diff --git a/webxr-api/Cargo.toml b/webxr-api/Cargo.toml
index 4e7388c..d1e3b67 100644
--- a/webxr-api/Cargo.toml
+++ b/webxr-api/Cargo.toml
@@ -22,7 +22,7 @@ path = "lib.rs"
 ipc = ["serde", "typetag", "ipc-channel", "euclid/serde"]
 
 [dependencies]
-euclid = "0.19"
+euclid = "0.20"
 gleam = "0.6"
 ipc-channel = { version = "0.11", optional = true }
 serde = { version = "1.0", optional = true }
diff --git a/webxr-api/device.rs b/webxr-api/device.rs
index a2c947a..a4829b0 100644
--- a/webxr-api/device.rs
+++ b/webxr-api/device.rs
@@ -15,9 +15,9 @@ use crate::SessionMode;
 use crate::Viewport;
 use crate::Views;
 
+use euclid::default::Size2D as UntypedSize2D;
+use euclid::RigidTransform3D;
 use euclid::Size2D;
-use euclid::TypedRigidTransform3D;
-use euclid::TypedSize2D;
 
 use gleam::gl::GLsync;
 
@@ -30,19 +30,19 @@ pub trait Discovery: 'static {
 /// A trait for using an XR device
 pub trait Device: 'static {
     /// The transform from native coordinates to the floor.
-    fn floor_transform(&self) -> TypedRigidTransform3D<f32, Native, Floor>;
+    fn floor_transform(&self) -> RigidTransform3D<f32, Native, Floor>;
 
     /// The transforms from viewer coordinates to the eyes, and their associated viewports.
     fn views(&self) -> Views;
 
     /// A resolution large enough to contain all the viewports.
     /// https://immersive-web.github.io/webxr/#native-webgl-framebuffer-resolution
-    fn recommended_framebuffer_resolution(&self) -> TypedSize2D<i32, Viewport> {
+    fn recommended_framebuffer_resolution(&self) -> Size2D<i32, Viewport> {
         let viewport = match self.views() {
             Views::Mono(view) => view.viewport,
             Views::Stereo(left, right) => left.viewport.union(&right.viewport),
         };
-        TypedSize2D::new(viewport.max_x(), viewport.max_y())
+        Size2D::new(viewport.max_x(), viewport.max_y())
     }
 
     /// This method should block waiting for the next frame,
@@ -52,7 +52,7 @@ pub trait Device: 'static {
     /// This method should render a GL texture to the device.
     /// While this method is being called, the device has unique access
     /// to the texture. The texture should be sync'd using glWaitSync before being used.
-    fn render_animation_frame(&mut self, texture_id: u32, size: Size2D<i32>, sync: GLsync);
+    fn render_animation_frame(&mut self, texture_id: u32, size: UntypedSize2D<i32>, sync: GLsync);
 
     /// Inputs registered with the device on initialization. More may be added, which
     /// should be communicated through a yet-undecided event mechanism
diff --git a/webxr-api/frame.rs b/webxr-api/frame.rs
index f96d1ef..e05f3a5 100644
--- a/webxr-api/frame.rs
+++ b/webxr-api/frame.rs
@@ -6,7 +6,7 @@ use crate::InputFrame;
 use crate::Native;
 use crate::Viewer;
 
-use euclid::TypedRigidTransform3D;
+use euclid::RigidTransform3D;
 
 /// The per-frame data that is provided by the device.
 /// https://www.w3.org/TR/webxr/#xrframe
@@ -18,7 +18,7 @@ pub struct Frame {
     ///
     /// This is equivalent to the pose of the viewer in native coordinates.
     /// This is the inverse of the view matrix.
-    pub transform: TypedRigidTransform3D<f32, Viewer, Native>,
+    pub transform: RigidTransform3D<f32, Viewer, Native>,
 
     /// Frame information for each connected input source
     pub inputs: Vec<InputFrame>,
diff --git a/webxr-api/input.rs b/webxr-api/input.rs
index 00d0da7..50f6e03 100644
--- a/webxr-api/input.rs
+++ b/webxr-api/input.rs
@@ -5,7 +5,7 @@
 use crate::Input;
 use crate::Native;
 
-use euclid::TypedRigidTransform3D;
+use euclid::RigidTransform3D;
 
 #[derive(Copy, Clone, Debug, PartialEq, Eq, Hash)]
 #[cfg_attr(feature = "ipc", derive(serde::Serialize, serde::Deserialize))]
@@ -39,5 +39,5 @@ pub struct InputSource {
 #[cfg_attr(feature = "ipc", derive(serde::Serialize, serde::Deserialize))]
 pub struct InputFrame {
     pub id: InputId,
-    pub target_ray_origin: TypedRigidTransform3D<f32, Input, Native>,
+    pub target_ray_origin: RigidTransform3D<f32, Input, Native>,
 }
diff --git a/webxr-api/mock.rs b/webxr-api/mock.rs
index 63f2bc2..af72078 100644
--- a/webxr-api/mock.rs
+++ b/webxr-api/mock.rs
@@ -10,7 +10,7 @@ use crate::Receiver;
 use crate::Viewer;
 use crate::Views;
 
-use euclid::TypedRigidTransform3D;
+use euclid::RigidTransform3D;
 
 #[cfg(feature = "ipc")]
 use serde::{Deserialize, Serialize};
@@ -27,17 +27,17 @@ pub trait MockDiscovery: 'static {
 #[derive(Clone, Debug)]
 #[cfg_attr(feature = "ipc", derive(Serialize, Deserialize))]
 pub struct MockDeviceInit {
-    pub floor_origin: TypedRigidTransform3D<f32, Floor, Native>,
+    pub floor_origin: RigidTransform3D<f32, Floor, Native>,
     pub supports_immersive: bool,
     pub supports_unbounded: bool,
-    pub viewer_origin: TypedRigidTransform3D<f32, Viewer, Native>,
+    pub viewer_origin: RigidTransform3D<f32, Viewer, Native>,
     pub views: Views,
 }
 
 #[derive(Debug)]
 #[cfg_attr(feature = "ipc", derive(Serialize, Deserialize))]
 pub enum MockDeviceMsg {
-    SetViewerOrigin(TypedRigidTransform3D<f32, Viewer, Native>),
+    SetViewerOrigin(RigidTransform3D<f32, Viewer, Native>),
     SetViews(Views),
     Focus,
     Blur,
diff --git a/webxr-api/session.rs b/webxr-api/session.rs
index 455b782..e720976 100644
--- a/webxr-api/session.rs
+++ b/webxr-api/session.rs
@@ -14,8 +14,8 @@ use crate::Viewport;
 use crate::Views;
 use crate::WebGLExternalImageApi;
 
-use euclid::TypedRigidTransform3D;
-use euclid::TypedSize2D;
+use euclid::RigidTransform3D;
+use euclid::Size2D;
 
 use std::thread;
 use std::time::Duration;
@@ -58,15 +58,15 @@ enum SessionMsg {
 /// https://www.w3.org/TR/webxr/#xrsession-interface
 #[cfg_attr(feature = "ipc", derive(Serialize, Deserialize))]
 pub struct Session {
-    floor_transform: TypedRigidTransform3D<f32, Native, Floor>,
+    floor_transform: RigidTransform3D<f32, Native, Floor>,
     views: Views,
-    resolution: TypedSize2D<i32, Viewport>,
+    resolution: Size2D<i32, Viewport>,
     sender: Sender<SessionMsg>,
     initial_inputs: Vec<InputSource>,
 }
 
 impl Session {
-    pub fn floor_transform(&self) -> TypedRigidTransform3D<f32, Native, Floor> {
+    pub fn floor_transform(&self) -> RigidTransform3D<f32, Native, Floor> {
         self.floor_transform.clone()
     }
 
@@ -78,7 +78,7 @@ impl Session {
         self.views.clone()
     }
 
-    pub fn recommended_framebuffer_resolution(&self) -> TypedSize2D<i32, Viewport> {
+    pub fn recommended_framebuffer_resolution(&self) -> Size2D<i32, Viewport> {
         self.resolution
     }
 
diff --git a/webxr-api/view.rs b/webxr-api/view.rs
index b93a64f..c5f8b2e 100644
--- a/webxr-api/view.rs
+++ b/webxr-api/view.rs
@@ -4,9 +4,9 @@
 
 //! This crate uses `euclid`'s typed units, and exposes different coordinate spaces.
 
-use euclid::TypedRect;
-use euclid::TypedRigidTransform3D;
-use euclid::TypedTransform3D;
+use euclid::Rect;
+use euclid::RigidTransform3D;
+use euclid::Transform3D;
 
 #[cfg(feature = "ipc")]
 use serde::{Deserialize, Serialize};
@@ -68,9 +68,9 @@ pub enum Input {}
 #[derive(Clone, Debug)]
 #[cfg_attr(feature = "ipc", derive(Serialize, Deserialize))]
 pub struct View<Eye> {
-    pub transform: TypedRigidTransform3D<f32, Viewer, Eye>,
-    pub projection: TypedTransform3D<f32, Eye, Display>,
-    pub viewport: TypedRect<i32, Viewport>,
+    pub transform: RigidTransform3D<f32, Viewer, Eye>,
+    pub projection: Transform3D<f32, Eye, Display>,
+    pub viewport: Rect<i32, Viewport>,
 }
 
 /// Whether a device is mono or stereo, and the views it supports.
diff --git a/webxr-api/webgl.rs b/webxr-api/webgl.rs
index 235fb58..843a519 100644
--- a/webxr-api/webgl.rs
+++ b/webxr-api/webgl.rs
@@ -5,7 +5,7 @@
 //! The WebGL functionality needed by WebXR.
 
 use crate::Error;
-use euclid::Size2D;
+use euclid::default::Size2D;
 use gleam::gl::GLsync;
 use gleam::gl::GLuint;
 
diff --git a/webxr/Cargo.toml b/webxr/Cargo.toml
index cfd4165..23c320b 100644
--- a/webxr/Cargo.toml
+++ b/webxr/Cargo.toml
@@ -25,7 +25,7 @@ ipc = ["webxr-api/ipc"]
 
 [dependencies]
 webxr-api = { path = "../webxr-api" }
-euclid = "0.19"
+euclid = "0.20"
 gleam = "0.6"
 glutin = { version = "0.21", optional = true }
 log = "0.4"
diff --git a/webxr/glwindow/mod.rs b/webxr/glwindow/mod.rs
index e7ba47a..d7e18bb 100644
--- a/webxr/glwindow/mod.rs
+++ b/webxr/glwindow/mod.rs
@@ -2,15 +2,15 @@
  * License, v. 2.0. If a copy of the MPL was not distributed with this
  * file, You can obtain one at https://mozilla.org/MPL/2.0/. */
 
+use euclid::default::Size2D as UntypedSize2D;
 use euclid::Angle;
+use euclid::Point2D;
+use euclid::Rect;
+use euclid::RigidTransform3D;
 use euclid::Size2D;
+use euclid::Transform3D;
 use euclid::Trig;
-use euclid::TypedPoint2D;
-use euclid::TypedRect;
-use euclid::TypedRigidTransform3D;
-use euclid::TypedSize2D;
-use euclid::TypedTransform3D;
-use euclid::TypedVector3D;
+use euclid::Vector3D;
 
 use gleam::gl;
 use gleam::gl::GLsizei;
@@ -45,7 +45,7 @@ const FAR: f32 = 100.0;
 pub trait GlWindow {
     fn make_current(&mut self);
     fn swap_buffers(&mut self);
-    fn size(&self) -> Size2D<GLsizei>;
+    fn size(&self) -> UntypedSize2D<GLsizei>;
     fn new_window(&self) -> Result<Box<dyn GlWindow>, ()>;
 }
 
@@ -86,9 +86,9 @@ pub struct GlWindowDevice {
 }
 
 impl Device for GlWindowDevice {
-    fn floor_transform(&self) -> TypedRigidTransform3D<f32, Native, Floor> {
-        let translation = TypedVector3D::new(-HEIGHT, 0.0, 0.0);
-        TypedRigidTransform3D::from_translation(translation)
+    fn floor_transform(&self) -> RigidTransform3D<f32, Native, Floor> {
+        let translation = Vector3D::new(-HEIGHT, 0.0, 0.0);
+        RigidTransform3D::from_translation(translation)
     }
 
     fn views(&self) -> Views {
@@ -99,15 +99,15 @@ impl Device for GlWindowDevice {
 
     fn wait_for_animation_frame(&mut self) -> Frame {
         self.window.swap_buffers();
-        let translation = TypedVector3D::new(0.0, 0.0, -5.0);
-        let transform = TypedRigidTransform3D::from_translation(translation);
+        let translation = Vector3D::new(0.0, 0.0, -5.0);
+        let transform = RigidTransform3D::from_translation(translation);
         Frame {
             transform,
             inputs: vec![],
         }
     }
 
-    fn render_animation_frame(&mut self, texture_id: u32, size: Size2D<i32>, sync: GLsync) {
+    fn render_animation_frame(&mut self, texture_id: u32, size: UntypedSize2D<i32>, sync: GLsync) {
         self.window.make_current();
 
         let width = size.width as GLsizei;
@@ -168,18 +168,18 @@ impl GlWindowDevice {
 
     fn view<Eye>(&self, is_right: bool) -> View<Eye> {
         let window_size = self.window.size();
-        let viewport_size = TypedSize2D::new(window_size.width / 2, window_size.height);
+        let viewport_size = Size2D::new(window_size.width / 2, window_size.height);
         let viewport_x_origin = if is_right { viewport_size.width } else { 0 };
-        let viewport_origin = TypedPoint2D::new(viewport_x_origin, 0);
-        let viewport = TypedRect::new(viewport_origin, viewport_size);
+        let viewport_origin = Point2D::new(viewport_x_origin, 0);
+        let viewport = Rect::new(viewport_origin, viewport_size);
         let projection = self.perspective(NEAR, FAR);
         let eye_distance = if is_right {
             EYE_DISTANCE
         } else {
             -EYE_DISTANCE
         };
-        let translation = TypedVector3D::new(eye_distance, 0.0, 0.0);
-        let transform = TypedRigidTransform3D::from_translation(translation);
+        let translation = Vector3D::new(eye_distance, 0.0, 0.0);
+        let transform = RigidTransform3D::from_translation(translation);
         View {
             transform,
             projection,
@@ -187,7 +187,7 @@ impl GlWindowDevice {
         }
     }
 
-    fn perspective<Eye>(&self, near: f32, far: f32) -> TypedTransform3D<f32, Eye, Display> {
+    fn perspective<Eye>(&self, near: f32, far: f32) -> Transform3D<f32, Eye, Display> {
         // https://github.com/toji/gl-matrix/blob/bd3307196563fbb331b40fc6ebecbbfcc2a4722c/src/mat4.js#L1271
         let size = self.window.size();
         let width = size.width as f32;
@@ -201,7 +201,7 @@ impl GlWindowDevice {
         {
             #[rustfmt::skip]
             // Sigh, row-major vs column-major
-            return TypedTransform3D::row_major(
+            return Transform3D::row_major(
                 f / aspect, 0.0, 0.0,                   0.0,
                 0.0,        f,   0.0,                   0.0,
                 0.0,        0.0, (far + near) * nf,     -1.0,
diff --git a/webxr/headless/mod.rs b/webxr/headless/mod.rs
index f408c20..f9692ee 100644
--- a/webxr/headless/mod.rs
+++ b/webxr/headless/mod.rs
@@ -19,8 +19,8 @@ use webxr_api::SessionMode;
 use webxr_api::Viewer;
 use webxr_api::Views;
 
-use euclid::Size2D;
-use euclid::TypedRigidTransform3D;
+use euclid::default::Size2D;
+use euclid::RigidTransform3D;
 
 use gleam::gl;
 use gleam::gl::GLsync;
@@ -41,8 +41,8 @@ struct HeadlessDiscovery {
 
 struct HeadlessDevice {
     gl: Rc<dyn Gl>,
-    floor_transform: TypedRigidTransform3D<f32, Native, Floor>,
-    viewer_origin: TypedRigidTransform3D<f32, Viewer, Native>,
+    floor_transform: RigidTransform3D<f32, Native, Floor>,
+    viewer_origin: RigidTransform3D<f32, Viewer, Native>,
     views: Views,
     receiver: Receiver<MockDeviceMsg>,
 }
@@ -88,7 +88,7 @@ impl Discovery for HeadlessDiscovery {
 }
 
 impl Device for HeadlessDevice {
-    fn floor_transform(&self) -> TypedRigidTransform3D<f32, Native, Floor> {
+    fn floor_transform(&self) -> RigidTransform3D<f32, Native, Floor> {
         self.floor_transform.clone()
     }