diff --git a/src/geopos.rs b/src/geopos.rs
index 75f6115..c5d7786 100644
--- a/src/geopos.rs
+++ b/src/geopos.rs
@@ -1,6 +1,5 @@
-use crate::{player::Position, tilemap::TileCoord, GalacticTransformOwned};
+use crate::{player::PlanetaryPosition, tilemap::TileCoord};
 use bevy::prelude::*;
-use big_space::FloatingOriginSettings;
 use glam::DVec3;
 use globe_rs::{CartesianPoint, GeographicPoint};
 use std::f32::consts::PI;
@@ -56,25 +55,16 @@ impl GeoPos {
         TileCoord::new(Vec2 { x, y }, zoom)
     }
 
-    /// Prefer using `to_cartesian`, which returns a [`Position`] that has a lot more convenience
-    /// methods.
-    pub fn to_cartesian_vec(self) -> DVec3 {
+    /// Compute the galactic position on the planet's surface.
+    pub fn to_cartesian(self) -> PlanetaryPosition {
         let geo = GeographicPoint::new(
             (self.lon as f64).to_radians(),
             (self.lat as f64).to_radians(),
             EARTH_RADIUS as f64,
         );
         let cart = CartesianPoint::from_geographic(&geo);
-        DVec3::new(-cart.x(), -cart.y(), cart.z())
-    }
-
-    /// Compute the galactic position on the planet's surface.
-    pub fn to_cartesian(self, space: &FloatingOriginSettings) -> Position<'_> {
-        let pos = self.to_cartesian_vec();
-        let (cell, pos) = space.translation_to_grid(pos);
-        let transform = Transform::from_translation(pos);
-        let pos = GalacticTransformOwned { transform, cell };
-        Position { pos, space }
+        let pos = DVec3::new(-cart.x(), -cart.y(), cart.z());
+        PlanetaryPosition { pos }
     }
 
     pub fn from_cartesian(pos: DVec3) -> Self {
@@ -89,9 +79,9 @@ impl GeoPos {
     /// Tile width and height in meters
     pub fn tile_size(self, zoom: u8) -> Vec2 {
         let coord = self.to_tile_coordinates(zoom);
-        let pos = self.to_cartesian_vec();
-        let x = coord.right().to_geo_pos().to_cartesian_vec().distance(pos) as f32;
-        let y = coord.down().to_geo_pos().to_cartesian_vec().distance(pos) as f32;
+        let pos = self.to_cartesian();
+        let x = coord.right().to_geo_pos().to_cartesian().distance(*pos) as f32;
+        let y = coord.down().to_geo_pos().to_cartesian().distance(*pos) as f32;
         Vec2 { x, y }
     }
 }
diff --git a/src/lib.rs b/src/lib.rs
index 5563dbd..9af9775 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -22,8 +22,8 @@ use big_space::{
     FloatingOriginPlugin, FloatingOriginSettings, GridCell,
 };
 use geopos::{GeoPos, EARTH_RADIUS};
-use glam::DVec3;
 use http_assets::HttpAssetReaderPlugin;
+use player::PlanetaryPosition;
 use tilemap::{TileIndex, TileMap, TILE_ZOOM};
 
 mod flycam;
@@ -45,7 +45,7 @@ type GalacticTransformItem<'a> = GridTransformItem<'a, GridPrecision>;
 
 #[derive(Resource)]
 struct Args {
-    starting_position: DVec3,
+    starting_position: PlanetaryPosition,
     height: f32,
     direction: f32,
     view: f32,
@@ -103,7 +103,7 @@ pub fn main() {
 
     let mut app = App::new();
     app.insert_resource(Args {
-        starting_position: pos.to_cartesian_vec(),
+        starting_position: pos.to_cartesian(),
         height,
         direction,
         view,
diff --git a/src/player.rs b/src/player.rs
index d8a1a23..b3679a1 100644
--- a/src/player.rs
+++ b/src/player.rs
@@ -27,6 +27,42 @@ pub struct Player<'w, 's> {
     pub(crate) space: Res<'w, FloatingOriginSettings>,
 }
 
+/// A helper for working with positions relative to the planet center.
+#[derive(Clone, Copy)]
+pub struct PlanetaryPosition {
+    pub pos: DVec3,
+}
+
+impl Into<DVec3> for PlanetaryPosition {
+    fn into(self) -> DVec3 {
+        self.pos
+    }
+}
+
+impl std::ops::Deref for PlanetaryPosition {
+    type Target = DVec3;
+
+    fn deref(&self) -> &Self::Target {
+        &self.pos
+    }
+}
+
+impl PlanetaryPosition {
+    pub fn to_galactic_position(self, space: &FloatingOriginSettings) -> Position<'_> {
+        let (cell, pos) = space.translation_to_grid(self.pos);
+        let transform = Transform::from_translation(pos);
+        let pos = GalacticTransformOwned { transform, cell };
+        Position { pos, space }
+    }
+
+    pub fn directions(self) -> Directions {
+        let up = self.pos.normalize().as_vec3();
+        let west = Vec3::Z.cross(up);
+        let north = up.cross(west);
+        Directions { up, north, west }
+    }
+}
+
 /// A helper for working with galactic positions.
 pub struct Position<'a> {
     pub pos: GalacticTransformOwned,
diff --git a/src/tilemap.rs b/src/tilemap.rs
index 3d6a063..feab86a 100644
--- a/src/tilemap.rs
+++ b/src/tilemap.rs
@@ -178,15 +178,10 @@ fn flat_tile(
 
     // Four corners of the tile in cartesian coordinates relative to the
     // planet's center.
-    let a = coord.to_geo_pos().to_cartesian_vec();
-    let b = pos.right().as_coord().to_geo_pos().to_cartesian_vec();
-    let c = pos
-        .down()
-        .right()
-        .as_coord()
-        .to_geo_pos()
-        .to_cartesian_vec();
-    let d = pos.down().as_coord().to_geo_pos().to_cartesian_vec();
+    let a = coord.to_geo_pos().to_cartesian();
+    let b = pos.right().as_coord().to_geo_pos().to_cartesian();
+    let c = pos.down().right().as_coord().to_geo_pos().to_cartesian();
+    let d = pos.down().as_coord().to_geo_pos().to_cartesian();
 
     // Normals on a sphere are just the position on the sphere normalized.
     let normals = vec![
@@ -197,9 +192,9 @@ fn flat_tile(
     ];
 
     // `a` is our anchor point, all others are relative
-    let b = b - a;
-    let c = c - a;
-    let d = d - a;
+    let b = *b - *a;
+    let c = *c - *a;
+    let d = *d - *a;
 
     let (grid, a) = space.translation_to_grid(a);
     let b = a + b.as_vec3();
diff --git a/src/tilemap/index.rs b/src/tilemap/index.rs
index a47f9f7..7051d9f 100644
--- a/src/tilemap/index.rs
+++ b/src/tilemap/index.rs
@@ -66,9 +66,9 @@ impl TileIndex {
 
     pub fn to_cartesian(self, space: &FloatingOriginSettings) -> GalacticTransformOwned {
         let coord = self.as_coord().center();
-        let pos = coord.to_geo_pos().to_cartesian(space);
+        let pos = coord.to_geo_pos().to_cartesian();
         let Directions { up, north, west: _ } = pos.directions();
-        let mut pos = pos.pos;
+        let mut pos = pos.to_galactic_position(space).pos;
         pos.transform.look_to(north, up);
         pos
     }