diff --git a/src/geo/ellipsoid.js b/src/geo/ellipsoid.js
index 45d67da0d..dbff51e3f 100644
--- a/src/geo/ellipsoid.js
+++ b/src/geo/ellipsoid.js
@@ -4,10 +4,20 @@
  * (ECEF) conversions, surface normals and projection onto the surface. The
  * formulas follow the default renderer's step for step, so they agree with
  * it to floating-point noise.
+ *
+ * Into ECEF, positions are arguments (`fromDegrees(lon, lat, height)`,
+ * `fromRadians` likewise); out of it, objects (`toLonLatH` gives
+ * `{lon, lat, height}` in degrees, `toCartographicRadians` the same in
+ * radians). Cesium's `Cartographic.fromDegrees(lon, lat, h)` is plain
+ * `{lon: toRadians(lon), lat: toRadians(lat), height: h}`; for its ECEF
+ * point, use `fromDegrees`.
+ *
+ * NaN in gives NaN fields out, never a throw (Cesium's debug build throws).
+ * The Earth's centre, and points so near it that their squares round to
+ * zero, answer null, as Cesium answers undefined.
  */
 import {
   add,
-  clone,
   dot,
   magnitude,
   normalize,
@@ -58,7 +68,7 @@ export function fromRadians(lon, lat, height = 0) {
   const r = WGS84.radiiSquared;
   let k = vec(r.x * n.x, r.y * n.y, r.z * n.z);
   const gamma = Math.sqrt(dot(n, k));
-  k = scale(k, 1 / gamma);
+  k = vec(k.x / gamma, k.y / gamma, k.z / gamma);
   return add(k, scale(n, height));
 }
 
@@ -66,13 +76,6 @@ export function fromRadians(lon, lat, height = 0) {
 export const fromDegrees = (lon, lat, height = 0) =>
   fromRadians(toRadians(lon), toRadians(lat), height);
 
-/** A position in either contract form, as ECEF. */
-export function toEcef(position) {
-  if ('lon' in position && 'lat' in position)
-    return fromDegrees(position.lon, position.lat, position.height ?? 0);
-  return clone(position);
-}
-
 /** The point on the ellipsoid along the geodetic normal, or null at the centre. */
 export function scaleToGeodeticSurface(p) {
   const { x: positionX, y: positionY, z: positionZ } = p;
diff --git a/src/geo/geo.test.mjs b/src/geo/geo.test.mjs
index 9e0ad1a58..e0fcde931 100644
--- a/src/geo/geo.test.mjs
+++ b/src/geo/geo.test.mjs
@@ -29,12 +29,20 @@ function points(count = 500) {
     { lon: 180, lat: 0, height: -400 },
     { lon: -97.7431, lat: 30.2672, height: 150 },
   ];
-  for (let i = 0; i < count; i++)
+  // Each height band gets its share: near the ground, low orbit, far out.
+  const bands = [
+    [-500, 1e4],
+    [1e4, 1e6],
+    [1e6, 4e7],
+  ];
+  for (let i = 0; i < count; i++) {
+    const [lo, hi] = bands[i % bands.length];
     out.push({
       lon: next() * 360 - 180,
       lat: next() * 180 - 90,
-      height: next() * 4e7 - 1e4,
+      height: lo + next() * (hi - lo),
     });
+  }
   return out;
 }
 
@@ -60,7 +68,7 @@ test('geodetic to ECEF matches the default renderer', () => {
   for (const p of points()) {
     const ours = fromDegrees(p.lon, p.lat, p.height);
     const theirs = Cesium.Cartesian3.fromDegrees(p.lon, p.lat, p.height);
-    closeVec(ours, theirs, 1e-6, `${p.lon},${p.lat},${p.height}`);
+    closeVec(ours, theirs, 0, `${p.lon},${p.lat},${p.height}`);
   }
 });
 
@@ -76,6 +84,37 @@ test('ECEF to geodetic matches the default renderer', () => {
     close(ours.lat, theirs.latitude, 1e-12, `${where} lat`);
     close(ours.height, theirs.height, 1e-6, `${where} height`);
   }
+  // Inside the Earth: within the centre cutoff (the first four) and between
+  // it and the surface (the last).
+  for (const p of [
+    { x: 1e6, y: 0, z: 0 },
+    { x: 1, y: 2, z: 3 },
+    { x: -2e5, y: 3e5, z: 1e5 },
+    { x: 1e6, y: 1e6, z: 5e5 },
+    { x: 2e6, y: 1.5e6, z: 1.5e6 },
+  ]) {
+    const ours = toCartographicRadians(p);
+    const theirs = Cesium.Cartographic.fromCartesian(
+      new Cesium.Cartesian3(p.x, p.y, p.z),
+    );
+    const where = `${p.x},${p.y},${p.z}`;
+    close(ours.lon, theirs.longitude, 1e-12, `${where} lon`);
+    close(ours.lat, theirs.latitude, 1e-12, `${where} lat`);
+    close(ours.height, theirs.height, 1e-6, `${where} height`);
+  }
+  for (const p of [
+    { x: NaN, y: 0, z: 0 },
+    { x: 7e6, y: NaN, z: 0 },
+    { x: 7e6, y: 0, z: NaN },
+  ]) {
+    const nan = toLonLatH(p);
+    assert.ok(
+      Number.isNaN(nan.lon) &&
+        Number.isNaN(nan.lat) &&
+        Number.isNaN(nan.height),
+      JSON.stringify(nan),
+    );
+  }
   assert.equal(toCartographicRadians({ x: 0, y: 0, z: 0 }), null);
   assert.equal(
     Cesium.Cartographic.fromCartesian(Cesium.Cartesian3.ZERO),
diff --git a/src/geo/vector.js b/src/geo/vector.js
index e020dd5cc..a5b7400fc 100644
--- a/src/geo/vector.js
+++ b/src/geo/vector.js
@@ -18,6 +18,7 @@ export const dot = (a, b) => a.x * b.x + a.y * b.y + a.z * b.z;
 export const cross = (a, b) =>
   vec(a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x);
 export const magnitude = (a) => Math.sqrt(dot(a, a));
+/** Straight-line (chord) distance, not along the surface. */
 export const distance = (a, b) => magnitude(sub(a, b));
 export function normalize(a) {
   const m = magnitude(a);
diff --git a/src/render/stub/math.js b/src/render/stub/math.js
index 4fa6665b1..896309eca 100644
--- a/src/render/stub/math.js
+++ b/src/render/stub/math.js
@@ -14,6 +14,8 @@ import {
   clamp,
   equalsEpsilon,
   negate,
+  clone,
+  fromDegrees,
   rotate,
   scale,
   vec,
@@ -22,6 +24,13 @@ import {
 
 export * from '../../geo/index.js';
 
+/** A contract `Position` (`Ecef` or `LonLatH`, degrees), as ECEF. */
+export function toEcef(position) {
+  if ('lon' in position && 'lat' in position)
+    return fromDegrees(position.lon, position.lat, position.height ?? 0);
+  return clone(position);
+}
+
 const EPSILON3 = 1e-3;
 const EPSILON10 = 1e-10;