diff --git a/doc/transformations.dox b/doc/transformations.dox
index 9a95ad7e1d..a29b258f20 100644
--- a/doc/transformations.dox
+++ b/doc/transformations.dox
@@ -263,9 +263,11 @@ Linear              | @ref Math::Complex | @ref Math::Complex | @ref Math::lerp(
 Linear              | @ref Math::Quaternion | @ref Math::Quaternion | @ref Math::lerp(const Quaternion<T>&, const Quaternion<T>&, T) "Math::lerp()", \n @ref Math::lerpShortestPath(const Quaternion<T>&, const Quaternion<T>&, T) "Math::lerpShortestPath()"
 Linear | @ref Math::CubicHermite "Math::CubicHermite<T>" | `T` | @ref Math::lerp(const CubicHermite<T>&, const CubicHermite<T>&, U) "Math::lerp()"
 Linear | @ref Math::CubicHermiteComplex | @ref Math::Complex | @ref Math::lerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T) "Math::lerp()"
-Linear | @ref Math::CubicHermiteQuaternion | @ref Math::Quaternion | @ref Math::lerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T) "Math::lerp()"
+Linear | @ref Math::CubicHermiteQuaternion | @ref Math::Quaternion | @ref Math::lerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T) "Math::lerp()", \n @ref Math::lerpShortestPath(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T) "Math::lerpShortestPath()"
 Spherical linear    | @ref Math::Complex | @ref Math::Complex | @ref Math::slerp(const Complex<T>&, const Complex<T>&, T) "Math::slerp()"
 Spherical linear    | @ref Math::Quaternion | @ref Math::Quaternion | @ref Math::slerp(const Quaternion<T>&, const Quaternion<T>&, T) "Math::slerp()", \n @ref Math::slerpShortestPath(const Quaternion<T>&, const Quaternion<T>&, T) "Math::slerpShortestPath()"
+Spherical linear    | @ref Math::CubicHermiteComplex | @ref Math::Complex | @ref Math::slerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T) "Math::slerp()"
+Spherical linear    | @ref Math::CubicHermiteQuaternion | @ref Math::Quaternion | @ref Math::slerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T) "Math::slerp()", \n @ref Math::slerpShortestPath(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T) "Math::slerpShortestPath()"
 Screw linear        | @ref Math::DualQuaternion | @ref Math::DualQuaternion | @ref Math::sclerp(const DualQuaternion<T>&, const DualQuaternion<T>&, T) "Math::sclerp()", \n @ref Math::sclerpShortestPath(const DualQuaternion<T>&, const DualQuaternion<T>&, T) "Math::sclerpShortestPath()"
 Spline | @ref Math::CubicHermite "Math::CubicHermite<T>" | `T` | @ref Math::splerp(const CubicHermite<T>&, const CubicHermite<T>&, U) "Math::splerp()"
 Spline | @ref Math::CubicHermiteComplex | @ref Math::Complex | @ref Math::splerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T) "Math::splerp()"
diff --git a/src/Magnum/Math/CubicHermite.h b/src/Magnum/Math/CubicHermite.h
index b5ed30df2e..cd088bad92 100644
--- a/src/Magnum/Math/CubicHermite.h
+++ b/src/Magnum/Math/CubicHermite.h
@@ -316,6 +316,10 @@ Equivalent to calling @ref lerp(const T&, const T&, U) on
 @ref CubicHermite::point() extracted from both @p a and @p b.
 @see @ref lerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T),
     @ref lerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T),
+    @ref lerpShortestPath(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T),
+    @ref slerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T),
+    @ref slerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T),
+    @ref slerpShortestPath(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T),
     @ref select(const CubicHermite<T>&, const CubicHermite<T>&, U),
     @ref splerp(const CubicHermite<T>&, const CubicHermite<T>&, U),
     @ref splerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T),
@@ -337,6 +341,7 @@ normalized complex number in both @p a and @p b.
 @see @ref Complex::isNormalized(),
     @ref lerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T),
     @ref select(const CubicHermite<T>&, const CubicHermite<T>&, U),
+    @ref slerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T),
     @ref splerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T)
 */
 template<class T> Complex<T> lerp(const CubicHermiteComplex<T>& a, const CubicHermiteComplex<T>& b, T t) {
@@ -352,14 +357,86 @@ on @ref CubicHermite::point() extracted from @p a and @p b. Compared to
 normalization step after. Expects that @ref CubicHermite::point() is a
 normalized quaternion in both @p a and @p b.
 @see @ref Quaternion::isNormalized(),
+    @ref lerpShortestPath(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T),
     @ref lerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T),
     @ref select(const CubicHermite<T>&, const CubicHermite<T>&, U),
+    @ref slerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T),
     @ref splerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T)
 */
 template<class T> Quaternion<T> lerp(const CubicHermiteQuaternion<T>& a, const CubicHermiteQuaternion<T>& b, T t) {
     return lerp(a.point(), b.point(), t);
 }
 
+/** @relatesalso CubicHermite
+@brief Linear shortest-path interpolation of two cubic Hermite quaternions
+
+Equivalent to calling @ref lerpShortestPath(const Quaternion<T>&, const Quaternion<T>&, T)
+on @ref CubicHermite::point() extracted from @p a and @p b. Expects that
+@ref CubicHermite::point() is a normalized quaternion in both @p a and @p b.
+
+Note that rotations interpolated with this function may go along a completely
+different path compared to @ref splerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T).
+Use @ref lerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T)
+for behavior that is consistent with spline interpolation.
+@see @ref Quaternion::isNormalized(),
+    @ref slerpShortestPath(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T)
+*/
+template<class T> Quaternion<T> lerpShortestPath(const CubicHermiteQuaternion<T>& a, const CubicHermiteQuaternion<T>& b, T t) {
+    return lerpShortestPath(a.point(), b.point(), t);
+}
+
+/** @relatesalso CubicHermite
+@brief Spherical linear interpolation of two cubic Hermite complex numbers
+
+Equivalent to calling @ref slerp(const Complex<T>&, const Complex<T>&, T) on
+@ref CubicHermite::point() extracted from @p a and @p b. Expects that
+@ref CubicHermite::point() is a normalized complex number in both @p a and @p b.
+@see @ref Complex::isNormalized(),
+    @ref slerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T),
+    @ref select(const CubicHermite<T>&, const CubicHermite<T>&, U),
+    @ref lerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T),
+    @ref splerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T)
+ */
+template<class T> inline Complex<T> slerp(const CubicHermiteComplex<T>& a, const CubicHermiteComplex<T>& b, T t) {
+    return slerp(a.point(), b.point(), t);
+}
+
+/** @relatesalso CubicHermite
+@brief Spherical linear interpolation of two cubic Hermite quaternions
+
+Equivalent to calling @ref slerp(const Quaternion<T>&, const Quaternion<T>&, T)
+on @ref CubicHermite::point() extracted from @p a and @p b. Expects that
+@ref CubicHermite::point() is a normalized complex number in both @p a and @p b.
+@see @ref Quaternion::isNormalized(),
+    @ref slerpShortestPath(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T),
+    @ref slerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T),
+    @ref select(const CubicHermite<T>&, const CubicHermite<T>&, U),
+    @ref lerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T),
+    @ref splerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T)
+ */
+template<class T> inline Quaternion<T> slerp(const CubicHermiteQuaternion<T>& a, const CubicHermiteQuaternion<T>& b, T t) {
+    return slerp(a.point(), b.point(), t);
+}
+
+/** @relatesalso CubicHermite
+@brief Spherical linear shortest-path interpolation of two cubic Hermite quaternions
+
+Equivalent to calling @ref slerpShortestPath(const Quaternion<T>&, const Quaternion<T>&, T)
+on @ref CubicHermite::point() extracted from @p a and @p b. Expects that
+@ref CubicHermite::point() is a normalized quaternion in both @p a and @p b.
+
+Note that rotations interpolated with this function may go along a completely
+different path compared to @ref splerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T).
+Use @ref slerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T)
+for spherical linear interpolation with behavior that is consistent with spline
+interpolation.
+@see @ref Quaternion::isNormalized(),
+    @ref lerpShortestPath(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T)
+*/
+template<class T> Quaternion<T> slerpShortestPath(const CubicHermiteQuaternion<T>& a, const CubicHermiteQuaternion<T>& b, T t) {
+    return slerpShortestPath(a.point(), b.point(), t);
+}
+
 /** @relatesalso CubicHermite
 @brief Spline interpolation of two cubic Hermite points
 @param a     First spline point
@@ -402,7 +479,8 @@ Expects that @ref CubicHermite::point() is a normalized complex number in both
 @see @ref Complex::isNormalized(),
     @ref splerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T),
     @ref select(const CubicHermite<T>&, const CubicHermite<T>&, U),
-    @ref lerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T)
+    @ref lerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T),
+    @ref slerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T)
 */
 template<class T> Complex<T> splerp(const CubicHermiteComplex<T>& a, const CubicHermiteComplex<T>& b, T t) {
     CORRADE_ASSERT(a.point().isNormalized() && b.point().isNormalized(),
@@ -431,7 +509,8 @@ and @p b.
 @see @ref Quaternion::isNormalized(),
     @ref splerp(const CubicHermiteComplex<T>&, const CubicHermiteComplex<T>&, T),
     @ref select(const CubicHermite<T>&, const CubicHermite<T>&, U),
-    @ref lerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T)
+    @ref lerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T),
+    @ref slerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T)
 */
 template<class T> Quaternion<T> splerp(const CubicHermiteQuaternion<T>& a, const CubicHermiteQuaternion<T>& b, T t) {
     CORRADE_ASSERT(a.point().isNormalized() && b.point().isNormalized(),
diff --git a/src/Magnum/Math/Quaternion.h b/src/Magnum/Math/Quaternion.h
index 86edc36ef6..6112fed47a 100644
--- a/src/Magnum/Math/Quaternion.h
+++ b/src/Magnum/Math/Quaternion.h
@@ -89,7 +89,8 @@ Expects that both quaternions are normalized. @f[
 @f]
 
 Note that this function does not check for shortest path interpolation, see
-@ref lerpShortestPath() for an alternative.
+@ref lerpShortestPath(const Quaternion<T>&, const Quaternion<T>&, T) for an
+alternative.
 @see @ref Quaternion::isNormalized(),
     @ref slerp(const Quaternion<T>&, const Quaternion<T>&, T), @ref sclerp(),
     @ref lerp(const T&, const T&, U),
@@ -122,7 +123,9 @@ both quaternions are normalized. @f[
         q_{LERP} & = & \cfrac{(1 - t) q'_A + t q_B}{|(1 - t) q'_A + t q_B|}
     \end{array}
 @f]
-@see @ref Quaternion::isNormalized(), @ref slerpShortestPath(),
+@see @ref Quaternion::isNormalized(),
+    @ref slerpShortestPath(const Quaternion<T>&, const Quaternion<T>&, T),
+    @ref lerpShortestPath(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T)
     @ref sclerpShortestPath()
 */
 template<class T> inline Quaternion<T> lerpShortestPath(const Quaternion<T>& normalizedA, const Quaternion<T>& normalizedB, T t) {
@@ -153,9 +156,11 @@ otherwise, the interpolation is performed as: @f[
 @f]
 
 Note that this function does not check for shortest path interpolation, see
-@ref slerpShortestPath() for an alternative.
+@ref slerpShortestPath(const Quaternion<T>&, const Quaternion<T>&, T) for an
+alternative.
 @see @ref Quaternion::isNormalized(), @ref lerp(const Quaternion<T>&, const Quaternion<T>&, T),
-    @ref slerp(const Complex<T>&, const Complex<T>&, T), @ref sclerp()
+    @ref slerp(const Complex<T>&, const Complex<T>&, T), @ref sclerp(),
+    @ref slerp(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T)
 */
 template<class T> inline Quaternion<T> slerp(const Quaternion<T>& normalizedA, const Quaternion<T>& normalizedB, T t) {
     CORRADE_ASSERT(normalizedA.isNormalized() && normalizedB.isNormalized(),
@@ -198,8 +203,10 @@ otherwise, the interpolation is performed as: @f[
         q_{SLERP} & = & \cfrac{\sin((1 - t) \theta) q'_A + \sin(t \theta) q_B}{\sin(\theta)}
     \end{array}
 @f]
-@see @ref Quaternion::isNormalized(), @ref lerpShortestPath(),
-        @ref sclerpShortestPath()
+@see @ref Quaternion::isNormalized(),
+    @ref lerpShortestPath(const Quaternion<T>&, const Quaternion<T>&, T),
+    @ref slerpShortestPath(const CubicHermiteQuaternion<T>&, const CubicHermiteQuaternion<T>&, T),
+    @ref sclerpShortestPath()
 */
 template<class T> inline Quaternion<T> slerpShortestPath(const Quaternion<T>& normalizedA, const Quaternion<T>& normalizedB, T t) {
     CORRADE_ASSERT(normalizedA.isNormalized() && normalizedB.isNormalized(),
diff --git a/src/Magnum/Math/Test/CubicHermiteTest.cpp b/src/Magnum/Math/Test/CubicHermiteTest.cpp
index c1ad7a9031..0555f115d3 100644
--- a/src/Magnum/Math/Test/CubicHermiteTest.cpp
+++ b/src/Magnum/Math/Test/CubicHermiteTest.cpp
@@ -94,6 +94,15 @@ struct CubicHermiteTest: Corrade::TestSuite::Tester {
     void lerpComplexNotNormalized();
     void lerpQuaternion();
     void lerpQuaternionNotNormalized();
+    void lerpQuaternionShortestPath();
+    void lerpQuaternionShortestPathNotNormalized();
+
+    void slerpComplex();
+    void slerpComplexNotNormalized();
+    void slerpQuaternion();
+    void slerpQuaternionNotNormalized();
+    void slerpQuaternionShortestPath();
+    void slerpQuaternionShortestPathNotNormalized();
 
     void splerpScalar();
     void splerpVector();
@@ -168,6 +177,15 @@ CubicHermiteTest::CubicHermiteTest() {
               &CubicHermiteTest::lerpComplexNotNormalized,
               &CubicHermiteTest::lerpQuaternion,
               &CubicHermiteTest::lerpQuaternionNotNormalized,
+              &CubicHermiteTest::lerpQuaternionShortestPath,
+              &CubicHermiteTest::lerpQuaternionShortestPathNotNormalized,
+
+              &CubicHermiteTest::slerpComplex,
+              &CubicHermiteTest::slerpComplexNotNormalized,
+              &CubicHermiteTest::slerpQuaternion,
+              &CubicHermiteTest::slerpQuaternionNotNormalized,
+              &CubicHermiteTest::slerpQuaternionShortestPath,
+              &CubicHermiteTest::slerpQuaternionShortestPathNotNormalized,
 
               &CubicHermiteTest::splerpScalar,
               &CubicHermiteTest::splerpVector,
@@ -183,7 +201,10 @@ CubicHermiteTest::CubicHermiteTest() {
               &CubicHermiteTest::debugQuaternion});
 }
 
+using namespace Math::Literals;
+
 typedef Math::Vector2<Float> Vector2;
+typedef Math::Vector3<Float> Vector3;
 typedef Math::Complex<Float> Complex;
 typedef Math::Quaternion<Float> Quaternion;
 typedef Math::CubicBezier2D<Float> CubicBezier2D;
@@ -821,6 +842,164 @@ void CubicHermiteTest::lerpQuaternionNotNormalized() {
         "Math::lerp(): quaternions must be normalized\n");
 }
 
+void CubicHermiteTest::lerpQuaternionShortestPath() {
+    /* Values from QuaternionTest::lerpShortestPath() */
+    CubicHermiteQuaternion a{
+        {{2.0f, 1.5f, 0.3f}, 1.1f},
+        Quaternion::rotation(0.0_degf, Vector3::zAxis()),
+        {{-1.0f, 0.0f, 0.3f}, 0.4f}};
+    CubicHermiteQuaternion b{
+        {{5.0f, 0.3f, 1.1f}, 0.5f},
+        Quaternion::rotation(225.0_degf, Vector3::zAxis()),
+        {{1.5f, 0.3f, 17.0f}, -7.0f}};
+
+    Quaternion lerp = Math::lerp(a, b, 0.25f);
+    Quaternion lerpShortestPath = Math::lerpShortestPath(a, b, 0.25f);
+    CORRADE_COMPARE(lerp.axis(), Vector3::zAxis());
+    CORRADE_COMPARE(lerpShortestPath.axis(), Vector3::zAxis());
+    CORRADE_COMPARE(lerp.angle(), 38.8848_degf);
+    CORRADE_COMPARE(lerpShortestPath.angle(), 329.448_degf);
+
+    Quaternion expected{{0.0f, 0.0f, 0.26347f}, -0.964667f};
+    CORRADE_COMPARE(lerpShortestPath, expected);
+    CORRADE_COMPARE(Math::lerpShortestPath(a.point(), b.point(), 0.25f), expected);
+}
+
+void CubicHermiteTest::lerpQuaternionShortestPathNotNormalized() {
+    std::ostringstream out;
+    Error redirectError{&out};
+
+    /* This one should not assert as the default constructor should create
+       identity point */
+    Math::lerpShortestPath(CubicHermiteQuaternion{}, {}, 0.3f);
+
+    /* These will, tho */
+    CubicHermiteQuaternion a{{}, Quaternion{}*2.0f, {}};
+    Math::lerpShortestPath({}, a, 0.3f);
+    Math::lerpShortestPath(a, {}, 0.3f);
+    /* lerpShortestPath() is calling lerp(), so the message is from there */
+    CORRADE_COMPARE(out.str(),
+        "Math::lerp(): quaternions must be normalized\n"
+        "Math::lerp(): quaternions must be normalized\n");
+}
+
+void CubicHermiteTest::slerpComplex() {
+    CubicHermiteComplex a{{2.0f, 1.5f}, {0.999445f, 0.0333148f}, {-1.0f, 0.0f}};
+    CubicHermiteComplex b{{5.0f, 0.3f}, {-0.876216f, 0.481919f}, {1.5f, 0.3f}};
+
+    CORRADE_COMPARE(Math::slerp(a, b, 0.0f), a.point());
+    CORRADE_COMPARE(Math::slerp(a, b, 1.0f), b.point());
+
+    Complex expected035{0.585564f, 0.810627f};
+    CORRADE_COMPARE(Math::slerp(a, b, 0.35f), expected035);
+    CORRADE_COMPARE(Math::slerp(a.point(), b.point(), 0.35f), expected035);
+    CORRADE_VERIFY(Math::slerp(a, b, 0.35f).isNormalized());
+
+    Complex expected08{-0.520014f, 0.854159f};
+    CORRADE_COMPARE(Math::slerp(a, b, 0.8f), expected08);
+    CORRADE_COMPARE(Math::slerp(a.point(), b.point(), 0.8f), expected08);
+    CORRADE_VERIFY(Math::slerp(a, b, 0.8f).isNormalized());
+}
+
+void CubicHermiteTest::slerpComplexNotNormalized() {
+    std::ostringstream out;
+    Error redirectError{&out};
+
+    /* This one should not assert as the default constructor should create
+       identity point */
+    CORRADE_COMPARE(Math::slerp(CubicHermiteComplex{}, {}, 0.3f), Complex{});
+
+    /* These will, tho */
+    CubicHermiteComplex a{{}, Complex{}*2.0f, {}};
+    Math::slerp({}, a, 0.3f);
+    Math::slerp(a, {}, 0.3f);
+    CORRADE_COMPARE(out.str(),
+        "Math::slerp(): complex numbers must be normalized\n"
+        "Math::slerp(): complex numbers must be normalized\n");
+}
+
+void CubicHermiteTest::slerpQuaternion() {
+    CubicHermiteQuaternion a{
+        {{2.0f, 1.5f, 0.3f}, 1.1f},
+        {{0.780076f, 0.0260025f, 0.598059f}, 0.182018f},
+        {{-1.0f, 0.0f, 0.3f}, 0.4f}};
+    CubicHermiteQuaternion b{
+        {{5.0f, 0.3f, 1.1f}, 0.5f},
+        {{-0.711568f, 0.391362f, 0.355784f}, 0.462519f},
+        {{1.5f, 0.3f, 17.0f}, -7.0f}};
+
+    CORRADE_COMPARE(Math::slerp(a, b, 0.0f), a.point());
+    CORRADE_COMPARE(Math::slerp(a, b, 1.0f), b.point());
+
+    Quaternion expected035{{0.308542f, 0.265288f, 0.790272f}, 0.458142f};
+    CORRADE_COMPARE(Math::slerp(a, b, 0.35f), expected035);
+    CORRADE_COMPARE(Math::slerp(a.point(), b.point(), 0.35f), expected035);
+    CORRADE_VERIFY(Math::slerp(a, b, 0.35f).isNormalized());
+
+    Quaternion expected08{{-0.442885f, 0.410928f, 0.584814f}, 0.541279f};
+    CORRADE_COMPARE(Math::slerp(a, b, 0.8f), expected08);
+    CORRADE_COMPARE(Math::slerp(a.point(), b.point(), 0.8f), expected08);
+    CORRADE_VERIFY(Math::slerp(a, b, 0.8f).isNormalized());
+}
+
+void CubicHermiteTest::slerpQuaternionNotNormalized() {
+    std::ostringstream out;
+    Error redirectError{&out};
+
+    /* This one should not assert as the default constructor should create
+       identity point */
+    Math::slerp(CubicHermiteQuaternion{}, {}, 0.3f);
+
+    /* These will, tho */
+    CubicHermiteQuaternion a{{}, Quaternion{}*2.0f, {}};
+    Math::slerp({}, a, 0.3f);
+    Math::slerp(a, {}, 0.3f);
+    CORRADE_COMPARE(out.str(),
+        "Math::slerp(): quaternions must be normalized\n"
+        "Math::slerp(): quaternions must be normalized\n");
+}
+
+void CubicHermiteTest::slerpQuaternionShortestPath() {
+    /* Values from QuaternionTest::slerpShortestPath() */
+    CubicHermiteQuaternion a{
+        {{2.0f, 1.5f, 0.3f}, 1.1f},
+        Quaternion::rotation(0.0_degf, Vector3::zAxis()),
+        {{-1.0f, 0.0f, 0.3f}, 0.4f}};
+    CubicHermiteQuaternion b{
+        {{5.0f, 0.3f, 1.1f}, 0.5f},
+        Quaternion::rotation(225.0_degf, Vector3::zAxis()),
+        {{1.5f, 0.3f, 17.0f}, -7.0f}};
+
+    Quaternion slerp = Math::slerp(a, b, 0.25f);
+    Quaternion slerpShortestPath = Math::slerpShortestPath(a, b, 0.25f);
+    CORRADE_COMPARE(slerp.axis(), Vector3::zAxis());
+    CORRADE_COMPARE(slerpShortestPath.axis(), Vector3::zAxis());
+    CORRADE_COMPARE(slerp.angle(), 56.25_degf);
+    CORRADE_COMPARE(slerpShortestPath.angle(), 326.25_degf);
+    CORRADE_COMPARE(slerp, (Quaternion{{0.0f, 0.0f, 0.471397f}, 0.881921f}));
+
+    Quaternion expected{{0.0f, 0.0f, 0.290285f}, -0.95694f};
+    CORRADE_COMPARE(slerpShortestPath, expected);
+    CORRADE_COMPARE(Math::slerpShortestPath(a.point(), b.point(), 0.25f), expected);
+}
+
+void CubicHermiteTest::slerpQuaternionShortestPathNotNormalized() {
+    std::ostringstream out;
+    Error redirectError{&out};
+
+    /* This one should not assert as the default constructor should create
+       identity point */
+    Math::slerpShortestPath(CubicHermiteQuaternion{}, {}, 0.3f);
+
+    /* These will, tho */
+    CubicHermiteQuaternion a{{}, Quaternion{}*2.0f, {}};
+    Math::slerpShortestPath({}, a, 0.3f);
+    Math::slerpShortestPath(a, {}, 0.3f);
+    CORRADE_COMPARE(out.str(),
+        "Math::slerpShortestPath(): quaternions must be normalized\n"
+        "Math::slerpShortestPath(): quaternions must be normalized\n");
+}
+
 void CubicHermiteTest::splerpScalar() {
     CubicHermite1D a{2.0f, 3.0f, -1.0f};
     CubicHermite1D b{5.0f, -2.0f, 1.5f};