diff --git a/crates/fj-host/src/lib.rs b/crates/fj-host/src/lib.rs
index f94b23459..910dd342f 100644
--- a/crates/fj-host/src/lib.rs
+++ b/crates/fj-host/src/lib.rs
@@ -21,6 +21,7 @@ use std::{
     collections::{HashMap, HashSet},
     ffi::OsStr,
     io,
+    ops::{Deref, DerefMut},
     path::{Path, PathBuf},
     process::Command,
     sync::mpsc,
@@ -279,7 +280,8 @@ impl Watcher {
     }
 }
 
-/// Parameters that are passed to a model
+/// Parameters that are passed to a model.
+#[derive(Debug, Clone, PartialEq)]
 pub struct Parameters(pub HashMap<String, String>);
 
 impl Parameters {
@@ -287,6 +289,31 @@ impl Parameters {
     pub fn empty() -> Self {
         Self(HashMap::new())
     }
+
+    /// Insert a value into the [`Parameters`] dictionary, implicitly converting
+    /// the arguments to strings and returning `&mut self` to enable chaining.
+    pub fn insert(
+        &mut self,
+        key: impl Into<String>,
+        value: impl ToString,
+    ) -> &mut Self {
+        self.0.insert(key.into(), value.to_string());
+        self
+    }
+}
+
+impl Deref for Parameters {
+    type Target = HashMap<String, String>;
+
+    fn deref(&self) -> &Self::Target {
+        &self.0
+    }
+}
+
+impl DerefMut for Parameters {
+    fn deref_mut(&mut self) -> &mut Self::Target {
+        &mut self.0
+    }
 }
 
 /// An error that can occur when loading or reloading a model
diff --git a/crates/fj/src/angle.rs b/crates/fj/src/angle.rs
index 7e8a8794f..9911b959e 100644
--- a/crates/fj/src/angle.rs
+++ b/crates/fj/src/angle.rs
@@ -6,7 +6,7 @@ use std::f64::consts::{PI, TAU};
 const GON_RAD: f64 = PI / 200.;
 
 /// An angle
-#[derive(Copy, Clone, Debug)]
+#[derive(Copy, Clone, Debug, PartialEq)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 pub struct Angle {
     // The value of the angle in radians
diff --git a/crates/fj/src/group.rs b/crates/fj/src/group.rs
index a870d816a..4921cedc8 100644
--- a/crates/fj/src/group.rs
+++ b/crates/fj/src/group.rs
@@ -11,7 +11,7 @@ use crate::Shape;
 /// # Limitations
 ///
 /// Whether the shapes in the group touch or overlap is not currently checked.
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, PartialEq)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 #[repr(C)]
 pub struct Group {
diff --git a/crates/fj/src/lib.rs b/crates/fj/src/lib.rs
index 6282b4cbe..74a717750 100644
--- a/crates/fj/src/lib.rs
+++ b/crates/fj/src/lib.rs
@@ -34,7 +34,7 @@ pub use fj_proc::*;
 use serde::{Deserialize, Serialize};
 
 /// A shape
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, PartialEq)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 #[repr(C)]
 pub enum Shape {
diff --git a/crates/fj/src/shape_2d.rs b/crates/fj/src/shape_2d.rs
index 1cd1e91c9..e1d3a43e4 100644
--- a/crates/fj/src/shape_2d.rs
+++ b/crates/fj/src/shape_2d.rs
@@ -6,7 +6,7 @@ use std::sync::atomic;
 use crate::Shape;
 
 /// A 2-dimensional shape
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, PartialEq)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 #[repr(C)]
 pub enum Shape2d {
@@ -28,7 +28,7 @@ impl Shape2d {
 }
 
 /// A difference between two shapes
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, PartialEq)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 #[repr(C)]
 pub struct Difference2d {
@@ -73,7 +73,7 @@ impl From<Difference2d> for Shape2d {
 /// Nothing about these edges is checked right now, but algorithms might assume
 /// that the edges are non-overlapping. If you create a `Sketch` with
 /// overlapping edges, you're on your own.
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, PartialEq)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 #[repr(C)]
 pub struct Sketch {
@@ -118,7 +118,7 @@ impl Sketch {
 }
 
 /// A chain of elements that is part of a [`Sketch`]
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, PartialEq)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 #[repr(C)]
 pub enum Chain {
@@ -130,7 +130,7 @@ pub enum Chain {
 }
 
 /// A circle that is part of a [`Sketch`]
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, PartialEq)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 #[repr(C)]
 pub struct Circle {
@@ -191,6 +191,11 @@ impl PolyChain {
         }
     }
 
+    /// Get a reference to the points in this [`PolyChain`].
+    fn points(&self) -> &[[f64; 2]] {
+        unsafe { std::slice::from_raw_parts(self.ptr, self.length) }
+    }
+
     /// Return the points that define the polygonal chain
     pub fn to_points(&self) -> Vec<[f64; 2]> {
         // This is sound. All invariants are automatically kept, as the raw
@@ -229,6 +234,12 @@ impl Clone for PolyChain {
     }
 }
 
+impl PartialEq for PolyChain {
+    fn eq(&self, other: &Self) -> bool {
+        self.points() == other.points()
+    }
+}
+
 impl Drop for PolyChain {
     fn drop(&mut self) {
         // Decrement the reference counter
diff --git a/crates/fj/src/sweep.rs b/crates/fj/src/sweep.rs
index afb6b1ebd..32153a016 100644
--- a/crates/fj/src/sweep.rs
+++ b/crates/fj/src/sweep.rs
@@ -4,7 +4,7 @@ use serde::{Deserialize, Serialize};
 use crate::{Shape, Shape2d};
 
 /// A sweep of a 2-dimensional shape along straight path
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, PartialEq)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 #[repr(C)]
 pub struct Sweep {
diff --git a/crates/fj/src/transform.rs b/crates/fj/src/transform.rs
index b826626ae..aebc14646 100644
--- a/crates/fj/src/transform.rs
+++ b/crates/fj/src/transform.rs
@@ -12,7 +12,7 @@ use crate::{Angle, Shape};
 ///
 /// See issue:
 /// <https://github.com/hannobraun/Fornjot/issues/101>
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, PartialEq)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 #[repr(C)]
 pub struct Transform {