::Circle(curve) => curve.point_from_circle_coords(point),
+            Self::Line(curve) => curve.point_from_line_coords(point),
         }
     }
 
     /// Convert a vector on the curve into model coordinates
-    pub fn vector_curve_to_model(&self, point: &Vector<1>) -> Vector<3> {
+    pub fn vector_from_curve_coords(
+        &self,
+        point: impl Into<Vector<1>>,
+    ) -> Vector<3> {
         match self {
-            Self::Circle(curve) => curve.vector_curve_to_model(point),
-            Self::Line(curve) => curve.vector_from_line_coords(*point),
+            Self::Circle(curve) => curve.vector_from_circle_coords(point),
+            Self::Line(curve) => curve.vector_from_line_coords(point),
         }
     }
 }
diff --git a/crates/fj-kernel/src/geometry/surfaces/mod.rs b/crates/fj-kernel/src/geometry/surfaces/mod.rs
index ebcca1430..c97a9c398 100644
--- a/crates/fj-kernel/src/geometry/surfaces/mod.rs
+++ b/crates/fj-kernel/src/geometry/surfaces/mod.rs
@@ -59,13 +59,15 @@ impl Surface {
     }
 
     /// Convert a point in model coordinates to surface coordinates
-    pub fn convert_point_to_surface_coords(
+    pub fn point_to_surface_coords(
         &self,
-        point_3d: Point<3>,
+        point_3d: impl Into<Point<3>>,
     ) -> geometry::Point<2> {
+        let point_3d = point_3d.into();
+
         let point_2d = match self {
             Self::SweptCurve(surface) => {
-                surface.convert_point_to_surface_coords(&point_3d)
+                surface.point_to_surface_coords(point_3d)
             }
         };
 
@@ -73,25 +75,25 @@ impl Surface {
     }
 
     /// Convert a point in surface coordinates to model coordinates
-    pub fn convert_point_from_surface_coords(
+    pub fn point_from_surface_coords(
         &self,
-        point: &Point<2>,
+        point: impl Into<Point<2>>,
     ) -> Point<3> {
         match self {
             Self::SweptCurve(surface) => {
-                surface.convert_point_from_surface_coords(point)
+                surface.point_from_surface_coords(point)
             }
         }
     }
 
     /// Convert a vector in surface coordinates to model coordinates
-    pub fn convert_vector_from_surface_coords(
+    pub fn vector_from_surface_coords(
         &self,
-        vector: &Vector<2>,
+        vector: impl Into<Vector<2>>,
     ) -> Vector<3> {
         match self {
             Self::SweptCurve(surface) => {
-                surface.convert_vector_from_surface_coords(vector)
+                surface.vector_from_surface_coords(vector)
             }
         }
     }
diff --git a/crates/fj-kernel/src/geometry/surfaces/swept.rs b/crates/fj-kernel/src/geometry/surfaces/swept.rs
index 0f66159a5..282747668 100644
--- a/crates/fj-kernel/src/geometry/surfaces/swept.rs
+++ b/crates/fj-kernel/src/geometry/surfaces/swept.rs
@@ -38,37 +38,41 @@ impl SweptCurve {
     }
 
     /// Convert a point in model coordinates to surface coordinates
-    pub fn convert_point_to_surface_coords(
+    pub fn point_to_surface_coords(
         &self,
-        point: &Point<3>,
+        point: impl Into<Point<3>>,
     ) -> Point<2> {
-        let u = self.curve.point_model_to_curve(point).t;
+        let point = point.into();
+
+        let u = self.curve.point_to_curve_coords(point).t;
         let v = {
             let line = Line {
                 origin: self.curve.origin(),
                 direction: self.path,
             };
 
-            line.point_to_line_coords(*point).t
+            line.point_to_line_coords(point).t
         };
 
         Point::from([u, v])
     }
 
     /// Convert a point in surface coordinates to model coordinates
-    pub fn convert_point_from_surface_coords(
+    pub fn point_from_surface_coords(
         &self,
-        point: &Point<2>,
+        point: impl Into<Point<2>>,
     ) -> Point<3> {
-        self.curve.point_curve_to_model(&point.to_t()) + self.path * point.v
+        let point = point.into();
+        self.curve.point_from_curve_coords([point.u]) + self.path * point.v
     }
 
     /// Convert a vector in surface coordinates to model coordinates
-    pub fn convert_vector_from_surface_coords(
+    pub fn vector_from_surface_coords(
         &self,
-        vector: &Vector<2>,
+        vector: impl Into<Vector<2>>,
     ) -> Vector<3> {
-        self.curve.vector_curve_to_model(&vector.to_t()) + self.path * vector.v
+        let vector = vector.into();
+        self.curve.vector_from_curve_coords([vector.u]) + self.path * vector.v
     }
 }
 
@@ -97,8 +101,8 @@ mod tests {
         verify(&swept, Point::from([2., 3.]));
 
         fn verify(swept: &SweptCurve, surface_point: Point<2>) {
-            let point = swept.convert_point_from_surface_coords(&surface_point);
-            let result = swept.convert_point_to_surface_coords(&point);
+            let point = swept.point_from_surface_coords(surface_point);
+            let result = swept.point_to_surface_coords(point);
 
             assert_eq!(result, surface_point);
         }
@@ -115,7 +119,7 @@ mod tests {
         };
 
         assert_eq!(
-            swept.convert_point_from_surface_coords(&Point::from([2., 4.])),
+            swept.point_from_surface_coords([2., 4.]),
             Point::from([1., 4., 8.]),
         );
     }
@@ -131,7 +135,7 @@ mod tests {
         };
 
         assert_eq!(
-            swept.convert_vector_from_surface_coords(&Vector::from([2., 4.])),
+            swept.vector_from_surface_coords([2., 4.]),
             Vector::from([0., 4., 8.]),
         );
     }
diff --git a/crates/fj-operations/src/sketch.rs b/crates/fj-operations/src/sketch.rs
index 4f8306196..60e2ef595 100644
--- a/crates/fj-operations/src/sketch.rs
+++ b/crates/fj-operations/src/sketch.rs
@@ -15,7 +15,7 @@ impl ToShape for fj::Sketch {
             .to_points()
             .into_iter()
             .map(Point::from)
-            .map(|point| surface.convert_point_from_surface_coords(&point));
+            .map(|point| surface.point_from_surface_coords(point));
 
         Face::builder(surface, &mut shape)
             .with_exterior_polygon(points)