math: create a quaternion from two vectors.

src/lol/math/vector.h

@@ -939,6 +939,10 @@ template <typename T> struct Quat
     static Quat<T> rotate(T degrees, T x, T y, T z);
     static Quat<T> rotate(T degrees, Vec3<T> const &v);
 
+    /* Create a unit quaternion representing a rotation between two vectors.
+     * Input vectors need not be normalised. */
+    static Quat<T> rotate(Vec3<T> const &src, Vec3<T> const &dst);
+
     /* Convert from Euler angles. The axes in fromeuler_xyx are
      * x, then y', then x", ie. the axes are attached to the model.
      * If you want to rotate around static axes, just reverse the order

src/math/vector.cpp

@@ -501,6 +501,14 @@ template<> quat quat::rotate(float degrees, float x, float y, float z)
     return quat::rotate(degrees, vec3(x, y, z));
 }
 
+template<> quat quat::rotate(vec3 const &src, vec3 const &dst)
+{
+    vec3 v = cross(src, dst);
+    float d = dot(src, dst) + lol::sqrt(sqlength(src) * sqlength(dst));
+
+    return normalize(quat(d, v.x, v.y, v.z));
+}
+
 template<> quat slerp(quat const &qa, quat const &qb, float f)
 {
     float const magnitude = lol::sqrt(sqlength(qa) * sqlength(qb));