diff --git a/CHANGELOG.md b/CHANGELOG.md
index 46df27ac..6d3af875 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -13,6 +13,9 @@
   instead of `&[f32]`.  This is more flexible for gradient evaluation, because
   it allows the caller to specify up to three gradients, without pinning them to
   specific argument.
+- Moved `tile_sizes_2d`, `tile_sizes_3d`, and `simplify_tree_during_meshing`
+  into a new `fidget::shape::RenderHits` trait.  This is a building block for
+  generic (_n_-variable) function evaluation.
 
 # 0.2.6
 This is a relatively small release; there are a few features to improve the
diff --git a/demo/src/main.rs b/demo/src/main.rs
index 8c552b32..b037fdd7 100644
--- a/demo/src/main.rs
+++ b/demo/src/main.rs
@@ -112,7 +112,7 @@ struct MeshSettings {
 }
 
 ////////////////////////////////////////////////////////////////////////////////
-fn run3d<S: fidget::eval::Shape>(
+fn run3d<S: fidget::eval::Shape + fidget::shape::RenderHints>(
     shape: S,
     settings: &ImageSettings,
     isometric: bool,
@@ -168,7 +168,7 @@ fn run3d<S: fidget::eval::Shape>(
 
 ////////////////////////////////////////////////////////////////////////////////
 
-fn run2d<S: fidget::eval::Shape>(
+fn run2d<S: fidget::eval::Shape + fidget::shape::RenderHints>(
     shape: S,
     settings: &ImageSettings,
     brute: bool,
@@ -236,10 +236,13 @@ fn run2d<S: fidget::eval::Shape>(
 
 ////////////////////////////////////////////////////////////////////////////////
 
-fn run_mesh<S: fidget::eval::Shape>(
+fn run_mesh<S: fidget::eval::Shape + fidget::shape::RenderHints>(
     shape: S,
     settings: &MeshSettings,
-) -> fidget::mesh::Mesh {
+) -> fidget::mesh::Mesh
+where
+    <S as fidget::eval::Shape>::TransformedShape: fidget::shape::RenderHints,
+{
     let mut mesh = fidget::mesh::Mesh::new();
 
     for _ in 0..settings.n {
diff --git a/fidget/benches/render.rs b/fidget/benches/render.rs
index a0e2cdce..204d46c1 100644
--- a/fidget/benches/render.rs
+++ b/fidget/benches/render.rs
@@ -4,7 +4,7 @@ use criterion::{
 
 const PROSPERO: &str = include_str!("../../models/prospero.vm");
 
-use fidget::eval::{MathShape, Shape};
+use fidget::{eval::MathShape, shape::RenderHints};
 
 pub fn prospero_size_sweep(c: &mut Criterion) {
     let (ctx, root) = fidget::Context::from_text(PROSPERO.as_bytes()).unwrap();
diff --git a/fidget/src/core/eval/mod.rs b/fidget/src/core/eval/mod.rs
index a7a7d136..1a10b1a1 100644
--- a/fidget/src/core/eval/mod.rs
+++ b/fidget/src/core/eval/mod.rs
@@ -157,22 +157,6 @@ pub trait Shape: Send + Sync + Clone {
     /// shapes, it's typically the length of the tape,
     fn size(&self) -> usize;
 
-    /// Recommended tile sizes for 3D rendering
-    fn tile_sizes_3d() -> &'static [usize];
-
-    /// Recommended tile sizes for 2D rendering
-    fn tile_sizes_2d() -> &'static [usize];
-
-    /// Indicates whether we run tape simplification at the given cell depth
-    /// during meshing.
-    ///
-    /// By default, this is always true; for evaluators where simplification is
-    /// more expensive than evaluation (i.e. the JIT), it may only be true at
-    /// certain depths.
-    fn simplify_tree_during_meshing(_d: usize) -> bool {
-        true
-    }
-
     /// Associated type returned when applying a transform
     ///
     /// This is normally [`TransformedShape<Self>`](TransformedShape), but if
diff --git a/fidget/src/core/eval/transform.rs b/fidget/src/core/eval/transform.rs
index 882cf71d..d5684b61 100644
--- a/fidget/src/core/eval/transform.rs
+++ b/fidget/src/core/eval/transform.rs
@@ -1,5 +1,6 @@
 use crate::{
     eval::{BulkEvaluator, Grad, Interval, Shape, Tape, TracingEvaluator},
+    shape::RenderHints,
     Error,
 };
 use nalgebra::{Matrix4, Point3, Vector3};
@@ -190,12 +191,6 @@ impl<S: Shape> Shape for TransformedShape<S> {
     type IntervalEval = TransformedTracingEval<<S as Shape>::IntervalEval>;
     type FloatSliceEval = TransformedBulkEval<<S as Shape>::FloatSliceEval>;
     type GradSliceEval = TransformedBulkEval<<S as Shape>::GradSliceEval>;
-    fn tile_sizes_2d() -> &'static [usize] {
-        S::tile_sizes_2d()
-    }
-    fn tile_sizes_3d() -> &'static [usize] {
-        S::tile_sizes_3d()
-    }
     fn size(&self) -> usize {
         self.shape.size()
     }
@@ -261,3 +256,12 @@ impl<S: Shape> Shape for TransformedShape<S> {
         self
     }
 }
+
+impl<S: RenderHints> RenderHints for TransformedShape<S> {
+    fn tile_sizes_2d() -> &'static [usize] {
+        S::tile_sizes_2d()
+    }
+    fn tile_sizes_3d() -> &'static [usize] {
+        S::tile_sizes_3d()
+    }
+}
diff --git a/fidget/src/core/shape/mod.rs b/fidget/src/core/shape/mod.rs
index 6d86a1dd..eb602598 100644
--- a/fidget/src/core/shape/mod.rs
+++ b/fidget/src/core/shape/mod.rs
@@ -1,3 +1,22 @@
 //! Shape-specific data types
 mod bounds;
 pub use bounds::Bounds;
+
+/// Hints for how to render this particular type
+pub trait RenderHints {
+    /// Recommended tile sizes for 3D rendering
+    fn tile_sizes_3d() -> &'static [usize];
+
+    /// Recommended tile sizes for 2D rendering
+    fn tile_sizes_2d() -> &'static [usize];
+
+    /// Indicates whether we run tape simplification at the given cell depth
+    /// during meshing.
+    ///
+    /// By default, this is always true; for evaluators where simplification is
+    /// more expensive than evaluation (i.e. the JIT), it may only be true at
+    /// certain depths.
+    fn simplify_tree_during_meshing(_d: usize) -> bool {
+        true
+    }
+}
diff --git a/fidget/src/core/vm/mod.rs b/fidget/src/core/vm/mod.rs
index c37a7a83..78f54fb7 100644
--- a/fidget/src/core/vm/mod.rs
+++ b/fidget/src/core/vm/mod.rs
@@ -6,6 +6,7 @@ use crate::{
         BulkEvaluator, MathShape, Shape, Tape, Trace, TracingEvaluator,
         TransformedShape,
     },
+    shape::RenderHints,
     types::{Grad, Interval},
     Context, Error,
 };
@@ -176,6 +177,13 @@ impl<const N: usize> Shape for GenericVmShape<N> {
         GenericVmShape::size(self)
     }
 
+    type TransformedShape = TransformedShape<Self>;
+    fn apply_transform(self, mat: Matrix4<f32>) -> Self::TransformedShape {
+        TransformedShape::new(self, mat)
+    }
+}
+
+impl<const N: usize> RenderHints for GenericVmShape<N> {
     fn tile_sizes_3d() -> &'static [usize] {
         &[256, 128, 64, 32, 16, 8]
     }
@@ -183,11 +191,6 @@ impl<const N: usize> Shape for GenericVmShape<N> {
     fn tile_sizes_2d() -> &'static [usize] {
         &[256, 128, 64, 32, 16, 8]
     }
-
-    type TransformedShape = TransformedShape<Self>;
-    fn apply_transform(self, mat: Matrix4<f32>) -> Self::TransformedShape {
-        TransformedShape::new(self, mat)
-    }
 }
 
 impl<const N: usize> MathShape for GenericVmShape<N> {
diff --git a/fidget/src/jit/mod.rs b/fidget/src/jit/mod.rs
index 4424d1e4..c183b730 100644
--- a/fidget/src/jit/mod.rs
+++ b/fidget/src/jit/mod.rs
@@ -31,6 +31,7 @@ use crate::{
         TransformedShape,
     },
     jit::mmap::Mmap,
+    shape::RenderHints,
     types::{Grad, Interval},
     vm::{Choice, GenericVmShape, VmData, VmTrace, VmWorkspace},
     Error,
@@ -898,6 +899,17 @@ impl Shape for JitShape {
         self.0.recycle()
     }
 
+    fn size(&self) -> usize {
+        self.0.size()
+    }
+
+    type TransformedShape = TransformedShape<Self>;
+    fn apply_transform(self, mat: Matrix4<f32>) -> Self::TransformedShape {
+        TransformedShape::new(self, mat)
+    }
+}
+
+impl RenderHints for JitShape {
     fn tile_sizes_3d() -> &'static [usize] {
         &[64, 16, 8]
     }
@@ -910,15 +922,6 @@ impl Shape for JitShape {
         // Unscientifically selected, but similar to tile_sizes_3d
         d % 8 == 4
     }
-
-    fn size(&self) -> usize {
-        self.0.size()
-    }
-
-    type TransformedShape = TransformedShape<Self>;
-    fn apply_transform(self, mat: Matrix4<f32>) -> Self::TransformedShape {
-        TransformedShape::new(self, mat)
-    }
 }
 
 ////////////////////////////////////////////////////////////////////////////////
diff --git a/fidget/src/mesh/mt/octree.rs b/fidget/src/mesh/mt/octree.rs
index e3174df1..e5e1631f 100644
--- a/fidget/src/mesh/mt/octree.rs
+++ b/fidget/src/mesh/mt/octree.rs
@@ -8,6 +8,7 @@ use crate::{
         types::Corner,
         Octree, Settings,
     },
+    shape::RenderHints,
 };
 use std::sync::{mpsc::TryRecvError, Arc};
 
@@ -88,7 +89,7 @@ struct Done<S: Shape> {
     completed_by: usize,
 }
 
-pub struct OctreeWorker<S: Shape> {
+pub struct OctreeWorker<S: Shape + RenderHints> {
     /// Global index of this worker thread
     ///
     /// For example, this is the thread's own index in `friend_queue` and
@@ -116,7 +117,7 @@ pub struct OctreeWorker<S: Shape> {
     friend_done: Vec<std::sync::mpsc::Sender<Done<S>>>,
 }
 
-impl<S: Shape> OctreeWorker<S> {
+impl<S: Shape + RenderHints> OctreeWorker<S> {
     pub fn scheduler(eval: Arc<EvalGroup<S>>, settings: Settings) -> Octree {
         let task_queues = QueuePool::new(settings.threads());
         let done_queues = std::iter::repeat_with(std::sync::mpsc::channel)
diff --git a/fidget/src/mesh/octree.rs b/fidget/src/mesh/octree.rs
index 4fcdcd35..0aca834e 100644
--- a/fidget/src/mesh/octree.rs
+++ b/fidget/src/mesh/octree.rs
@@ -12,6 +12,7 @@ use super::{
 };
 use crate::{
     eval::{BulkEvaluator, Shape, Tape, TracingEvaluator},
+    shape::RenderHints,
     types::Grad,
 };
 use std::{num::NonZeroUsize, sync::Arc, sync::OnceLock};
@@ -90,7 +91,13 @@ impl Octree {
     /// Builds an octree to the given depth
     ///
     /// The shape is evaluated on the region specified by `settings.bounds`.
-    pub fn build<S: Shape + Clone>(shape: &S, settings: Settings) -> Self {
+    pub fn build<S: Shape + RenderHints + Clone>(
+        shape: &S,
+        settings: Settings,
+    ) -> Self
+    where
+        <S as Shape>::TransformedShape: RenderHints,
+    {
         // Transform the shape given our bounds
         let t = settings.bounds.transform();
         if t == nalgebra::Transform::identity() {
@@ -109,7 +116,10 @@ impl Octree {
         }
     }
 
-    fn build_inner<S: Shape + Clone>(shape: &S, settings: Settings) -> Self {
+    fn build_inner<S: Shape + RenderHints + Clone>(
+        shape: &S,
+        settings: Settings,
+    ) -> Self {
         let eval = Arc::new(EvalGroup::new(shape.clone()));
 
         if settings.threads() == 1 {
@@ -228,7 +238,7 @@ impl std::ops::IndexMut<CellIndex> for Octree {
 
 /// Data structure for an under-construction octree
 #[derive(Debug)]
-pub(crate) struct OctreeBuilder<S: Shape> {
+pub(crate) struct OctreeBuilder<S: Shape + RenderHints> {
     /// Internal octree
     ///
     /// Note that in this internal octree, the `index` field of leaf nodes
@@ -261,13 +271,13 @@ pub(crate) struct OctreeBuilder<S: Shape> {
     workspace: S::Workspace,
 }
 
-impl<S: Shape> Default for OctreeBuilder<S> {
+impl<S: Shape + RenderHints> Default for OctreeBuilder<S> {
     fn default() -> Self {
         Self::new()
     }
 }
 
-impl<S: Shape> From<OctreeBuilder<S>> for Octree {
+impl<S: Shape + RenderHints> From<OctreeBuilder<S>> for Octree {
     fn from(o: OctreeBuilder<S>) -> Self {
         // Convert from "leaf index into self.leafs" (in the builder) to
         // "leaf index into self.verts" (in the resulting Octree)
@@ -293,7 +303,7 @@ impl<S: Shape> From<OctreeBuilder<S>> for Octree {
     }
 }
 
-impl<S: Shape> OctreeBuilder<S> {
+impl<S: Shape + RenderHints> OctreeBuilder<S> {
     /// Builds a new octree, which allocates data for 8 root cells
     pub(crate) fn new() -> Self {
         Self {
@@ -903,7 +913,7 @@ impl<S: Shape> OctreeBuilder<S> {
 
 /// `OctreeBuilder` functions which are only used during multithreaded rendering
 #[cfg(not(target_arch = "wasm32"))]
-impl<S: Shape> OctreeBuilder<S> {
+impl<S: Shape + RenderHints> OctreeBuilder<S> {
     /// Builds a new empty octree
     ///
     /// This still allocates data to reserve the lowest slot in `hermite`
diff --git a/models/foo.vm b/models/foo.vm
new file mode 100644
index 00000000..0621f77b
--- /dev/null
+++ b/models/foo.vm
@@ -0,0 +1,8 @@
+X var-x
+Y var-y
+X2 square X
+Y2 square Y
+out add X2 Y2
+s sqrt out
+one const 0.1
+foo sub s one
diff --git a/viewer/src/main.rs b/viewer/src/main.rs
index f8e1841b..95f0aaba 100644
--- a/viewer/src/main.rs
+++ b/viewer/src/main.rs
@@ -82,7 +82,9 @@ fn render_thread<S>(
     wake: Sender<()>,
 ) -> Result<()>
 where
-    S: fidget::eval::Shape + fidget::eval::MathShape,
+    S: fidget::eval::Shape
+        + fidget::eval::MathShape
+        + fidget::shape::RenderHints,
 {
     let mut config = None;
     let mut script_ctx = None;
@@ -148,7 +150,7 @@ where
     }
 }
 
-fn render<S: fidget::eval::Shape>(
+fn render<S: fidget::eval::Shape + fidget::shape::RenderHints>(
     mode: &RenderMode,
     shape: S,
     image_size: usize,