diff --git a/.github/Xargo.toml b/.github/Xargo.toml
new file mode 100644
index 00000000..919803b5
--- /dev/null
+++ b/.github/Xargo.toml
@@ -0,0 +1,5 @@
+[target.x86_64-unknown-linux-gnu.dependencies]
+alloc = {}
+
+[target.thumbv7em-none-eabihf.dependencies]
+alloc = {}
\ No newline at end of file
diff --git a/.github/workflows/parry-ci-build.yml b/.github/workflows/parry-ci-build.yml
index 309c8b58..4125d356 100644
--- a/.github/workflows/parry-ci-build.yml
+++ b/.github/workflows/parry-ci-build.yml
@@ -44,3 +44,32 @@ jobs:
         run: cd build/parry2d && cargo build --verbose --target wasm32-unknown-unknown;
       - name: build parry3d
         run: cd build/parry3d && cargo build --verbose --target wasm32-unknown-unknown;
+  build-no-std:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v2
+      - name: Install latest nightly
+        uses: actions-rs/toolchain@v1
+        with:
+          toolchain: nightly
+          override: true
+          components: rustfmt
+      - name: install xargo
+        run: cp .github/Xargo.toml .; rustup component add rust-src; cargo install -f xargo;
+      - name: build x86_64-unknown-linux-gnu
+        run: xargo build --verbose --no-default-features --features required-features --target=x86_64-unknown-linux-gnu;
+      - name: build thumbv7em-none-eabihf
+        run: xargo build --verbose --no-default-features --features required-features --target=thumbv7em-none-eabihf;
+  build-cuda:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: Jimver/cuda-toolkit@v0.2.4
+      - name: Install nightly-2021-10-17
+        uses: actions-rs/toolchain@v1
+        with:
+          toolchain: nightly-2021-10-17
+          override: true
+      - uses: actions/checkout@v2
+      - run: rustup target add nvptx64-nvidia-cuda
+      - run: cargo build --no-default-features --features required-features,cuda
+      - run: cargo build --no-default-features --features required-features,cuda --target=nvptx64-nvidia-cuda
\ No newline at end of file
diff --git a/Cargo.toml b/Cargo.toml
index 0c1c71ea..a8abf899 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -1,8 +1,11 @@
 [workspace]
 members = ["build/parry2d", "build/parry3d", "build/parry2d-f64", "build/parry3d-f64"]
+resolver = "2"
 
 [patch.crates-io]
 parry2d = { path = "build/parry2d" }
 parry3d = { path = "build/parry3d" }
 parry2d-f64 = { path = "build/parry2d-f64" }
 parry3d-f64 = { path = "build/parry3d-f64" }
+simba = { git = "https://github.com/dimforge/simba" }
+nalgebra = { git = "https://github.com/dimforge/nalgebra", branch = "rust-cuda" }
\ No newline at end of file
diff --git a/build/parry2d-f64/Cargo.toml b/build/parry2d-f64/Cargo.toml
index 909fdced..ce08cfd5 100644
--- a/build/parry2d-f64/Cargo.toml
+++ b/build/parry2d-f64/Cargo.toml
@@ -17,13 +17,17 @@ edition = "2018"
 maintenance = { status = "actively-developed" }
 
 [features]
-default = [ "dim2", "f64" ]
+default = [ "required-features", "std" ]
+required-features = [ "dim2", "f64" ]
+std     = [ "nalgebra/std", "slab", "rustc-hash", "simba/std", "arrayvec" ]
 dim2    = [ ]
 f64     = [ ]
 serde-serialize = [ "serde", "nalgebra/serde-serialize", "arrayvec/serde" ]
 simd-stable = [ "simba/wide", "simd-is-enabled" ]
 simd-nightly = [ "simba/packed_simd", "simd-is-enabled" ]
 enhanced-determinism = [ "simba/libm_force", "indexmap" ]
+cuda   = [ "cust", "nalgebra/cuda" ]
+
 # Do not enable this feature directly. It is automatically
 # enabled with the "simd-stable" or "simd-nightly" feature.
 simd-is-enabled = [ ]
@@ -31,24 +35,27 @@ simd-is-enabled = [ ]
 [lib]
 name = "parry2d_f64"
 path = "../../src/lib.rs"
-required-features = [ "dim2", "f64" ]
+required-features = [ "required-features" ]
 
 [dependencies]
-either          = "1"
+either          = { version = "1", default-features = false }
 bitflags        = "1"
-downcast-rs     = "1"
+downcast-rs     = { version = "1", default-features = false }
 num-traits      = { version = "0.2", default-features = false }
 smallvec        = "1"
-slab            = "0.4"
-arrayvec        = "0.7"
-simba           = "0.6"
-nalgebra        = "0.29"
+slab            = { version = "0.4", optional = true }
+arrayvec        = { version = "0.7", optional = true }
+simba           = { version = "0.6", default-features = false }
+nalgebra        = { version = "0.29", default-features = false, features = [ "libm" ] }
 approx          = { version = "0.5", default-features = false }
 serde           = { version = "1.0", optional = true, features = ["derive"]}
 num-derive      = "0.3"
-indexmap = { version = "1", features = [ "serde-1" ], optional = true }
-rustc-hash = "1"
+indexmap        = { version = "1", features = [ "serde-1" ], optional = true }
+rustc-hash      = { version = "1", optional = true }
+
+[target.'cfg(not(target_os = "cuda"))'.dependencies]
+cust       = { version = "0.1", optional = true }
 
 [dev-dependencies]
-simba = { version = "0.6", features = [ "partial_fixed_point_support" ] }
+simba = { version = "0.6", default-features = false, features = [ "partial_fixed_point_support" ] }
 oorandom = "11"
diff --git a/build/parry2d/Cargo.toml b/build/parry2d/Cargo.toml
index 6a1ec45a..c236b916 100644
--- a/build/parry2d/Cargo.toml
+++ b/build/parry2d/Cargo.toml
@@ -17,13 +17,17 @@ edition = "2018"
 maintenance = { status = "actively-developed" }
 
 [features]
-default = [ "dim2", "f32" ]
+default = [ "required-features", "std" ]
+required-features = [ "dim2", "f32" ]
+std     = [ "nalgebra/std", "slab", "rustc-hash", "simba/std", "arrayvec" ]
 dim2    = [ ]
 f32     = [ ]
 serde-serialize = [ "serde", "nalgebra/serde-serialize", "arrayvec/serde" ]
 simd-stable = [ "simba/wide", "simd-is-enabled" ]
 simd-nightly = [ "simba/packed_simd", "simd-is-enabled" ]
 enhanced-determinism = [ "simba/libm_force", "indexmap" ]
+cuda   = [ "cust", "nalgebra/cuda" ]
+
 # Do not enable this feature directly. It is automatically
 # enabled with the "simd-stable" or "simd-nightly" feature.
 simd-is-enabled = [ ]
@@ -31,24 +35,27 @@ simd-is-enabled = [ ]
 [lib]
 name = "parry2d"
 path = "../../src/lib.rs"
-required-features = [ "dim2", "f32" ]
+required-features = [ "required-features" ]
 
 [dependencies]
-either          = "1"
+either          = { version = "1", default-features = false }
 bitflags        = "1"
-downcast-rs     = "1"
+downcast-rs     = { version = "1", default-features = false }
 num-traits      = { version = "0.2", default-features = false }
 smallvec        = "1"
-slab            = "0.4"
-arrayvec        = "0.7"
-simba           = "0.6"
-nalgebra        = "0.29"
+slab            = { version = "0.4", optional = true }
+arrayvec        = { version = "0.7", optional = true }
+simba           = { version = "0.6", default-features = false }
+nalgebra        = { version = "0.29", default-features = false, features = [ "libm" ] }
 approx          = { version = "0.5", default-features = false }
 serde           = { version = "1.0", optional = true, features = ["derive"]}
 num-derive      = "0.3"
 indexmap        = { version = "1", features = [ "serde-1" ], optional = true }
-rustc-hash      = "1"
+rustc-hash      = { version = "1", optional = true }
+
+[target.'cfg(not(target_os = "cuda"))'.dependencies]
+cust = { version = "0.1", optional = true }
 
 [dev-dependencies]
-simba = { version = "0.6", features = [ "partial_fixed_point_support" ] }
+simba = { version = "0.6", default-features = false, features = [ "partial_fixed_point_support" ] }
 oorandom = "11"
diff --git a/build/parry3d-f64/Cargo.toml b/build/parry3d-f64/Cargo.toml
index a1453d00..7ccb96b9 100644
--- a/build/parry3d-f64/Cargo.toml
+++ b/build/parry3d-f64/Cargo.toml
@@ -17,13 +17,17 @@ edition = "2018"
 maintenance = { status = "actively-developed" }
 
 [features]
-default = [ "dim3", "f64" ]
+default = [ "required-features", "std" ]
+required-features = [ "dim3", "f64" ]
+std     = [ "nalgebra/std", "slab", "rustc-hash", "simba/std" ]
 dim3    = [ ]
 f64     = [ ]
 serde-serialize = [ "serde", "nalgebra/serde-serialize" ]
 simd-stable = [ "simba/wide", "simd-is-enabled" ]
 simd-nightly = [ "simba/packed_simd", "simd-is-enabled" ]
 enhanced-determinism = [ "simba/libm_force", "indexmap" ]
+cuda   = [ "cust", "nalgebra/cuda" ]
+
 # Do not enable this feature directly. It is automatically
 # enabled with the "simd-stable" or "simd-nightly" feature.
 simd-is-enabled = [ ]
@@ -31,23 +35,25 @@ simd-is-enabled = [ ]
 [lib]
 name = "parry3d_f64"
 path = "../../src/lib.rs"
-required-features = [ "dim3", "f64" ]
+required-features = [ "required-features" ]
 
 [dependencies]
-either      = "1"
+either      = { version = "1", default-features = false }
 bitflags    = "1"
-downcast-rs = "1"
+downcast-rs = { version = "1", default-features = false }
 num-traits = { version = "0.2", default-features = false }
 smallvec   = "1"
-slab       = "0.4"
-simba      = "0.6"
-nalgebra   = "0.29"
+slab       = { version = "0.4", optional = true }
+simba      = { version = "0.6", default-features = false }
+nalgebra   = { version = "0.29", default-features = false, features = [ "libm" ] }
 approx     = { version = "0.5", default-features = false }
 serde      = { version = "1.0", optional = true, features = ["derive", "rc"]}
-num-derive   = "0.3"
-indexmap = { version = "1", features = [ "serde-1" ], optional = true }
-rustc-hash = "1"
+num-derive = "0.3"
+indexmap   = { version = "1", features = [ "serde-1" ], optional = true }
+rustc-hash = { version = "1", optional = true }
 
+[target.'cfg(not(target_os = "cuda"))'.dependencies]
+cust       = { version = "0.1", optional = true }
 
 [dev-dependencies]
 oorandom = "11"
diff --git a/build/parry3d/Cargo.toml b/build/parry3d/Cargo.toml
index e212833d..9bfa1f30 100644
--- a/build/parry3d/Cargo.toml
+++ b/build/parry3d/Cargo.toml
@@ -17,13 +17,17 @@ edition = "2018"
 maintenance = { status = "actively-developed" }
 
 [features]
-default = [ "dim3", "f32" ]
+default = [ "required-features", "std" ]
+required-features = [ "dim3", "f32" ]
+std     = [ "nalgebra/std", "slab", "rustc-hash", "simba/std" ]
 dim3    = [ ]
 f32     = [ ]
 serde-serialize = [ "serde", "nalgebra/serde-serialize" ]
 simd-stable = [ "simba/wide", "simd-is-enabled" ]
 simd-nightly = [ "simba/packed_simd", "simd-is-enabled" ]
 enhanced-determinism = [ "simba/libm_force", "indexmap" ]
+cuda   = [ "cust", "nalgebra/cuda" ]
+
 # Do not enable this feature directly. It is automatically
 # enabled with the "simd-stable" or "simd-nightly" feature.
 simd-is-enabled = [ ]
@@ -31,23 +35,25 @@ simd-is-enabled = [ ]
 [lib]
 name = "parry3d"
 path = "../../src/lib.rs"
-required-features = [ "dim3", "f32" ]
+required-features = [ "required-features" ]
 
 [dependencies]
-either      = "1"
+either      = { version = "1", default-features = false }
 bitflags    = "1"
-downcast-rs = "1"
+downcast-rs = { version = "1", default-features = false }
 num-traits = { version = "0.2", default-features = false }
 smallvec   = "1"
-slab       = "0.4"
-simba      = "0.6"
-nalgebra   = "0.29"
+slab       = { version = "0.4", optional = true }
+simba      = { version = "0.6", default-features = false }
+nalgebra   = { version = "0.29", default-features = false, features = [ "libm" ] }
 approx     = { version = "0.5", default-features = false }
 serde      = { version = "1.0", optional = true, features = ["derive", "rc"]}
-num-derive   = "0.3"
-indexmap = { version = "1", features = [ "serde-1" ], optional = true }
-rustc-hash = "1"
+num-derive = "0.3"
+indexmap   = { version = "1", features = [ "serde-1" ], optional = true }
+rustc-hash = { version = "1", optional = true }
 
+[target.'cfg(not(target_os = "cuda"))'.dependencies]
+cust       = { version = "0.1", optional = true }
 
 [dev-dependencies]
 oorandom = "11"
diff --git a/src/bounding_volume/aabb.rs b/src/bounding_volume/aabb.rs
index 614ffbfb..d85ccdba 100644
--- a/src/bounding_volume/aabb.rs
+++ b/src/bounding_volume/aabb.rs
@@ -7,6 +7,9 @@ use crate::utils::IsometryOps;
 use na;
 use num::Bounded;
 
+#[cfg(not(feature = "std"))]
+use na::ComplexField; // for .abs()
+
 /// An Axis Aligned Bounding Box.
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 #[derive(Debug, PartialEq, Copy, Clone)]
@@ -270,6 +273,7 @@ impl AABB {
     }
 
     #[cfg(feature = "dim3")]
+    #[cfg(feature = "std")]
     pub fn intersects_spiral(
         &self,
         point: &Point<Real>,
diff --git a/src/bounding_volume/mod.rs b/src/bounding_volume/mod.rs
index 8386ae01..05dbaac6 100644
--- a/src/bounding_volume/mod.rs
+++ b/src/bounding_volume/mod.rs
@@ -16,11 +16,14 @@ pub mod bounding_volume;
 pub mod aabb;
 mod aabb_ball;
 #[cfg(feature = "dim2")]
+#[cfg(feature = "std")]
 mod aabb_convex_polygon;
 #[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
 mod aabb_convex_polyhedron;
 mod aabb_cuboid;
 mod aabb_halfspace;
+#[cfg(feature = "std")]
 mod aabb_heightfield;
 mod aabb_support_map;
 mod aabb_triangle;
@@ -34,17 +37,22 @@ mod bounding_sphere_capsule;
 #[cfg(feature = "dim3")]
 mod bounding_sphere_cone;
 #[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
 mod bounding_sphere_convex;
 #[cfg(feature = "dim2")]
+#[cfg(feature = "std")]
 mod bounding_sphere_convex_polygon;
 mod bounding_sphere_cuboid;
 #[cfg(feature = "dim3")]
 mod bounding_sphere_cylinder;
 mod bounding_sphere_halfspace;
+#[cfg(feature = "std")]
 mod bounding_sphere_heightfield;
+#[cfg(feature = "std")]
 mod bounding_sphere_polyline;
 mod bounding_sphere_segment;
 mod bounding_sphere_triangle;
+#[cfg(feature = "std")]
 mod bounding_sphere_trimesh;
 mod bounding_sphere_utils;
 mod simd_aabb;
diff --git a/src/lib.rs b/src/lib.rs
index ef1c05d6..124b0115 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -16,6 +16,7 @@ the rust programming language.
 #![warn(unused_imports)]
 #![allow(missing_copy_implementations)]
 #![doc(html_root_url = "http://docs.rs/parry/0.1.1")]
+#![cfg_attr(not(feature = "std"), no_std)]
 
 #[cfg(all(
     feature = "simd-is-enabled",
@@ -46,6 +47,13 @@ macro_rules! array(
     }
 );
 
+#[cfg(all(feature = "alloc", not(feature = "std")))]
+#[cfg_attr(test, macro_use)]
+extern crate alloc;
+
+#[cfg(not(feature = "std"))]
+extern crate core as std;
+
 #[cfg(feature = "serde")]
 #[macro_use]
 extern crate serde;
@@ -61,9 +69,11 @@ pub extern crate simba;
 
 pub mod bounding_volume;
 pub mod mass_properties;
+#[cfg(feature = "std")]
 pub mod partitioning;
 pub mod query;
 pub mod shape;
+#[cfg(feature = "std")]
 pub mod transformation;
 pub mod utils;
 
diff --git a/src/mass_properties/mass_properties.rs b/src/mass_properties/mass_properties.rs
index 74bc6b26..6808574b 100644
--- a/src/mass_properties/mass_properties.rs
+++ b/src/mass_properties/mass_properties.rs
@@ -2,7 +2,6 @@ use crate::math::{AngVector, AngularInertia, Isometry, Point, Real, Rotation, Ve
 use crate::utils;
 use na::ComplexField;
 use num::Zero;
-use std::iter::Sum;
 use std::ops::{Add, AddAssign, Sub, SubAssign};
 #[cfg(feature = "dim3")]
 use {na::Matrix3, std::ops::MulAssign};
@@ -350,7 +349,8 @@ impl AddAssign<MassProperties> for MassProperties {
     }
 }
 
-impl Sum<MassProperties> for MassProperties {
+#[cfg(feature = "std")]
+impl std::iter::Sum<MassProperties> for MassProperties {
     #[cfg(feature = "dim2")]
     fn sum<I>(iter: I) -> Self
     where
diff --git a/src/mass_properties/mod.rs b/src/mass_properties/mod.rs
index 4dd74c55..b58afa4f 100644
--- a/src/mass_properties/mod.rs
+++ b/src/mass_properties/mod.rs
@@ -5,30 +5,35 @@ pub use self::mass_properties::MassProperties;
 mod mass_properties;
 mod mass_properties_ball;
 mod mass_properties_capsule;
+#[cfg(feature = "std")]
 mod mass_properties_compound;
 #[cfg(feature = "dim3")]
 mod mass_properties_cone;
-#[cfg(featuer = "dim2")]
-mod mass_properties_convex_polygon;
 #[cfg(feature = "dim2")]
+#[cfg(feature = "std")]
 mod mass_properties_convex_polygon;
 #[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
 mod mass_properties_convex_polyhedron;
 mod mass_properties_cuboid;
 mod mass_properties_cylinder;
 #[cfg(feature = "dim2")]
 mod mass_properties_triangle;
 #[cfg(feature = "dim2")]
+#[cfg(feature = "std")]
 mod mass_properties_trimesh;
 
 /// Free functions for some special-cases of mass-properties computation.
 pub mod details {
     #[cfg(feature = "dim2")]
+    #[cfg(feature = "std")]
     pub use super::mass_properties_convex_polygon::convex_polygon_area_and_center_of_mass;
     #[cfg(feature = "dim3")]
+    #[cfg(feature = "std")]
     pub use super::mass_properties_convex_polyhedron::{
         convex_mesh_volume_and_center_of_mass_unchecked, tetrahedron_unit_inertia_tensor_wrt_point,
     };
     #[cfg(feature = "dim2")]
+    #[cfg(feature = "std")]
     pub use super::mass_properties_trimesh::trimesh_area_and_center_of_mass;
 }
diff --git a/src/query/clip/mod.rs b/src/query/clip/mod.rs
index 26189a1f..3a17f804 100644
--- a/src/query/clip/mod.rs
+++ b/src/query/clip/mod.rs
@@ -1,10 +1,13 @@
 pub use self::clip_aabb_line::clip_aabb_line;
+#[cfg(feature = "std")]
 pub use self::clip_halfspace_polygon::clip_halfspace_polygon;
 pub use self::clip_segment_segment::clip_segment_segment;
 #[cfg(feature = "dim2")]
 pub use self::clip_segment_segment::clip_segment_segment_with_normal;
 
 mod clip_aabb_line;
+#[cfg(feature = "std")]
 mod clip_aabb_polygon;
+#[cfg(feature = "std")]
 mod clip_halfspace_polygon;
 mod clip_segment_segment;
diff --git a/src/query/closest_points/mod.rs b/src/query/closest_points/mod.rs
index 9204c8f8..43cae0b3 100644
--- a/src/query/closest_points/mod.rs
+++ b/src/query/closest_points/mod.rs
@@ -5,6 +5,7 @@ pub use self::closest_points_ball_ball::closest_points_ball_ball;
 pub use self::closest_points_ball_convex_polyhedron::{
     closest_points_ball_convex_polyhedron, closest_points_convex_polyhedron_ball,
 };
+#[cfg(feature = "std")]
 pub use self::closest_points_composite_shape_shape::{
     closest_points_composite_shape_shape, closest_points_shape_composite_shape,
     CompositeShapeAgainstShapeClosestPointsVisitor,
@@ -31,6 +32,7 @@ pub use self::closest_points_support_map_support_map::closest_points_support_map
 mod closest_points;
 mod closest_points_ball_ball;
 mod closest_points_ball_convex_polyhedron;
+#[cfg(feature = "std")]
 mod closest_points_composite_shape_shape;
 mod closest_points_cuboid_cuboid;
 mod closest_points_cuboid_triangle;
diff --git a/src/query/contact/mod.rs b/src/query/contact/mod.rs
index 46d61add..6a6dcd9c 100644
--- a/src/query/contact/mod.rs
+++ b/src/query/contact/mod.rs
@@ -5,6 +5,7 @@ pub use self::contact_ball_ball::contact_ball_ball;
 pub use self::contact_ball_convex_polyhedron::{
     contact_ball_convex_polyhedron, contact_convex_polyhedron_ball,
 };
+#[cfg(feature = "std")]
 pub use self::contact_composite_shape_shape::{
     contact_composite_shape_shape, contact_shape_composite_shape,
 };
@@ -13,14 +14,18 @@ pub use self::contact_halfspace_support_map::{
     contact_halfspace_support_map, contact_support_map_halfspace,
 };
 pub use self::contact_shape_shape::contact;
-pub use self::contact_support_map_support_map::contact_support_map_support_map;
-pub use self::contact_support_map_support_map::contact_support_map_support_map_with_params;
+#[cfg(feature = "std")] // TODO: doesn’t work without std because of EPA
+pub use self::contact_support_map_support_map::{
+    contact_support_map_support_map, contact_support_map_support_map_with_params,
+};
 
 mod contact;
 mod contact_ball_ball;
 mod contact_ball_convex_polyhedron;
+#[cfg(feature = "std")]
 mod contact_composite_shape_shape;
 mod contact_cuboid_cuboid;
 mod contact_halfspace_support_map;
 mod contact_shape_shape;
+#[cfg(feature = "std")] // TODO: doesn’t work without std because of EPA
 mod contact_support_map_support_map;
diff --git a/src/query/contact_manifolds/contact_manifolds_capsule_capsule.rs b/src/query/contact_manifolds/contact_manifolds_capsule_capsule.rs
index c5cc5dac..e39464db 100644
--- a/src/query/contact_manifolds/contact_manifolds_capsule_capsule.rs
+++ b/src/query/contact_manifolds/contact_manifolds_capsule_capsule.rs
@@ -6,6 +6,9 @@ use crate::shape::{Capsule, Shape};
 use approx::AbsDiffEq;
 use na::Unit;
 
+#[cfg(not(feature = "std"))]
+use na::ComplexField; // for .abs()
+
 /// Computes the contact manifold between two capsules given as `Shape` trait-objects.
 pub fn contact_manifold_capsule_capsule_shapes<ManifoldData, ContactData>(
     pos12: &Isometry<Real>,
diff --git a/src/query/default_query_dispatcher.rs b/src/query/default_query_dispatcher.rs
index 7ed5e015..33674d06 100644
--- a/src/query/default_query_dispatcher.rs
+++ b/src/query/default_query_dispatcher.rs
@@ -1,9 +1,12 @@
 use crate::math::{Isometry, Point, Real, Vector};
-use crate::query::contact_manifolds::ContactManifoldsWorkspace;
-use crate::query::query_dispatcher::PersistentQueryDispatcher;
 use crate::query::{
-    self, details::NonlinearTOIMode, ClosestPoints, Contact, ContactManifold, NonlinearRigidMotion,
-    QueryDispatcher, Unsupported, TOI,
+    self, details::NonlinearTOIMode, ClosestPoints, Contact, NonlinearRigidMotion, QueryDispatcher,
+    Unsupported, TOI,
+};
+#[cfg(feature = "std")]
+use crate::query::{
+    contact_manifolds::ContactManifoldsWorkspace, query_dispatcher::PersistentQueryDispatcher,
+    ContactManifold,
 };
 use crate::shape::{HalfSpace, Segment, Shape, ShapeType};
 
@@ -57,15 +60,18 @@ impl QueryDispatcher for DefaultQueryDispatcher {
             Ok(query::details::intersection_test_support_map_support_map(
                 pos12, s1, s2,
             ))
-        } else if let Some(c1) = shape1.as_composite_shape() {
-            Ok(query::details::intersection_test_composite_shape_shape(
-                self, pos12, c1, shape2,
-            ))
-        } else if let Some(c2) = shape2.as_composite_shape() {
-            Ok(query::details::intersection_test_shape_composite_shape(
-                self, pos12, shape1, c2,
-            ))
         } else {
+            #[cfg(feature = "std")]
+            if let Some(c1) = shape1.as_composite_shape() {
+                return Ok(query::details::intersection_test_composite_shape_shape(
+                    self, pos12, c1, shape2,
+                ));
+            } else if let Some(c2) = shape2.as_composite_shape() {
+                return Ok(query::details::intersection_test_shape_composite_shape(
+                    self, pos12, shape1, c2,
+                ));
+            }
+
             Err(Unsupported)
         }
     }
@@ -113,15 +119,18 @@ impl QueryDispatcher for DefaultQueryDispatcher {
             Ok(query::details::distance_support_map_support_map(
                 pos12, s1, s2,
             ))
-        } else if let Some(c1) = shape1.as_composite_shape() {
-            Ok(query::details::distance_composite_shape_shape(
-                self, pos12, c1, shape2,
-            ))
-        } else if let Some(c2) = shape2.as_composite_shape() {
-            Ok(query::details::distance_shape_composite_shape(
-                self, pos12, shape1, c2,
-            ))
         } else {
+            #[cfg(feature = "std")]
+            if let Some(c1) = shape1.as_composite_shape() {
+                return Ok(query::details::distance_composite_shape_shape(
+                    self, pos12, c1, shape2,
+                ));
+            } else if let Some(c2) = shape2.as_composite_shape() {
+                return Ok(query::details::distance_shape_composite_shape(
+                    self, pos12, shape1, c2,
+                ));
+            }
+
             Err(Unsupported)
         }
     }
@@ -162,19 +171,22 @@ impl QueryDispatcher for DefaultQueryDispatcher {
             Ok(query::details::contact_convex_polyhedron_ball(
                 pos12, shape1, b2, prediction,
             ))
-        } else if let (Some(s1), Some(s2)) = (shape1.as_support_map(), shape2.as_support_map()) {
-            Ok(query::details::contact_support_map_support_map(
-                pos12, s1, s2, prediction,
-            ))
-        } else if let Some(c1) = shape1.as_composite_shape() {
-            Ok(query::details::contact_composite_shape_shape(
-                self, pos12, c1, shape2, prediction,
-            ))
-        } else if let Some(c2) = shape2.as_composite_shape() {
-            Ok(query::details::contact_shape_composite_shape(
-                self, pos12, shape1, c2, prediction,
-            ))
         } else {
+            #[cfg(feature = "std")]
+            if let (Some(s1), Some(s2)) = (shape1.as_support_map(), shape2.as_support_map()) {
+                return Ok(query::details::contact_support_map_support_map(
+                    pos12, s1, s2, prediction,
+                ));
+            } else if let Some(c1) = shape1.as_composite_shape() {
+                return Ok(query::details::contact_composite_shape_shape(
+                    self, pos12, c1, shape2, prediction,
+                ));
+            } else if let Some(c2) = shape2.as_composite_shape() {
+                return Ok(query::details::contact_shape_composite_shape(
+                    self, pos12, shape1, c2, prediction,
+                ));
+            }
+
             Err(Unsupported)
         }
     }
@@ -239,15 +251,18 @@ impl QueryDispatcher for DefaultQueryDispatcher {
             Ok(query::details::closest_points_support_map_support_map(
                 &pos12, s1, s2, max_dist,
             ))
-        } else if let Some(c1) = shape1.as_composite_shape() {
-            Ok(query::details::closest_points_composite_shape_shape(
-                self, &pos12, c1, shape2, max_dist,
-            ))
-        } else if let Some(c2) = shape2.as_composite_shape() {
-            Ok(query::details::closest_points_shape_composite_shape(
-                self, &pos12, shape1, c2, max_dist,
-            ))
         } else {
+            #[cfg(feature = "std")]
+            if let Some(c1) = shape1.as_composite_shape() {
+                return Ok(query::details::closest_points_composite_shape_shape(
+                    self, &pos12, c1, shape2, max_dist,
+                ));
+            } else if let Some(c2) = shape2.as_composite_shape() {
+                return Ok(query::details::closest_points_shape_composite_shape(
+                    self, &pos12, shape1, c2, max_dist,
+                ));
+            }
+
             Err(Unsupported)
         }
     }
@@ -296,25 +311,28 @@ impl QueryDispatcher for DefaultQueryDispatcher {
                 s2,
                 max_toi,
             ))
-        } else if let Some(c1) = shape1.as_composite_shape() {
-            Ok(query::details::time_of_impact_composite_shape_shape(
-                self,
-                pos12,
-                local_vel12,
-                c1,
-                shape2,
-                max_toi,
-            ))
-        } else if let Some(c2) = shape2.as_composite_shape() {
-            Ok(query::details::time_of_impact_shape_composite_shape(
-                self,
-                pos12,
-                local_vel12,
-                shape1,
-                c2,
-                max_toi,
-            ))
         } else {
+            #[cfg(feature = "std")]
+            if let Some(c1) = shape1.as_composite_shape() {
+                return Ok(query::details::time_of_impact_composite_shape_shape(
+                    self,
+                    pos12,
+                    local_vel12,
+                    c1,
+                    shape2,
+                    max_toi,
+                ));
+            } else if let Some(c2) = shape2.as_composite_shape() {
+                return Ok(query::details::time_of_impact_shape_composite_shape(
+                    self,
+                    pos12,
+                    local_vel12,
+                    shape1,
+                    c2,
+                    max_toi,
+                ));
+            }
+
             Err(Unsupported)
         }
     }
@@ -341,44 +359,48 @@ impl QueryDispatcher for DefaultQueryDispatcher {
                     self, motion1, sm1, shape1, motion2, sm2, shape2, start_time, end_time, mode,
                 ),
             )
-        } else if let Some(c1) = shape1.as_composite_shape() {
-            Ok(
-                query::details::nonlinear_time_of_impact_composite_shape_shape(
-                    self,
-                    motion1,
-                    c1,
-                    motion2,
-                    shape2,
-                    start_time,
-                    end_time,
-                    stop_at_penetration,
-                ),
-            )
-        } else if let Some(c2) = shape2.as_composite_shape() {
-            Ok(
-                query::details::nonlinear_time_of_impact_shape_composite_shape(
-                    self,
-                    motion1,
-                    shape1,
-                    motion2,
-                    c2,
-                    start_time,
-                    end_time,
-                    stop_at_penetration,
-                ),
-            )
-        /* } else if let (Some(p1), Some(s2)) = (shape1.as_shape::<HalfSpace>(), shape2.as_support_map()) {
-        //        query::details::nonlinear_time_of_impact_halfspace_support_map(m1, vel1, p1, m2, vel2, s2)
-                unimplemented!()
-            } else if let (Some(s1), Some(p2)) = (shape1.as_support_map(), shape2.as_shape::<HalfSpace>()) {
-        //        query::details::nonlinear_time_of_impact_support_map_halfspace(m1, vel1, s1, m2, vel2, p2)
-                unimplemented!() */
         } else {
+            #[cfg(feature = "std")]
+            if let Some(c1) = shape1.as_composite_shape() {
+                return Ok(
+                    query::details::nonlinear_time_of_impact_composite_shape_shape(
+                        self,
+                        motion1,
+                        c1,
+                        motion2,
+                        shape2,
+                        start_time,
+                        end_time,
+                        stop_at_penetration,
+                    ),
+                );
+            } else if let Some(c2) = shape2.as_composite_shape() {
+                return Ok(
+                    query::details::nonlinear_time_of_impact_shape_composite_shape(
+                        self,
+                        motion1,
+                        shape1,
+                        motion2,
+                        c2,
+                        start_time,
+                        end_time,
+                        stop_at_penetration,
+                    ),
+                );
+            }
+            /* } else if let (Some(p1), Some(s2)) = (shape1.as_shape::<HalfSpace>(), shape2.as_support_map()) {
+            //        query::details::nonlinear_time_of_impact_halfspace_support_map(m1, vel1, p1, m2, vel2, s2)
+                    unimplemented!()
+                } else if let (Some(s1), Some(p2)) = (shape1.as_support_map(), shape2.as_shape::<HalfSpace>()) {
+            //        query::details::nonlinear_time_of_impact_support_map_halfspace(m1, vel1, s1, m2, vel2, p2)
+                    unimplemented!() */
+
             Err(Unsupported)
         }
     }
 }
 
+#[cfg(feature = "std")]
 impl<ManifoldData, ContactData> PersistentQueryDispatcher<ManifoldData, ContactData>
     for DefaultQueryDispatcher
 where
diff --git a/src/query/distance/mod.rs b/src/query/distance/mod.rs
index 4bcbf360..9d243bea 100644
--- a/src/query/distance/mod.rs
+++ b/src/query/distance/mod.rs
@@ -5,6 +5,7 @@ pub use self::distance_ball_ball::distance_ball_ball;
 pub use self::distance_ball_convex_polyhedron::{
     distance_ball_convex_polyhedron, distance_convex_polyhedron_ball,
 };
+#[cfg(feature = "std")]
 pub use self::distance_composite_shape_shape::{
     distance_composite_shape_shape, distance_shape_composite_shape,
     CompositeShapeAgainstAnyDistanceVisitor,
@@ -21,6 +22,7 @@ pub use self::distance_support_map_support_map::{
 mod distance;
 mod distance_ball_ball;
 mod distance_ball_convex_polyhedron;
+#[cfg(feature = "std")]
 mod distance_composite_shape_shape;
 mod distance_cuboid_cuboid;
 mod distance_halfspace_support_map;
diff --git a/src/query/error.rs b/src/query/error.rs
index 62da6eb5..8c8e7582 100644
--- a/src/query/error.rs
+++ b/src/query/error.rs
@@ -10,4 +10,5 @@ impl fmt::Display for Unsupported {
     }
 }
 
+#[cfg(feature = "std")]
 impl std::error::Error for Unsupported {}
diff --git a/src/query/gjk/voronoi_simplex3.rs b/src/query/gjk/voronoi_simplex3.rs
index 40fa1d1b..4bf11c02 100644
--- a/src/query/gjk/voronoi_simplex3.rs
+++ b/src/query/gjk/voronoi_simplex3.rs
@@ -6,6 +6,9 @@ use crate::shape::{
     TrianglePointLocation,
 };
 
+#[cfg(not(feature = "std"))]
+use na::ComplexField; // for .abs()
+
 /// A simplex of dimension up to 3 that uses Voronoï regions for computing point projections.
 #[derive(Clone, Debug)]
 pub struct VoronoiSimplex {
diff --git a/src/query/intersection_test/mod.rs b/src/query/intersection_test/mod.rs
index 152af9b8..610da44d 100644
--- a/src/query/intersection_test/mod.rs
+++ b/src/query/intersection_test/mod.rs
@@ -5,6 +5,7 @@ pub use self::intersection_test_ball_ball::intersection_test_ball_ball;
 pub use self::intersection_test_ball_point_query::{
     intersection_test_ball_point_query, intersection_test_point_query_ball,
 };
+#[cfg(feature = "std")]
 pub use self::intersection_test_composite_shape_shape::{
     intersection_test_composite_shape_shape, intersection_test_shape_composite_shape,
     IntersectionCompositeShapeShapeBestFirstVisitor,
@@ -27,6 +28,7 @@ pub use self::intersection_test_support_map_support_map::intersection_test_suppo
 mod intersection_test;
 mod intersection_test_ball_ball;
 mod intersection_test_ball_point_query;
+#[cfg(feature = "std")]
 mod intersection_test_composite_shape_shape;
 mod intersection_test_cuboid_cuboid;
 mod intersection_test_cuboid_segment;
diff --git a/src/query/mod.rs b/src/query/mod.rs
index ae0a7871..cb3915ef 100644
--- a/src/query/mod.rs
+++ b/src/query/mod.rs
@@ -27,6 +27,7 @@
 
 pub use self::closest_points::{closest_points, ClosestPoints};
 pub use self::contact::{contact, Contact};
+#[cfg(feature = "std")]
 pub use self::contact_manifolds::{
     ContactManifold, ContactManifoldsWorkspace, TrackedContact, TypedWorkspaceData, WorkspaceData,
 };
@@ -36,18 +37,20 @@ pub use self::error::Unsupported;
 pub use self::intersection_test::intersection_test;
 pub use self::nonlinear_time_of_impact::{nonlinear_time_of_impact, NonlinearRigidMotion};
 pub use self::point::{PointProjection, PointQuery, PointQueryWithLocation};
-pub use self::query_dispatcher::{
-    PersistentQueryDispatcher, QueryDispatcher, QueryDispatcherChain,
-};
+#[cfg(feature = "std")]
+pub use self::query_dispatcher::PersistentQueryDispatcher;
+pub use self::query_dispatcher::{QueryDispatcher, QueryDispatcherChain};
 pub use self::ray::{Ray, RayCast, RayIntersection, SimdRay};
 pub use self::time_of_impact::{time_of_impact, TOIStatus, TOI};
 
 mod clip;
 pub mod closest_points;
 pub mod contact;
+#[cfg(feature = "std")]
 mod contact_manifolds;
 mod default_query_dispatcher;
 mod distance;
+#[cfg(feature = "std")]
 pub mod epa;
 mod error;
 pub mod gjk;
@@ -58,61 +61,20 @@ mod query_dispatcher;
 mod ray;
 pub mod sat;
 mod time_of_impact;
+#[cfg(feature = "std")]
 pub mod visitors;
 
 /// Queries dedicated to specific pairs of shapes.
 pub mod details {
     pub use super::clip::*;
     pub use super::closest_points::*;
-    pub use super::contact::{
-        contact_ball_ball, contact_ball_convex_polyhedron, contact_composite_shape_shape,
-        contact_convex_polyhedron_ball, contact_cuboid_cuboid, contact_halfspace_support_map,
-        contact_shape_composite_shape, contact_support_map_halfspace,
-        contact_support_map_support_map, contact_support_map_support_map_with_params,
-    };
-    pub use super::contact_manifolds::{
-        contact_manifold_ball_ball, contact_manifold_ball_ball_shapes,
-        contact_manifold_capsule_capsule, contact_manifold_capsule_capsule_shapes,
-        contact_manifold_convex_ball, contact_manifold_convex_ball_shapes,
-        contact_manifold_cuboid_cuboid, contact_manifold_cuboid_cuboid_shapes,
-        contact_manifold_cuboid_triangle, contact_manifold_cuboid_triangle_shapes,
-        contact_manifold_halfspace_pfm, contact_manifold_halfspace_pfm_shapes,
-        contact_manifold_pfm_pfm, contact_manifold_pfm_pfm_shapes,
-        contact_manifolds_heightfield_shape, contact_manifolds_heightfield_shape_shapes,
-        contact_manifolds_trimesh_shape_shapes,
-    };
-
-    pub use super::distance::{
-        distance_ball_ball, distance_ball_convex_polyhedron, distance_composite_shape_shape,
-        distance_convex_polyhedron_ball, distance_cuboid_cuboid, distance_halfspace_support_map,
-        distance_segment_segment, distance_shape_composite_shape, distance_support_map_halfspace,
-        distance_support_map_support_map, distance_support_map_support_map_with_params,
-        CompositeShapeAgainstAnyDistanceVisitor,
-    };
+    pub use super::contact::*;
+    #[cfg(feature = "std")]
+    pub use super::contact_manifolds::*;
+    pub use super::distance::*;
     pub use super::intersection_test::*;
-    pub use super::nonlinear_time_of_impact::{
-        nonlinear_time_of_impact_composite_shape_shape,
-        nonlinear_time_of_impact_shape_composite_shape,
-        nonlinear_time_of_impact_support_map_support_map,
-        NonlinearTOICompositeShapeShapeBestFirstVisitor, NonlinearTOIMode,
-    };
-    pub use super::point::local_point_projection_on_support_map;
-    pub use super::point::{
-        PointCompositeShapeProjBestFirstVisitor,
-        PointCompositeShapeProjWithFeatureBestFirstVisitor,
-        PointCompositeShapeProjWithLocationBestFirstVisitor,
-    };
-    #[cfg(feature = "dim3")]
-    pub use super::ray::local_ray_intersection_with_triangle;
-    pub use super::ray::{
-        line_toi_with_halfspace, local_ray_intersection_with_support_map_with_params,
-        ray_toi_with_ball, ray_toi_with_halfspace, RayCompositeShapeToiAndNormalBestFirstVisitor,
-        RayCompositeShapeToiBestFirstVisitor,
-    };
-    pub use super::time_of_impact::{
-        time_of_impact_ball_ball, time_of_impact_composite_shape_shape,
-        time_of_impact_halfspace_support_map, time_of_impact_shape_composite_shape,
-        time_of_impact_support_map_halfspace, time_of_impact_support_map_support_map,
-        TOICompositeShapeShapeBestFirstVisitor,
-    };
+    pub use super::nonlinear_time_of_impact::*;
+    pub use super::point::*;
+    pub use super::ray::*;
+    pub use super::time_of_impact::*;
 }
diff --git a/src/query/nonlinear_time_of_impact/mod.rs b/src/query/nonlinear_time_of_impact/mod.rs
index b91b37ed..03e1937f 100644
--- a/src/query/nonlinear_time_of_impact/mod.rs
+++ b/src/query/nonlinear_time_of_impact/mod.rs
@@ -1,5 +1,6 @@
 //! Implementation details of the `nonlinear_time_of_impact` function.
 
+#[cfg(feature = "std")]
 pub use self::nonlinear_time_of_impact_composite_shape_shape::{
     nonlinear_time_of_impact_composite_shape_shape, nonlinear_time_of_impact_shape_composite_shape,
     NonlinearTOICompositeShapeShapeBestFirstVisitor,
@@ -11,6 +12,7 @@ pub use self::nonlinear_time_of_impact_support_map_support_map::{
     nonlinear_time_of_impact_support_map_support_map, NonlinearTOIMode,
 };
 
+#[cfg(feature = "std")]
 mod nonlinear_time_of_impact_composite_shape_shape;
 //mod nonlinear_time_of_impact_halfspace_support_map;
 mod nonlinear_rigid_motion;
diff --git a/src/query/nonlinear_time_of_impact/nonlinear_time_of_impact_support_map_support_map.rs b/src/query/nonlinear_time_of_impact/nonlinear_time_of_impact_support_map_support_map.rs
index ffa2ce41..3d55f4c8 100644
--- a/src/query/nonlinear_time_of_impact/nonlinear_time_of_impact_support_map_support_map.rs
+++ b/src/query/nonlinear_time_of_impact/nonlinear_time_of_impact_support_map_support_map.rs
@@ -1,3 +1,5 @@
+#[cfg(not(feature = "std"))]
+use na::ComplexField; // for .abs()
 use na::{RealField, Unit};
 
 use crate::math::{Point, Real, Vector};
@@ -124,7 +126,7 @@ where
 
         // TODO: use the _with_params version of the closest points query.
         match dispatcher
-            .closest_points(&pos12, g1, g2, Real::max_value())
+            .closest_points(&pos12, g1, g2, Bounded::max_value())
             .ok()?
         {
             ClosestPoints::Intersecting => {
diff --git a/src/query/point/mod.rs b/src/query/point/mod.rs
index a7aa422f..2e3e3067 100644
--- a/src/query/point/mod.rs
+++ b/src/query/point/mod.rs
@@ -1,17 +1,20 @@
 //! Point inclusion and projection.
 
+#[cfg(feature = "std")]
 pub use self::point_composite_shape::{
     PointCompositeShapeProjBestFirstVisitor, PointCompositeShapeProjWithFeatureBestFirstVisitor,
     PointCompositeShapeProjWithLocationBestFirstVisitor,
 };
 #[doc(inline)]
 pub use self::point_query::{PointProjection, PointQuery, PointQueryWithLocation};
+#[cfg(feature = "std")] // TODO: can’t be used without std because of EPA
 pub use self::point_support_map::local_point_projection_on_support_map;
 
 mod point_aabb;
 mod point_ball;
 mod point_bounding_sphere;
 mod point_capsule;
+#[cfg(feature = "std")]
 mod point_composite_shape;
 #[cfg(feature = "dim3")]
 mod point_cone;
@@ -19,11 +22,13 @@ mod point_cuboid;
 #[cfg(feature = "dim3")]
 mod point_cylinder;
 mod point_halfspace;
+#[cfg(feature = "std")]
 mod point_heightfield;
 #[doc(hidden)]
 pub mod point_query;
 mod point_round_shape;
 mod point_segment;
+#[cfg(feature = "std")]
 mod point_support_map;
 #[cfg(feature = "dim3")]
 mod point_tetrahedron;
diff --git a/src/query/point/point_round_shape.rs b/src/query/point/point_round_shape.rs
index 10a9f245..3d0be151 100644
--- a/src/query/point/point_round_shape.rs
+++ b/src/query/point/point_round_shape.rs
@@ -8,12 +8,18 @@ use crate::shape::{FeatureId, RoundShape, SupportMap};
 impl<S: SupportMap> PointQuery for RoundShape<S> {
     #[inline]
     fn project_local_point(&self, point: &Point<Real>, solid: bool) -> PointProjection {
-        crate::query::details::local_point_projection_on_support_map(
+        #[cfg(not(feature = "std"))] // FIXME: can’t be used without std because of EPA
+        return unimplemented!(
+            "The projection of points on a round shapes isn’t supported on no-std platforms yet."
+        );
+
+        #[cfg(feature = "std")] // FIXME: can’t be used without std because of EPA
+        return crate::query::details::local_point_projection_on_support_map(
             self,
             &mut VoronoiSimplex::new(),
             point,
             solid,
-        )
+        );
     }
 
     #[inline]
diff --git a/src/query/point/point_support_map.rs b/src/query/point/point_support_map.rs
index 0f79109c..78e2a181 100644
--- a/src/query/point/point_support_map.rs
+++ b/src/query/point/point_support_map.rs
@@ -1,12 +1,15 @@
 use na::Unit;
 
 use crate::math::{Isometry, Point, Real, Vector};
+#[cfg(feature = "std")]
 use crate::query::epa::EPA;
 use crate::query::gjk::{self, CSOPoint, ConstantOrigin, VoronoiSimplex};
 use crate::query::{PointProjection, PointQuery};
 #[cfg(feature = "dim2")]
+#[cfg(feature = "std")]
 use crate::shape::ConvexPolygon;
 #[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
 use crate::shape::ConvexPolyhedron;
 use crate::shape::{FeatureId, SupportMap};
 
diff --git a/src/query/query_dispatcher.rs b/src/query/query_dispatcher.rs
index af4b8454..c98917bd 100644
--- a/src/query/query_dispatcher.rs
+++ b/src/query/query_dispatcher.rs
@@ -1,10 +1,10 @@
 use crate::math::{Isometry, Real, Vector};
-use crate::query::contact_manifolds::ContactManifoldsWorkspace;
-use crate::query::{
-    ClosestPoints, Contact, ContactManifold, NonlinearRigidMotion, Unsupported, TOI,
-};
+#[cfg(feature = "std")]
+use crate::query::{contact_manifolds::ContactManifoldsWorkspace, ContactManifold};
+use crate::query::{ClosestPoints, Contact, NonlinearRigidMotion, Unsupported, TOI};
 use crate::shape::Shape;
 
+#[cfg(feature = "std")]
 /// A query dispatcher for queries relying on spatial coherence, including contact-manifold computation.
 pub trait PersistentQueryDispatcher<ManifoldData = (), ContactData = ()>: QueryDispatcher {
     /// Compute all the contacts between two shapes.
@@ -200,6 +200,7 @@ where
     ) -> Option<TOI>);
 }
 
+#[cfg(feature = "std")]
 impl<ManifoldData, ContactData, T, U> PersistentQueryDispatcher<ManifoldData, ContactData>
     for QueryDispatcherChain<T, U>
 where
diff --git a/src/query/ray/mod.rs b/src/query/ray/mod.rs
index f3ec957b..71c90f7b 100644
--- a/src/query/ray/mod.rs
+++ b/src/query/ray/mod.rs
@@ -3,6 +3,7 @@
 #[doc(inline)]
 pub use self::ray::{Ray, RayCast, RayIntersection};
 pub use self::ray_ball::ray_toi_with_ball;
+#[cfg(feature = "std")]
 pub use self::ray_composite_shape::{
     RayCompositeShapeToiAndNormalBestFirstVisitor, RayCompositeShapeToiBestFirstVisitor,
 };
@@ -17,9 +18,11 @@ pub mod ray;
 mod ray_aabb;
 mod ray_ball;
 mod ray_bounding_sphere;
+#[cfg(feature = "std")]
 mod ray_composite_shape;
 mod ray_cuboid;
 mod ray_halfspace;
+#[cfg(feature = "std")]
 mod ray_heightfield;
 mod ray_round_shape;
 mod ray_support_map;
diff --git a/src/query/ray/ray.rs b/src/query/ray/ray.rs
index a01c9eca..9609523d 100644
--- a/src/query/ray/ray.rs
+++ b/src/query/ray/ray.rs
@@ -5,6 +5,12 @@ use crate::shape::FeatureId;
 
 /// A Ray.
 #[derive(Debug, Clone, Copy)]
+#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
+#[cfg_attr(
+    all(not(target_os = "cuda"), feature = "cuda"),
+    derive(cust::DeviceCopy)
+)]
+#[repr(C)]
 pub struct Ray {
     /// Starting point of the ray.
     pub origin: Point<Real>,
diff --git a/src/query/ray/ray_support_map.rs b/src/query/ray/ray_support_map.rs
index 4a14fc11..bc25e907 100644
--- a/src/query/ray/ray_support_map.rs
+++ b/src/query/ray/ray_support_map.rs
@@ -1,15 +1,20 @@
 use na;
+#[cfg(not(feature = "std"))]
+use na::ComplexField; // for .abs()
 
 use crate::math::Real;
 #[cfg(feature = "dim2")]
 use crate::query;
 use crate::query::gjk::{self, CSOPoint, VoronoiSimplex};
 use crate::query::{Ray, RayCast, RayIntersection};
-#[cfg(feature = "dim2")]
+#[cfg(all(feature = "std", feature = "dim2"))]
 use crate::shape::ConvexPolygon;
+#[cfg(all(feature = "std", feature = "dim3"))]
+use crate::shape::ConvexPolyhedron;
 use crate::shape::{Capsule, FeatureId, Segment, SupportMap};
 #[cfg(feature = "dim3")]
-use crate::shape::{Cone, ConvexPolyhedron, Cylinder};
+use crate::shape::{Cone, Cylinder};
+
 use num::Zero;
 
 /// Cast a ray on a shape using the GJK algorithm.
@@ -114,6 +119,7 @@ impl RayCast for Capsule {
 }
 
 #[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
 impl RayCast for ConvexPolyhedron {
     fn cast_local_ray_and_get_normal(
         &self,
@@ -132,6 +138,7 @@ impl RayCast for ConvexPolyhedron {
 }
 
 #[cfg(feature = "dim2")]
+#[cfg(feature = "std")]
 impl RayCast for ConvexPolygon {
     fn cast_local_ray_and_get_normal(
         &self,
diff --git a/src/query/ray/ray_triangle.rs b/src/query/ray/ray_triangle.rs
index 385cf4fe..827a9137 100644
--- a/src/query/ray/ray_triangle.rs
+++ b/src/query/ray/ray_triangle.rs
@@ -6,6 +6,9 @@ use crate::shape::{FeatureId, Triangle};
 #[cfg(feature = "dim3")]
 use {crate::math::Point, na::Vector3};
 
+#[cfg(not(feature = "std"))]
+use na::ComplexField; // for .abs()
+
 impl RayCast for Triangle {
     #[inline]
     #[cfg(feature = "dim2")]
diff --git a/src/query/sat/sat_cuboid_cuboid.rs b/src/query/sat/sat_cuboid_cuboid.rs
index c8caf6f9..fc28b0f1 100644
--- a/src/query/sat/sat_cuboid_cuboid.rs
+++ b/src/query/sat/sat_cuboid_cuboid.rs
@@ -1,5 +1,7 @@
 use crate::math::{Isometry, Real, Vector, DIM};
 use crate::shape::{Cuboid, SupportMap};
+#[cfg(not(feature = "std"))]
+use na::RealField; // For .copysign()
 
 /// Computes the separation of two cuboids along `axis1`.
 #[cfg(feature = "dim3")]
diff --git a/src/query/sat/sat_cuboid_triangle.rs b/src/query/sat/sat_cuboid_triangle.rs
index 1960f530..48ce10a9 100644
--- a/src/query/sat/sat_cuboid_triangle.rs
+++ b/src/query/sat/sat_cuboid_triangle.rs
@@ -6,6 +6,7 @@ use crate::query::sat;
 #[cfg(feature = "dim2")]
 use crate::query::sat::support_map_support_map_compute_separation;
 use crate::shape::{Cuboid, SupportMap, Triangle};
+use na::ComplexField;
 
 /// Finds the best separating edge between a cuboid and a triangle.
 ///
@@ -65,7 +66,7 @@ pub fn cuboid_triangle_find_local_separating_edge_twoway(
         let axis_norm_squared = axis.norm_squared();
 
         if axis_norm_squared > Real::default_epsilon() {
-            let axis_norm = axis_norm_squared.sqrt();
+            let axis_norm = ComplexField::sqrt(axis_norm_squared);
 
             // NOTE: for both axis and -axis, the dot1 will have the same
             // value because of the cuboid's symmetry.
diff --git a/src/query/time_of_impact/mod.rs b/src/query/time_of_impact/mod.rs
index cbed231f..0e96fba5 100644
--- a/src/query/time_of_impact/mod.rs
+++ b/src/query/time_of_impact/mod.rs
@@ -2,6 +2,7 @@
 
 pub use self::time_of_impact::{time_of_impact, TOIStatus, TOI};
 pub use self::time_of_impact_ball_ball::time_of_impact_ball_ball;
+#[cfg(feature = "std")]
 pub use self::time_of_impact_composite_shape_shape::{
     time_of_impact_composite_shape_shape, time_of_impact_shape_composite_shape,
     TOICompositeShapeShapeBestFirstVisitor,
@@ -13,6 +14,7 @@ pub use self::time_of_impact_support_map_support_map::time_of_impact_support_map
 
 mod time_of_impact;
 mod time_of_impact_ball_ball;
+#[cfg(feature = "std")]
 mod time_of_impact_composite_shape_shape;
 mod time_of_impact_halfspace_support_map;
 mod time_of_impact_support_map_support_map;
diff --git a/src/shape/ball.rs b/src/shape/ball.rs
index 63790543..99b76e9b 100644
--- a/src/shape/ball.rs
+++ b/src/shape/ball.rs
@@ -5,7 +5,12 @@ use crate::shape::SupportMap;
 
 /// A Ball shape.
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
+#[cfg_attr(
+    all(not(target_os = "cuda"), feature = "cuda"),
+    derive(cust::DeviceCopy)
+)]
 #[derive(PartialEq, Debug, Copy, Clone)]
+#[repr(C)]
 pub struct Ball {
     /// The radius of the ball.
     pub radius: Real,
diff --git a/src/shape/capsule.rs b/src/shape/capsule.rs
index c190e94a..d6bde620 100644
--- a/src/shape/capsule.rs
+++ b/src/shape/capsule.rs
@@ -4,6 +4,11 @@ use na::Unit;
 
 #[derive(Copy, Clone, Debug)]
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
+#[cfg_attr(
+    all(not(target_os = "cuda"), feature = "cuda"),
+    derive(cust::DeviceCopy)
+)]
+#[repr(C)]
 /// A capsule shape defined as a round segment.
 pub struct Capsule {
     /// The axis and endpoint of the capsule.
diff --git a/src/shape/cone.rs b/src/shape/cone.rs
index 91a61f64..c55f8f10 100644
--- a/src/shape/cone.rs
+++ b/src/shape/cone.rs
@@ -5,9 +5,17 @@ use crate::shape::SupportMap;
 use na;
 use num::Zero;
 
+#[cfg(not(feature = "std"))]
+use na::RealField; // for .copysign()
+
 /// Cone shape with its principal axis aligned with the `y` axis.
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
+#[cfg_attr(
+    all(not(target_os = "cuda"), feature = "cuda"),
+    derive(cust::DeviceCopy)
+)]
 #[derive(PartialEq, Debug, Copy, Clone)]
+#[repr(C)]
 pub struct Cone {
     /// The half-height of the cone.
     pub half_height: Real,
diff --git a/src/shape/convex_polyhedron.rs b/src/shape/convex_polyhedron.rs
index 3b8114df..f4bd6b5f 100644
--- a/src/shape/convex_polyhedron.rs
+++ b/src/shape/convex_polyhedron.rs
@@ -6,6 +6,9 @@ use crate::utils::{self, SortedPair};
 use na::{self, ComplexField, Point2, Unit};
 use std::f64;
 
+#[cfg(not(feature = "std"))]
+use na::ComplexField; // for .abs()
+
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 #[derive(PartialEq, Debug, Copy, Clone)]
 pub struct Vertex {
diff --git a/src/shape/cuboid.rs b/src/shape/cuboid.rs
index 88b4d55e..2b60398b 100644
--- a/src/shape/cuboid.rs
+++ b/src/shape/cuboid.rs
@@ -7,9 +7,17 @@ use crate::shape::{FeatureId, PolygonalFeature, SupportMap};
 use crate::utils::WSign;
 use na::Unit;
 
+#[cfg(not(feature = "std"))]
+use na::RealField; // for .copysign()
+
 /// Shape of a box.
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
+#[cfg_attr(
+    all(not(target_os = "cuda"), feature = "cuda"),
+    derive(cust::DeviceCopy)
+)]
 #[derive(PartialEq, Debug, Copy, Clone)]
+#[repr(C)]
 pub struct Cuboid {
     /// The half-extents of the cuboid.
     pub half_extents: Vector<Real>,
diff --git a/src/shape/cylinder.rs b/src/shape/cylinder.rs
index 0ad8a41f..28f43592 100644
--- a/src/shape/cylinder.rs
+++ b/src/shape/cylinder.rs
@@ -5,9 +5,17 @@ use crate::shape::SupportMap;
 use na;
 use num::Zero;
 
+#[cfg(not(feature = "std"))]
+use na::RealField; // for .copysign()
+
 /// Cylinder shape with its principal axis aligned with the `y` axis.
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
+#[cfg_attr(
+    all(not(target_os = "cuda"), feature = "cuda"),
+    derive(cust::DeviceCopy)
+)]
 #[derive(PartialEq, Debug, Copy, Clone)]
+#[repr(C)]
 pub struct Cylinder {
     /// The half-height of the cylinder.
     pub half_height: Real,
diff --git a/src/shape/half_space.rs b/src/shape/half_space.rs
index 29b85acf..40f3425b 100644
--- a/src/shape/half_space.rs
+++ b/src/shape/half_space.rs
@@ -3,8 +3,13 @@ use crate::math::{Real, Vector};
 use na::Unit;
 
 /// A half-space delimited by an infinite plane.
-#[derive(PartialEq, Debug, Clone)]
+#[derive(PartialEq, Debug, Clone, Copy)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
+#[cfg_attr(
+    all(not(target_os = "cuda"), feature = "cuda"),
+    derive(cust::DeviceCopy)
+)]
+#[repr(C)]
 pub struct HalfSpace {
     /// The halfspace planar boundary outward normal.
     pub normal: Unit<Vector<Real>>,
diff --git a/src/shape/heightfield2.rs b/src/shape/heightfield2.rs
index cfec4bdc..265bc277 100644
--- a/src/shape/heightfield2.rs
+++ b/src/shape/heightfield2.rs
@@ -26,7 +26,7 @@ impl HeightField {
 
         let max = heights.max();
         let min = heights.min();
-        let hscale = scale * na::convert::<_, Real>(0.5);
+        let hscale = scale * 0.5;
         let aabb = AABB::new(
             Point2::new(-hscale.x, min * scale.y),
             Point2::new(hscale.x, max * scale.y),
diff --git a/src/shape/mod.rs b/src/shape/mod.rs
index 7c57566c..69b4aebb 100644
--- a/src/shape/mod.rs
+++ b/src/shape/mod.rs
@@ -3,12 +3,15 @@
 pub use self::ball::Ball;
 pub use self::capsule::Capsule;
 #[doc(inline)]
+#[cfg(feature = "std")]
 pub use self::composite_shape::{SimdCompositeShape, TypedSimdCompositeShape};
+#[cfg(feature = "std")]
 pub use self::compound::Compound;
 pub use self::cuboid::Cuboid;
 pub use self::feature_id::FeatureId;
 pub use self::half_space::HalfSpace;
 pub use self::polygonal_feature_map::PolygonalFeatureMap;
+#[cfg(feature = "std")]
 pub use self::polyline::Polyline;
 pub use self::round_shape::RoundShape;
 pub use self::segment::{Segment, SegmentPointLocation};
@@ -16,14 +19,17 @@ pub use self::segment::{Segment, SegmentPointLocation};
 pub(crate) use self::shape::DeserializableTypedShape;
 #[doc(inline)]
 pub use self::shape::{Shape, ShapeType, TypedShape};
+#[cfg(feature = "std")]
 pub use self::shared_shape::SharedShape;
 #[doc(inline)]
 pub use self::support_map::SupportMap;
 pub use self::triangle::{Triangle, TrianglePointLocation};
 
 #[cfg(feature = "dim2")]
+#[cfg(feature = "std")]
 pub use self::convex_polygon::ConvexPolygon;
 #[cfg(feature = "dim2")]
+#[cfg(feature = "std")]
 pub use self::heightfield2::HeightField;
 #[cfg(feature = "dim2")]
 pub use self::polygonal_feature2d::PolygonalFeature;
@@ -31,15 +37,18 @@ pub use self::polygonal_feature2d::PolygonalFeature;
 #[cfg(feature = "dim3")]
 pub use self::cone::Cone;
 #[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
 pub use self::convex_polyhedron::ConvexPolyhedron;
 #[cfg(feature = "dim3")]
 pub use self::cylinder::Cylinder;
 #[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
 pub use self::heightfield3::{HeightField, HeightFieldCellStatus};
 #[cfg(feature = "dim3")]
 pub use self::polygonal_feature3d::PolygonalFeature;
 #[cfg(feature = "dim3")]
 pub use self::tetrahedron::{Tetrahedron, TetrahedronPointLocation};
+#[cfg(feature = "std")]
 pub use self::trimesh::TriMesh;
 
 /// A cylinder dilated by a sphere (so it has round corners).
@@ -54,18 +63,23 @@ pub type RoundCuboid = RoundShape<Cuboid>;
 pub type RoundTriangle = RoundShape<Triangle>;
 /// A convex polyhedron dilated by a sphere (so it has round corners).
 #[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
 pub type RoundConvexPolyhedron = RoundShape<ConvexPolyhedron>;
 /// A convex polygon dilated by a sphere (so it has round corners).
 #[cfg(feature = "dim2")]
+#[cfg(feature = "std")]
 pub type RoundConvexPolygon = RoundShape<ConvexPolygon>;
 
 mod ball;
 mod capsule;
 #[doc(hidden)]
+#[cfg(feature = "std")]
 pub mod composite_shape;
+#[cfg(feature = "std")]
 mod compound;
 mod cuboid;
 mod half_space;
+#[cfg(feature = "std")]
 mod polyline;
 mod round_shape;
 mod segment;
@@ -76,26 +90,32 @@ pub mod support_map;
 mod triangle;
 
 #[cfg(feature = "dim2")]
+#[cfg(feature = "std")]
 mod convex_polygon;
 #[cfg(feature = "dim2")]
+#[cfg(feature = "std")]
 mod heightfield2;
 
 #[cfg(feature = "dim3")]
 mod cone;
 #[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
 mod convex_polyhedron;
 #[cfg(feature = "dim3")]
 mod cylinder;
 #[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
 mod heightfield3;
 #[cfg(feature = "dim3")]
 mod polygonal_feature3d;
 mod polygonal_feature_map;
 #[cfg(feature = "dim3")]
 mod tetrahedron;
+#[cfg(feature = "std")]
 mod trimesh;
 // TODO: move this elsewhere?
 mod feature_id;
 #[cfg(feature = "dim2")]
 mod polygonal_feature2d;
+#[cfg(feature = "std")]
 mod shared_shape;
diff --git a/src/shape/polygonal_feature2d.rs b/src/shape/polygonal_feature2d.rs
index e0f04a75..bb83ad35 100644
--- a/src/shape/polygonal_feature2d.rs
+++ b/src/shape/polygonal_feature2d.rs
@@ -1,4 +1,5 @@
 use crate::math::{Isometry, Point, Real, Vector};
+#[cfg(feature = "std")]
 use crate::query::{self, ContactManifold, TrackedContact};
 use crate::shape::Segment;
 
@@ -46,6 +47,7 @@ impl PolygonalFeature {
     }
 
     /// Computes the contacts between two polygonal features.
+    #[cfg(feature = "std")]
     pub fn contacts<ManifoldData, ContactData: Default + Copy>(
         pos12: &Isometry<Real>,
         pos21: &Isometry<Real>,
@@ -74,6 +76,7 @@ impl PolygonalFeature {
     /// Compute contacts points between a face and a vertex.
     ///
     /// This method assume we already know that at least one contact exists.
+    #[cfg(feature = "std")]
     pub fn face_vertex_contacts<ManifoldData, ContactData: Default + Copy>(
         pos12: &Isometry<Real>,
         face1: &Self,
@@ -104,6 +107,7 @@ impl PolygonalFeature {
     }
 
     /// Computes the contacts between two polygonal faces.
+    #[cfg(feature = "std")]
     pub fn face_face_contacts<ManifoldData, ContactData: Default + Copy>(
         pos12: &Isometry<Real>,
         face1: &Self,
diff --git a/src/shape/polygonal_feature3d.rs b/src/shape/polygonal_feature3d.rs
index 1e6e6f9d..15c47314 100644
--- a/src/shape/polygonal_feature3d.rs
+++ b/src/shape/polygonal_feature3d.rs
@@ -1,5 +1,6 @@
 use crate::approx::AbsDiffEq;
 use crate::math::{Isometry, Point, Real, Vector};
+#[cfg(feature = "std")]
 use crate::query::{ContactManifold, TrackedContact};
 use crate::shape::{Segment, Triangle};
 use crate::utils::WBasis;
@@ -79,6 +80,7 @@ impl PolygonalFeature {
     }
 
     /// Computes all the contacts between two polygonal features.
+    #[cfg(feature = "std")]
     pub fn contacts<ManifoldData, ContactData: Default + Copy>(
         pos12: &Isometry<Real>,
         _pos21: &Isometry<Real>,
@@ -100,6 +102,7 @@ impl PolygonalFeature {
         }
     }
 
+    #[cfg(feature = "std")]
     fn contacts_edge_edge<ManifoldData, ContactData: Default + Copy>(
         pos12: &Isometry<Real>,
         face1: &PolygonalFeature,
@@ -208,6 +211,7 @@ impl PolygonalFeature {
         }
     }
 
+    #[cfg(feature = "std")]
     fn contacts_face_face<ManifoldData, ContactData: Default + Copy>(
         pos12: &Isometry<Real>,
         face1: &PolygonalFeature,
diff --git a/src/shape/polygonal_feature_map.rs b/src/shape/polygonal_feature_map.rs
index 80d18ece..a251823d 100644
--- a/src/shape/polygonal_feature_map.rs
+++ b/src/shape/polygonal_feature_map.rs
@@ -10,6 +10,9 @@ use {
     approx::AbsDiffEq,
 };
 
+#[cfg(not(feature = "std"))]
+use na::{ComplexField, RealField}; // for .abs() and .copysign()
+
 /// Trait implemented by convex shapes with features with polyhedral approximations.
 pub trait PolygonalFeatureMap: SupportMap {
     /// Compute the support polygonal face of `self` towards the `dir`.
diff --git a/src/shape/polyline.rs b/src/shape/polyline.rs
index 2b440b31..122cf59d 100644
--- a/src/shape/polyline.rs
+++ b/src/shape/polyline.rs
@@ -5,6 +5,9 @@ use crate::query::{PointProjection, PointQueryWithLocation};
 use crate::shape::composite_shape::SimdCompositeShape;
 use crate::shape::{FeatureId, Segment, SegmentPointLocation, Shape, TypedSimdCompositeShape};
 
+#[cfg(not(feature = "std"))]
+use na::ComplexField; // for .abs()
+
 #[derive(Clone)]
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 /// A polyline.
diff --git a/src/shape/round_shape.rs b/src/shape/round_shape.rs
index 3a18837a..8f49b8ae 100644
--- a/src/shape/round_shape.rs
+++ b/src/shape/round_shape.rs
@@ -3,7 +3,12 @@ use crate::shape::SupportMap;
 use na::Unit;
 
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
+#[cfg_attr(
+    all(not(target_os = "cuda"), feature = "cuda"),
+    derive(cust::DeviceCopy)
+)]
 #[derive(Copy, Clone, Debug)]
+#[repr(C)]
 /// A shape with rounded borders.
 pub struct RoundShape<S> {
     /// The shape being rounded.
diff --git a/src/shape/segment.rs b/src/shape/segment.rs
index ca50c4ae..37f2fff6 100644
--- a/src/shape/segment.rs
+++ b/src/shape/segment.rs
@@ -8,8 +8,12 @@ use std::mem;
 
 /// A segment shape.
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
-#[repr(C)]
+#[cfg_attr(
+    all(not(target_os = "cuda"), feature = "cuda"),
+    derive(cust::DeviceCopy)
+)]
 #[derive(PartialEq, Debug, Copy, Clone)]
+#[repr(C)]
 pub struct Segment {
     /// The segment first point.
     pub a: Point<Real>,
diff --git a/src/shape/shape.rs b/src/shape/shape.rs
index 6467778c..75821e08 100644
--- a/src/shape/shape.rs
+++ b/src/shape/shape.rs
@@ -2,18 +2,23 @@ use crate::bounding_volume::{BoundingSphere, BoundingVolume, AABB};
 use crate::mass_properties::MassProperties;
 use crate::math::{Isometry, Point, Real, Vector};
 use crate::query::{PointQuery, RayCast};
-use crate::shape::composite_shape::SimdCompositeShape;
 #[cfg(feature = "serde-serialize")]
 use crate::shape::SharedShape;
+#[cfg(feature = "std")]
+use crate::shape::{composite_shape::SimdCompositeShape, Compound, HeightField, Polyline, TriMesh};
 use crate::shape::{
-    Ball, Capsule, Compound, Cuboid, FeatureId, HalfSpace, HeightField, PolygonalFeatureMap,
-    Polyline, RoundCuboid, RoundShape, RoundTriangle, Segment, SupportMap, TriMesh, Triangle,
+    Ball, Capsule, Cuboid, FeatureId, HalfSpace, PolygonalFeatureMap, RoundCuboid, RoundShape,
+    RoundTriangle, Segment, SupportMap, Triangle,
 };
 #[cfg(feature = "dim3")]
-use crate::shape::{
-    Cone, ConvexPolyhedron, Cylinder, RoundCone, RoundConvexPolyhedron, RoundCylinder,
-};
+use crate::shape::{Cone, Cylinder, RoundCone, RoundCylinder};
+
+#[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
+use crate::shape::{ConvexPolyhedron, RoundConvexPolyhedron};
+
 #[cfg(feature = "dim2")]
+#[cfg(feature = "std")]
 use crate::shape::{ConvexPolygon, RoundConvexPolygon};
 use downcast_rs::{impl_downcast, DowncastSync};
 use na::{RealField, Unit};
@@ -95,18 +100,24 @@ pub enum TypedShape<'a> {
     /// A triangle shape.
     Triangle(&'a Triangle),
     /// A triangle mesh shape.
+    #[cfg(feature = "std")]
     TriMesh(&'a TriMesh),
     /// A set of segments.
+    #[cfg(feature = "std")]
     Polyline(&'a Polyline),
     /// A shape representing a full half-space.
     HalfSpace(&'a HalfSpace),
     /// A heightfield shape.
+    #[cfg(feature = "std")]
     HeightField(&'a HeightField),
     /// A Compound shape.
+    #[cfg(feature = "std")]
     Compound(&'a Compound),
     #[cfg(feature = "dim2")]
+    #[cfg(feature = "std")]
     ConvexPolygon(&'a ConvexPolygon),
     #[cfg(feature = "dim3")]
+    #[cfg(feature = "std")]
     /// A convex polyhedron.
     ConvexPolyhedron(&'a ConvexPolyhedron),
     #[cfg(feature = "dim3")]
@@ -133,9 +144,11 @@ pub enum TypedShape<'a> {
     RoundCone(&'a RoundCone),
     /// A convex polyhedron with rounded corners.
     #[cfg(feature = "dim3")]
+    #[cfg(feature = "std")]
     RoundConvexPolyhedron(&'a RoundConvexPolyhedron),
     /// A convex polygon with rounded corners.
     #[cfg(feature = "dim2")]
+    #[cfg(feature = "std")]
     RoundConvexPolygon(&'a RoundConvexPolygon),
     /// A custom user-defined shape with a type identified by a number.
     Custom(u32),
@@ -157,18 +170,24 @@ pub(crate) enum DeserializableTypedShape {
     /// A triangle shape.
     Triangle(Triangle),
     /// A triangle mesh shape.
+    #[cfg(feature = "std")]
     TriMesh(TriMesh),
     /// A set of segments.
+    #[cfg(feature = "std")]
     Polyline(Polyline),
     /// A shape representing a full half-space.
     HalfSpace(HalfSpace),
     /// A heightfield shape.
+    #[cfg(feature = "std")]
     HeightField(HeightField),
     /// A Compound shape.
+    #[cfg(feature = "std")]
     Compound(Compound),
     #[cfg(feature = "dim2")]
+    #[cfg(feature = "std")]
     ConvexPolygon(ConvexPolygon),
     #[cfg(feature = "dim3")]
+    #[cfg(feature = "std")]
     /// A convex polyhedron.
     ConvexPolyhedron(ConvexPolyhedron),
     #[cfg(feature = "dim3")]
@@ -195,9 +214,11 @@ pub(crate) enum DeserializableTypedShape {
     RoundCone(RoundCone),
     /// A convex polyhedron with rounded corners.
     #[cfg(feature = "dim3")]
+    #[cfg(feature = "std")]
     RoundConvexPolyhedron(RoundConvexPolyhedron),
     /// A convex polygon with rounded corners.
     #[cfg(feature = "dim2")]
+    #[cfg(feature = "std")]
     RoundConvexPolygon(RoundConvexPolygon),
     /// A custom user-defined shape identified by a number.
     Custom(u32),
@@ -213,14 +234,20 @@ impl DeserializableTypedShape {
             DeserializableTypedShape::Capsule(s) => Some(SharedShape::new(s)),
             DeserializableTypedShape::Segment(s) => Some(SharedShape::new(s)),
             DeserializableTypedShape::Triangle(s) => Some(SharedShape::new(s)),
+            #[cfg(feature = "std")]
             DeserializableTypedShape::TriMesh(s) => Some(SharedShape::new(s)),
+            #[cfg(feature = "std")]
             DeserializableTypedShape::Polyline(s) => Some(SharedShape::new(s)),
             DeserializableTypedShape::HalfSpace(s) => Some(SharedShape::new(s)),
+            #[cfg(feature = "std")]
             DeserializableTypedShape::HeightField(s) => Some(SharedShape::new(s)),
+            #[cfg(feature = "std")]
             DeserializableTypedShape::Compound(s) => Some(SharedShape::new(s)),
             #[cfg(feature = "dim2")]
+            #[cfg(feature = "std")]
             DeserializableTypedShape::ConvexPolygon(s) => Some(SharedShape::new(s)),
             #[cfg(feature = "dim3")]
+            #[cfg(feature = "std")]
             DeserializableTypedShape::ConvexPolyhedron(s) => Some(SharedShape::new(s)),
             #[cfg(feature = "dim3")]
             DeserializableTypedShape::Cylinder(s) => Some(SharedShape::new(s)),
@@ -233,8 +260,10 @@ impl DeserializableTypedShape {
             #[cfg(feature = "dim3")]
             DeserializableTypedShape::RoundCone(s) => Some(SharedShape::new(s)),
             #[cfg(feature = "dim3")]
+            #[cfg(feature = "std")]
             DeserializableTypedShape::RoundConvexPolyhedron(s) => Some(SharedShape::new(s)),
             #[cfg(feature = "dim2")]
+            #[cfg(feature = "std")]
             DeserializableTypedShape::RoundConvexPolygon(s) => Some(SharedShape::new(s)),
             DeserializableTypedShape::Custom(_) => None,
         }
@@ -249,6 +278,7 @@ pub trait Shape: RayCast + PointQuery + DowncastSync {
     fn compute_local_bounding_sphere(&self) -> BoundingSphere;
 
     /// Clones this shape into a boxed trait-object.
+    #[cfg(feature = "std")]
     fn clone_box(&self) -> Box<dyn Shape>;
 
     /// Computes the AABB of this shape with the given position.
@@ -293,6 +323,7 @@ pub trait Shape: RayCast + PointQuery + DowncastSync {
         None
     }
 
+    #[cfg(feature = "std")]
     fn as_composite_shape(&self) -> Option<&dyn SimdCompositeShape> {
         None
     }
@@ -391,37 +422,45 @@ impl dyn Shape {
     }
 
     /// Converts this abstract shape to a compound shape, if it is one.
+    #[cfg(feature = "std")]
     pub fn as_compound(&self) -> Option<&Compound> {
         self.downcast_ref()
     }
     /// Converts this abstract shape to a mutable compound shape, if it is one.
+    #[cfg(feature = "std")]
     pub fn as_compound_mut(&mut self) -> Option<&mut Compound> {
         self.downcast_mut()
     }
 
     /// Converts this abstract shape to a triangle mesh, if it is one.
+    #[cfg(feature = "std")]
     pub fn as_trimesh(&self) -> Option<&TriMesh> {
         self.downcast_ref()
     }
     /// Converts this abstract shape to a mutable triangle mesh, if it is one.
+    #[cfg(feature = "std")]
     pub fn as_trimesh_mut(&mut self) -> Option<&mut TriMesh> {
         self.downcast_mut()
     }
 
     /// Converts this abstract shape to a polyline, if it is one.
+    #[cfg(feature = "std")]
     pub fn as_polyline(&self) -> Option<&Polyline> {
         self.downcast_ref()
     }
     /// Converts this abstract shape to a mutable polyline, if it is one.
+    #[cfg(feature = "std")]
     pub fn as_polyline_mut(&mut self) -> Option<&mut Polyline> {
         self.downcast_mut()
     }
 
     /// Converts this abstract shape to a heightfield, if it is one.
+    #[cfg(feature = "std")]
     pub fn as_heightfield(&self) -> Option<&HeightField> {
         self.downcast_ref()
     }
     /// Converts this abstract shape to a mutable heightfield, if it is one.
+    #[cfg(feature = "std")]
     pub fn as_heightfield_mut(&mut self) -> Option<&mut HeightField> {
         self.downcast_mut()
     }
@@ -446,31 +485,37 @@ impl dyn Shape {
 
     /// Converts this abstract shape to a convex polygon, if it is one.
     #[cfg(feature = "dim2")]
+    #[cfg(feature = "std")]
     pub fn as_convex_polygon(&self) -> Option<&ConvexPolygon> {
         self.downcast_ref()
     }
     /// Converts this abstract shape to a mutable convex polygon, if it is one.
     #[cfg(feature = "dim2")]
+    #[cfg(feature = "std")]
     pub fn as_convex_polygon_mut(&mut self) -> Option<&mut ConvexPolygon> {
         self.downcast_mut()
     }
 
     /// Converts this abstract shape to a round convex polygon, if it is one.
     #[cfg(feature = "dim2")]
+    #[cfg(feature = "std")]
     pub fn as_round_convex_polygon(&self) -> Option<&RoundConvexPolygon> {
         self.downcast_ref()
     }
     /// Converts this abstract shape to a mutable round convex polygon, if it is one.
     #[cfg(feature = "dim2")]
+    #[cfg(feature = "std")]
     pub fn as_round_convex_polygon_mut(&mut self) -> Option<&mut RoundConvexPolygon> {
         self.downcast_mut()
     }
 
     #[cfg(feature = "dim3")]
+    #[cfg(feature = "std")]
     pub fn as_convex_polyhedron(&self) -> Option<&ConvexPolyhedron> {
         self.downcast_ref()
     }
     #[cfg(feature = "dim3")]
+    #[cfg(feature = "std")]
     pub fn as_convex_polyhedron_mut(&mut self) -> Option<&mut ConvexPolyhedron> {
         self.downcast_mut()
     }
@@ -521,17 +566,20 @@ impl dyn Shape {
 
     /// Converts this abstract shape to a round convex polyhedron, if it is one.
     #[cfg(feature = "dim3")]
+    #[cfg(feature = "std")]
     pub fn as_round_convex_polyhedron(&self) -> Option<&RoundConvexPolyhedron> {
         self.downcast_ref()
     }
     /// Converts this abstract shape to a mutable round convex polyhedron, if it is one.
     #[cfg(feature = "dim3")]
+    #[cfg(feature = "std")]
     pub fn as_round_convex_polyhedron_mut(&mut self) -> Option<&mut RoundConvexPolyhedron> {
         self.downcast_mut()
     }
 }
 
 impl Shape for Ball {
+    #[cfg(feature = "std")]
     fn clone_box(&self) -> Box<dyn Shape> {
         Box::new(self.clone())
     }
@@ -588,6 +636,7 @@ impl Shape for Ball {
 }
 
 impl Shape for Cuboid {
+    #[cfg(feature = "std")]
     fn clone_box(&self) -> Box<dyn Shape> {
         Box::new(self.clone())
     }
@@ -646,6 +695,7 @@ impl Shape for Cuboid {
 }
 
 impl Shape for Capsule {
+    #[cfg(feature = "std")]
     fn clone_box(&self) -> Box<dyn Shape> {
         Box::new(self.clone())
     }
@@ -696,6 +746,7 @@ impl Shape for Capsule {
 }
 
 impl Shape for Triangle {
+    #[cfg(feature = "std")]
     fn clone_box(&self) -> Box<dyn Shape> {
         Box::new(self.clone())
     }
@@ -758,6 +809,7 @@ impl Shape for Triangle {
 }
 
 impl Shape for Segment {
+    #[cfg(feature = "std")]
     fn clone_box(&self) -> Box<dyn Shape> {
         Box::new(self.clone())
     }
@@ -815,6 +867,7 @@ impl Shape for Segment {
     }
 }
 
+#[cfg(feature = "std")]
 impl Shape for Compound {
     fn clone_box(&self) -> Box<dyn Shape> {
         Box::new(self.clone())
@@ -856,11 +909,13 @@ impl Shape for Compound {
         })
     }
 
+    #[cfg(feature = "std")]
     fn as_composite_shape(&self) -> Option<&dyn SimdCompositeShape> {
         Some(self as &dyn SimdCompositeShape)
     }
 }
 
+#[cfg(feature = "std")]
 impl Shape for Polyline {
     fn clone_box(&self) -> Box<dyn Shape> {
         Box::new(self.clone())
@@ -900,11 +955,13 @@ impl Shape for Polyline {
         Real::frac_pi_4()
     }
 
+    #[cfg(feature = "std")]
     fn as_composite_shape(&self) -> Option<&dyn SimdCompositeShape> {
         Some(self as &dyn SimdCompositeShape)
     }
 }
 
+#[cfg(feature = "std")]
 impl Shape for TriMesh {
     fn clone_box(&self) -> Box<dyn Shape> {
         Box::new(self.clone())
@@ -948,11 +1005,13 @@ impl Shape for TriMesh {
         Real::frac_pi_4()
     }
 
+    #[cfg(feature = "std")]
     fn as_composite_shape(&self) -> Option<&dyn SimdCompositeShape> {
         Some(self as &dyn SimdCompositeShape)
     }
 }
 
+#[cfg(feature = "std")]
 impl Shape for HeightField {
     fn clone_box(&self) -> Box<dyn Shape> {
         Box::new(self.clone())
@@ -994,6 +1053,7 @@ impl Shape for HeightField {
 }
 
 #[cfg(feature = "dim2")]
+#[cfg(feature = "std")]
 impl Shape for ConvexPolygon {
     fn clone_box(&self) -> Box<dyn Shape> {
         Box::new(self.clone())
@@ -1056,6 +1116,7 @@ impl Shape for ConvexPolygon {
 }
 
 #[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
 impl Shape for ConvexPolyhedron {
     fn clone_box(&self) -> Box<dyn Shape> {
         Box::new(self.clone())
@@ -1120,6 +1181,7 @@ impl Shape for ConvexPolyhedron {
 
 #[cfg(feature = "dim3")]
 impl Shape for Cylinder {
+    #[cfg(feature = "std")]
     fn clone_box(&self) -> Box<dyn Shape> {
         Box::new(self.clone())
     }
@@ -1171,6 +1233,7 @@ impl Shape for Cylinder {
 
 #[cfg(feature = "dim3")]
 impl Shape for Cone {
+    #[cfg(feature = "std")]
     fn clone_box(&self) -> Box<dyn Shape> {
         Box::new(self.clone())
     }
@@ -1224,6 +1287,7 @@ impl Shape for Cone {
 }
 
 impl Shape for HalfSpace {
+    #[cfg(feature = "std")]
     fn clone_box(&self) -> Box<dyn Shape> {
         Box::new(self.clone())
     }
@@ -1268,6 +1332,7 @@ impl Shape for HalfSpace {
 macro_rules! impl_shape_for_round_shape(
     ($($S: ty, $Tag: ident);*) => {$(
         impl Shape for RoundShape<$S> {
+            #[cfg(feature = "std")]
             fn clone_box(&self) -> Box<dyn Shape> {
                 Box::new(self.clone())
             }
@@ -1326,10 +1391,14 @@ impl_shape_for_round_shape!(
     Triangle, RoundTriangle
 );
 #[cfg(feature = "dim2")]
+#[cfg(feature = "std")]
 impl_shape_for_round_shape!(ConvexPolygon, RoundConvexPolygon);
 #[cfg(feature = "dim3")]
 impl_shape_for_round_shape!(
     Cylinder, RoundCylinder;
-    Cone, RoundCone;
-    ConvexPolyhedron, RoundConvexPolyhedron
+    Cone, RoundCone
 );
+
+#[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
+impl_shape_for_round_shape!(ConvexPolyhedron, RoundConvexPolyhedron);
diff --git a/src/shape/tetrahedron.rs b/src/shape/tetrahedron.rs
index ce937ad5..5b74efea 100644
--- a/src/shape/tetrahedron.rs
+++ b/src/shape/tetrahedron.rs
@@ -6,10 +6,17 @@ use crate::utils;
 use na::Matrix3;
 use std::mem;
 
+#[cfg(not(feature = "std"))]
+use na::ComplexField; // for .abs()
+
 /// A tetrahedron with 4 vertices.
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
-#[repr(C)]
+#[cfg_attr(
+    all(not(target_os = "cuda"), feature = "cuda"),
+    derive(cust::DeviceCopy)
+)]
 #[derive(Copy, Clone, Debug)]
+#[repr(C)]
 pub struct Tetrahedron {
     /// The tetrahedron first point.
     pub a: Point<Real>,
diff --git a/src/shape/triangle.rs b/src/shape/triangle.rs
index 4d3d63e1..d1d96099 100644
--- a/src/shape/triangle.rs
+++ b/src/shape/triangle.rs
@@ -13,8 +13,12 @@ use std::mem;
 
 /// A triangle shape.
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
-#[repr(C)]
+#[cfg_attr(
+    all(not(target_os = "cuda"), feature = "cuda"),
+    derive(cust::DeviceCopy)
+)]
 #[derive(PartialEq, Debug, Copy, Clone)]
+#[repr(C)]
 pub struct Triangle {
     /// The triangle first point.
     pub a: Point<Real>,
diff --git a/src/utils/isometry_ops.rs b/src/utils/isometry_ops.rs
index 63ad73dc..3c6d11b2 100644
--- a/src/utils/isometry_ops.rs
+++ b/src/utils/isometry_ops.rs
@@ -1,4 +1,6 @@
 use crate::math::{Isometry, Point, Real, Vector};
+#[cfg(not(feature = "std"))]
+use na::ComplexField; // for .abs()
 use na::Unit;
 
 /// Extra operations with isometries.
diff --git a/src/utils/mod.rs b/src/utils/mod.rs
index 46039aba..15732cf2 100644
--- a/src/utils/mod.rs
+++ b/src/utils/mod.rs
@@ -2,9 +2,11 @@
 
 pub use self::ccw_face_normal::ccw_face_normal;
 pub use self::center::center;
+#[cfg(feature = "std")]
 pub use self::deterministic_state::DeterministicState;
 
 #[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
 pub use self::cleanup::remove_unused_points;
 pub(crate) use self::inv::inv;
 pub use self::isometry_ops::{IsometryOps, IsometryOpt};
@@ -19,6 +21,7 @@ pub use self::as_bytes::AsBytes;
 pub(crate) use self::consts::*;
 pub use self::cov::{center_cov, cov};
 pub use self::hashable_partial_eq::HashablePartialEq;
+#[cfg(feature = "std")]
 pub use self::interval::{find_root_intervals, find_root_intervals_to, Interval, IntervalFunction};
 pub use self::obb::obb;
 #[cfg(feature = "dim3")]
@@ -32,12 +35,16 @@ mod as_bytes;
 mod ccw_face_normal;
 mod center;
 #[cfg(feature = "dim3")]
+#[cfg(feature = "std")]
 mod cleanup;
 mod consts;
 mod cov;
+#[cfg(feature = "std")]
 mod deterministic_state;
 mod hashable_partial_eq;
+#[cfg(feature = "std")]
 pub mod hashmap;
+#[cfg(feature = "std")]
 mod interval;
 mod inv;
 mod isometry_ops;