diff --git a/rtchallenge/src/spheres.rs b/rtchallenge/src/spheres.rs
index 940cbe0..ca3e0db 100644
--- a/rtchallenge/src/spheres.rs
+++ b/rtchallenge/src/spheres.rs
@@ -76,21 +76,27 @@ impl Sphere {
     ///     3_f32.sqrt() / 3.,
     /// ));
     /// assert_eq!(n, n.normalize());
-    /// ```
-    /// ```should_panic
-    /// use rtchallenge::{spheres::Sphere, tuples::Tuple};
     ///
-    /// // In debug builds points not on the sphere should fail.
-    /// let s = Sphere::default();
-    /// let n = s.normal_at(Tuple::point(0., 0., 0.5));
+    /// // Compute the normal on a translated sphere.
+    /// let mut s = Sphere::default();
+    /// s.transform = Matrix4x4::translation(0., 1., 0.);
+    /// let n = s.normal_at(Tuple::point(0., 1.70711, -0.70711));
+    /// assert_eq!(n, Tuple::vector(0., 0.70711, -0.70711));
+
+    /// // Compute the normal on a transformed sphere.
+    /// use std::f32::consts::PI;
+    ///
+    /// let mut s = Sphere::default();
+    /// s.transform = Matrix4x4::scaling(1.,0.5,1.) * Matrix4x4::rotation_z(PI/5.);
+    /// let n = s.normal_at(Tuple::point(0., 2_f32.sqrt()/2., -2_f32.sqrt()/2.));
+    /// assert_eq!(n, Tuple::vector(0., 0.97014, -0.24254));
     /// ```
-    pub fn normal_at(&self, point: Tuple) -> Tuple {
-        debug_assert!(
-            ((point - Tuple::point(0., 0., 0.)).magnitude() - 1.).abs() < EPSILON,
-            "{} != 1.",
-            (point - Tuple::point(0., 0., 0.)).magnitude()
-        );
-        (point - Tuple::point(0., 0., 0.)).normalize()
+    pub fn normal_at(&self, world_point: Tuple) -> Tuple {
+        let object_point = self.transform.inverse() * world_point;
+        let object_normal = object_point - Tuple::point(0., 0., 0.);
+        let mut world_normal = self.transform.inverse().transpose() * object_normal;
+        world_normal.w = 0.;
+        world_normal.normalize()
     }
 }