quaternion: add slerp and nlerp

quaternion.cpp

@@ -104,6 +104,49 @@ quaternion<T>::operator- () const noexcept
 }
 
 
+///////////////////////////////////////////////////////////////////////////////
+template <typename T>
+quaternion<T>
+cruft::slerp (quaternion<T> a, quaternion<T> b, T t)
+{
+    // calc cosine theta
+    T cosine = dot (a, b);
+
+    // adjust signs (if necessary)
+    if (cosine < 0) {
+        cosine = -cosine;
+        b      = -b;
+    }
+
+    // Calculate coefficients
+    T p, q;
+    if (T(0.9995) > cosine) {
+        T omega = std::acos (cosine); // extract theta from dot product's cos theta
+        T sine = std::sin (omega);
+
+        p = std::sin ((1 - t) * omega) / sine;
+        q = std::sin (     t  * omega) / sine;
+    } else {
+        // Very close, do linear interp (because it's faster)
+        p = 1 - t;
+        q =     t;
+    }
+
+    return a * p + b * q;
+}
+
+
+//-----------------------------------------------------------------------------
+template <typename T>
+quaternion<T>
+cruft::nlerp (cruft::quaternion<T> a, cruft::quaternion<T> b, T t)
+{
+    return cruft::normalised (
+        cruft::mix (a, b, t)
+    );
+}
+
+
 ///////////////////////////////////////////////////////////////////////////////
 template <typename T>
 quaternion<T>
@@ -311,6 +354,8 @@ namespace cruft::debug {
 ///////////////////////////////////////////////////////////////////////////////
 #define INSTANTIATE(T)                                                          \
 template cruft::vector3<T> cruft::rotate (cruft::vector3<T>, cruft::quaternion<T>); \
+template quaternion<T> cruft::slerp (quaternion<T>, quaternion<T>, T);              \
+template quaternion<T> cruft::nlerp (quaternion<T>, quaternion<T>, T);              \
 template quaternion<T> cruft::conjugate (quaternion<T>);                         \
 template quaternion<T> cruft::operator* (quaternion<T>, quaternion<T>);          \
 template quaternion<T>& cruft::operator*= (quaternion<T>&, quaternion<T>);       \

quaternion.hpp

@@ -141,6 +141,18 @@ namespace cruft {
     }
 
 
+    ///////////////////////////////////////////////////////////////////////////
+    template <typename T>
+    quaternion<T>
+    slerp (quaternion<T> a, quaternion<T> b, T t);
+
+
+    //-------------------------------------------------------------------------
+    template <typename T>
+    quaternion<T>
+    nlerp (quaternion<T> a, quaternion<T> b, T t);
+
+
     ///////////////////////////////////////////////////////////////////////////
     template <typename T>
     quaternion<T>