Math: ability to construct DualQuaternion from dual vector and scalar.

As opposed to real and dual quaternion.

src/Magnum/Math/DualQuaternion.h

@@ -201,6 +201,19 @@ template<class T> class DualQuaternion: public Dual<Quaternion<T>> {
          */
         constexpr /*implicit*/ DualQuaternion(const Quaternion<T>& real, const Quaternion<T>& dual = Quaternion<T>({}, T(0))): Dual<Quaternion<T>>(real, dual) {}
 
+        /**
+         * @brief Construct dual quaternion from dual vector and scalar parts
+         *
+         * @f[
+         *      \hat q = [\hat{\boldsymbol v}, \hat s] = [\boldsymbol v_0, s_0] + \epsilon [\boldsymbol v_\epsilon, s_\epsilon]
+         * @f]
+         */
+        constexpr /*implicit*/ DualQuaternion(const Dual<Vector3<T>>& vector, const Dual<T>& scalar)
+            #ifndef DOXYGEN_GENERATING_OUTPUT
+            : Dual<Quaternion<T>>{{vector.real(), scalar.real()}, {vector.dual(), scalar.dual()}}
+            #endif
+            {}
+
         /**
          * @brief Construct dual quaternion from vector
          *

src/Magnum/Math/Test/DualQuaternionTest.cpp

@@ -60,6 +60,7 @@ struct DualQuaternionTest: Corrade::TestSuite::Tester {
     explicit DualQuaternionTest();
 
     void construct();
+    void constructVectorScalar();
     void constructIdentity();
     void constructZero();
     void constructNoInit();
@@ -102,6 +103,7 @@ typedef Math::Vector3<Float> Vector3;
 
 DualQuaternionTest::DualQuaternionTest() {
     addTests({&DualQuaternionTest::construct,
+              &DualQuaternionTest::constructVectorScalar,
               &DualQuaternionTest::constructIdentity,
               &DualQuaternionTest::constructZero,
               &DualQuaternionTest::constructNoInit,
@@ -148,6 +150,17 @@ void DualQuaternionTest::construct() {
     CORRADE_COMPARE(d, DualQuaternion({{1.0f, 2.0f, 3.0f}, -4.0f}, {{0.0f, 0.0f, 0.0f}, 0.0f}));
 }
 
+void DualQuaternionTest::constructVectorScalar() {
+    constexpr DualQuaternion a = {{{1.0f, 2.0f, 3.0f}, {0.5f, -3.1f, 3.3f}}, {-4.0f, 2.0f}};
+    CORRADE_COMPARE(a, DualQuaternion({{1.0f, 2.0f, 3.0f}, -4.0f}, {{0.5f, -3.1f, 3.3f}, 2.0f}));
+
+    constexpr Quaternion b = a.real();
+    CORRADE_COMPARE(b, Quaternion({1.0f, 2.0f, 3.0f}, -4.0f));
+
+    constexpr Quaternion c = a.dual();
+    CORRADE_COMPARE(c, Quaternion({0.5f, -3.1f, 3.3f}, 2.0f));
+}
+
 void DualQuaternionTest::constructIdentity() {
     constexpr DualQuaternion a;
     constexpr DualQuaternion b{IdentityInit};