diff --git a/crates/fj-core/src/geometry/curve.rs b/crates/fj-core/src/geometry/curve.rs
new file mode 100644
index 000000000..a85d43329
--- /dev/null
+++ b/crates/fj-core/src/geometry/curve.rs
@@ -0,0 +1,36 @@
+use crate::{storage::Handle, topology::Surface};
+
+use super::SurfacePath;
+
+/// The geometric definition of a curve
+#[derive(Clone)]
+pub struct CurveGeom {
+    /// # The redundant local definitions of the curve geometry
+    ///
+    /// ## Implementation Note
+    ///
+    /// Having multiple redundant definitions is undesirable. However, we can't
+    /// just use one global definition in 3D, as we need the local 2D
+    /// definitions to approximate and triangulate curves, and we currently
+    /// don't have the tools to project a global definition into a local
+    /// context.
+    ///
+    /// Eventually, it should be possible to define the geometry of a curve
+    /// once, either locally or globally, and then convert that single
+    /// definition into (other) local contexts, as needed. There currently is no
+    /// issue to track that specifically, but there is the following issue,
+    /// which is a prerequisite for making the required tooling practical:
+    ///
+    /// <https://github.com/hannobraun/fornjot/issues/2118>
+    pub definitions: Vec<LocalCurveGeom>,
+}
+
+/// The geometric definition of a curve in 2D surface coordinates
+#[derive(Clone)]
+pub struct LocalCurveGeom {
+    /// The path that defines the curve on its surface
+    pub path: SurfacePath,
+
+    /// The surface that the curve is defined on
+    pub surface: Handle<Surface>,
+}
diff --git a/crates/fj-core/src/geometry/geometry.rs b/crates/fj-core/src/geometry/geometry.rs
index 6a83194dd..6b76d3661 100644
--- a/crates/fj-core/src/geometry/geometry.rs
+++ b/crates/fj-core/src/geometry/geometry.rs
@@ -4,13 +4,14 @@ use fj_math::Vector;
 
 use crate::{
     storage::Handle,
-    topology::{HalfEdge, Surface, Topology},
+    topology::{Curve, HalfEdge, Surface, Topology},
 };
 
-use super::{GlobalPath, HalfEdgeGeom, SurfaceGeom};
+use super::{CurveGeom, GlobalPath, HalfEdgeGeom, SurfaceGeom};
 
 /// Geometric data that is associated with topological objects
 pub struct Geometry {
+    curve: BTreeMap<Handle<Curve>, CurveGeom>,
     half_edge: BTreeMap<Handle<HalfEdge>, HalfEdgeGeom>,
     surface: BTreeMap<Handle<Surface>, SurfaceGeom>,
 
@@ -25,6 +26,7 @@ impl Geometry {
     /// Create a new instance of `Geometry`
     pub fn new(topology: &Topology) -> Self {
         let mut self_ = Self {
+            curve: BTreeMap::new(),
             half_edge: BTreeMap::new(),
             surface: BTreeMap::new(),
 
@@ -60,6 +62,14 @@ impl Geometry {
         self_
     }
 
+    pub(crate) fn define_curve_inner(
+        &mut self,
+        curve: Handle<Curve>,
+        geometry: CurveGeom,
+    ) {
+        self.curve.insert(curve, geometry);
+    }
+
     pub(crate) fn define_half_edge_inner(
         &mut self,
         half_edge: Handle<HalfEdge>,
@@ -88,6 +98,17 @@ impl Geometry {
         self.surface.insert(surface, geometry);
     }
 
+    /// # Access the geometry of the provided curve
+    ///
+    /// ## Panics
+    ///
+    /// Panics, if the geometry of the curve is not defined.
+    pub fn of_curve(&self, curve: &Handle<Curve>) -> &CurveGeom {
+        self.curve
+            .get(curve)
+            .expect("Expected geometry of half-edge to be defined")
+    }
+
     /// # Access the geometry of the provided half-edge
     ///
     /// ## Panics
diff --git a/crates/fj-core/src/geometry/mod.rs b/crates/fj-core/src/geometry/mod.rs
index f4db527be..194e9167e 100644
--- a/crates/fj-core/src/geometry/mod.rs
+++ b/crates/fj-core/src/geometry/mod.rs
@@ -1,6 +1,7 @@
 //! Types that are tied to objects, but aren't objects themselves
 
 mod boundary;
+mod curve;
 mod geometry;
 mod half_edge;
 mod path;
@@ -8,6 +9,7 @@ mod surface;
 
 pub use self::{
     boundary::{CurveBoundary, CurveBoundaryElement},
+    curve::{CurveGeom, LocalCurveGeom},
     geometry::Geometry,
     half_edge::HalfEdgeGeom,
     path::{GlobalPath, SurfacePath},
diff --git a/crates/fj-core/src/layers/geometry.rs b/crates/fj-core/src/layers/geometry.rs
index b23aa5cd2..b621acfff 100644
--- a/crates/fj-core/src/layers/geometry.rs
+++ b/crates/fj-core/src/layers/geometry.rs
@@ -1,14 +1,20 @@
 //! Layer infrastructure for [`Geometry`]
 
 use crate::{
-    geometry::{Geometry, HalfEdgeGeom, SurfaceGeom},
+    geometry::{CurveGeom, Geometry, HalfEdgeGeom, SurfaceGeom},
     storage::Handle,
-    topology::{HalfEdge, Surface},
+    topology::{Curve, HalfEdge, Surface},
 };
 
 use super::{Command, Event, Layer};
 
 impl Layer<Geometry> {
+    /// Define the geometry of the provided curve
+    pub fn define_curve(&mut self, curve: Handle<Curve>, geometry: CurveGeom) {
+        let mut events = Vec::new();
+        self.process(DefineCurve { curve, geometry }, &mut events);
+    }
+
     /// Define the geometry of the provided half-edge
     pub fn define_half_edge(
         &mut self,
@@ -41,6 +47,31 @@ impl Layer<Geometry> {
     }
 }
 
+/// Define the geometry of a curve
+pub struct DefineCurve {
+    curve: Handle<Curve>,
+    geometry: CurveGeom,
+}
+
+impl Command<Geometry> for DefineCurve {
+    type Result = ();
+    type Event = Self;
+
+    fn decide(
+        self,
+        _: &Geometry,
+        events: &mut Vec<Self::Event>,
+    ) -> Self::Result {
+        events.push(self);
+    }
+}
+
+impl Event<Geometry> for DefineCurve {
+    fn evolve(&self, state: &mut Geometry) {
+        state.define_curve_inner(self.curve.clone(), self.geometry.clone());
+    }
+}
+
 /// Define the geometry of a half-edge
 pub struct DefineHalfEdge {
     half_edge: Handle<HalfEdge>,