Fleshing out the quaternion implementation a bit.

NOTES.txt

@@ -16,3 +16,7 @@ This will mean unprojecting the screen coordinates from the previous and current
 mouse positions and subtracting the previous from the current to find the
 translation vector. Add that vector to the camera position & that should be it,
 I think?
+
+A decent (and mercifully brief!) explanation of quaternions is at:
+http://www.genesis3d.com/~kdtop/Quaternions-UsingToRepresentRotation.htm
+

src/vgl_quaternion.h

@@ -65,7 +65,10 @@ Quaternion<Num> operator - (const Quaternion<Num>& a, const Quaternion<Num>& b)
 template <typename Num>
 Quaternion<Num> operator * (const Quaternion<Num>& a, const Quaternion<Num>& b)
 {
-  // TODO
+  Vec3<Num> av(a.x, a.y, a.z);
+  Vec3<Num> bv(b.x, b.y, b.z);
+  Vec3<Num> rv = a.w * bv + b.w * av + cross(av, bv);
+  return Quaternion<Num>(rv.x, rv.y, rv.z, a.w * b.w - dot(av, bv));
 }
 
 
@@ -142,14 +145,14 @@ const Quaternion<Num>& operator /= (Quaternion<Num>& a, Num k)
 template <typename Num>
 Num lengthSqr(const Quaternion<Num>& a)
 {
-  // TODO
+  return sqr(a.x) + sqr(a.y) + sqr(a.z) + sqr(a.w);
 }
 
 
 template <typename Num>
 Num length(const Quaternion<Num>& a)
 {
-  // TODO
+  std::sqrt(lengthSqr(a));
 }
 
 
@@ -167,6 +170,46 @@ Quaternion<Num> norm(const Quaternion<Num>& a)
 }
 
 
+template <typename Num>
+Quaternion<Num> conjugate(const Quaternion<Num>& a)
+{
+  return Quaternion<Num>(-a.x, -a.y, -a.z, a.w);
+}
+
+
+template <typename Num>
+Quaternion<Num> inverse(const Quaternion<Num>& a)
+{
+  const Quaternion<Num> c = conjugate(a);
+  return c / (a * c);
+}
+
+
+// Rotate vector v by quaternion q.
+template <typename Num>
+Vec3<Num> rotate(const Quaternion<Num>& q, const Vec3<Num>& v)
+{
+  // FIXME: need to define multiplication operators for quaternion * vec3  and vec3 * quaternion
+  return q * v * inverse(q);
+}
+
+
+// Rotate vector v by quaternion q.
+template <typename Num>
+Vec4<Num> rotate(const Quaternion<Num>& q, const Vec4<Num>& v)
+{
+  // FIXME: need to define multiplication operators for quaternion * vec3  and vec3 * quaternion
+  return q * v * inverse(q);
+}
+
+
+template <typename Num>
+Quaternion<Num> slerp(const Quaternion<Num>& a, const Quaternion<Num>& b, Num k)
+{
+  return k * a + (1 - k) * b;
+}
+
+
 } // namespace vgl
 
 #endif // vgl_quaternion_h