Math: added lerpInverted().

src/Math/Functions.h

@@ -279,7 +279,7 @@ template<std::size_t size, class T> Vector<size, T> clamp(const Vector<size, T>&
 The interpolation for vectors is done as in following, similarly for scalars: @f[
     \boldsymbol v_{LERP} = (1 - t) \boldsymbol v_A + t \boldsymbol v_B
 @f]
-@see Quaternion::lerp()
+@see lerpInverted(), Quaternion::lerp()
 @todo http://fgiesen.wordpress.com/2012/08/15/linear-interpolation-past-present-and-future/
     (when SIMD is in place)
 */
@@ -294,6 +294,28 @@ template<std::size_t size, class T, class U> inline Vector<size, T> lerp(const V
 }
 #endif
 
+/**
+@brief Inverse linear interpolation of two values
+@param a    First value
+@param b    Second value
+@param lerp Interpolated value
+
+Returns interpolation phase *t*: @f[
+    t = \frac{\boldsymbol v_{LERP} - \boldsymbol v_A}{\boldsymbol v_B - \boldsymbol v_A}
+@f]
+@see lerp()
+*/
+#ifdef DOXYGEN_GENERATING_OUTPUT
+template<class T> inline T lerpInverted(const T& a, const T& b, const T& lerp);
+#else
+template<class T> inline T lerpInverted(T a, T b, T lerp) {
+    return (lerp - a)/(b - a);
+}
+template<std::size_t size, class T, class U> inline Vector<size, T> lerpInverted(const Vector<size, T>& a, const Vector<size, T>& b, const Vector<size, T>& lerp) {
+    return (lerp - a)/(b - a);
+}
+#endif
+
 /**
 @brief Fused multiply-add
 

src/Math/Test/FunctionsTest.cpp

@@ -43,6 +43,7 @@ class FunctionsTest: public Corrade::TestSuite::Tester {
         void sqrtInverted();
         void clamp();
         void lerp();
+        void lerpInverted();
         void fma();
         void normalizeUnsigned();
         void normalizeSigned();
@@ -79,6 +80,7 @@ FunctionsTest::FunctionsTest() {
               &FunctionsTest::sqrtInverted,
               &FunctionsTest::clamp,
               &FunctionsTest::lerp,
+              &FunctionsTest::lerpInverted,
               &FunctionsTest::fma,
               &FunctionsTest::normalizeUnsigned,
               &FunctionsTest::normalizeSigned,
@@ -171,6 +173,16 @@ void FunctionsTest::lerp() {
     CORRADE_COMPARE(Math::lerp(a, b, Vector3(0.25f, 0.5f, 0.75f)), Vector3(0.0f, 0.0f, 9.0f));
 }
 
+void FunctionsTest::lerpInverted() {
+    /* Floating-point scalar */
+    CORRADE_COMPARE(Math::lerpInverted(2.0f, 5.0f, 3.5f), 0.5f);
+
+    /* Floating-point vector */
+    Vector3 a(-1.0f, 2.0f, 3.0f);
+    Vector3 b(3.0f, -2.0f, 11.0f);
+    CORRADE_COMPARE(Math::lerpInverted(a, b, Vector3(0.0f, 0.0f, 9.0f)), Vector3(0.25f, 0.5f, 0.75f));
+}
+
 void FunctionsTest::fma() {
     CORRADE_COMPARE(Math::fma(2.0f, 3.0f, 0.75f), 6.75f);
     CORRADE_COMPARE(Math::fma(Vector3( 2.0f,  1.5f,  0.5f),