Math: utility function for conversion between CIE xyY and CIE XYZ.

src/Magnum/Math/Color.h

@@ -406,7 +406,7 @@ template<class T> class Color3: public Vector3<T> {
          *          0.0557 & -0.2040 & 1.0570
          *      \end{bmatrix} \begin{bmatrix} X \\ Y \\ Z \end{bmatrix}
          * @f]
-         * @see @ref toXyz(), @ref toSrgb()
+         * @see @ref toXyz(), @ref toSrgb(), @ref xyYToXyz()
          */
         static Color3<T> fromXyz(const Vector3<FloatingPointType>& xyz) {
             return Implementation::fromXyz<T>(xyz);
@@ -572,7 +572,7 @@ template<class T> class Color3: public Vector3<T> {
          * Please note that @ref x(), @ref y() and @ref z() *do not* correspond
          * to primaries in CIE XYZ color space, but are rather aliases to
          * @ref r(), @ref g() and @ref b().
-         * @see @ref fromXyz(), @ref fromSrgb()
+         * @see @ref fromXyz(), @ref fromSrgb(), @ref xyzToXyY()
          */
         Vector3<FloatingPointType> toXyz() const {
             return Implementation::toXyz<T>(*this);
@@ -786,7 +786,7 @@ class Color4: public Vector4<T> {
          *
          * Applies transformation matrix, returning the input in linear RGB
          * color space. See @ref Color3::fromXyz() for more information.
-         * @see @ref toXyz(), @ref toSrgbAlpha()
+         * @see @ref toXyz(), @ref toSrgbAlpha(), @ref xyYToXyz()
          */
         static Color4<T> fromXyz(const Vector3<FloatingPointType> xyz, T a = Implementation::fullChannel<T>()) {
             return {Implementation::fromXyz<T>(xyz), a};
@@ -944,7 +944,7 @@ class Color4: public Vector4<T> {
          * Please note that @ref xyz(), @ref x(), @ref y() and @ref z() *do not*
          * correspond to primaries in CIE XYZ color space, but are rather
          * aliases to @ref rgb(), @ref r(), @ref g() and @ref b().
-         * @see @ref fromXyz()
+         * @see @ref fromXyz(), @ref xyzToXyY()
          */
         Vector3<FloatingPointType> toXyz() const {
             return Implementation::toXyz<T>(rgb());
@@ -962,6 +962,36 @@ class Color4: public Vector4<T> {
         MAGNUM_VECTOR_SUBCLASS_IMPLEMENTATION(4, Color4)
 };
 
+/** @relatesalso Color3
+@brief Convert color from CIE xyY representation to CIE XYZ
+
+@f[
+    \begin{array}{rcl}
+        X & = & \dfrac{Y}{y}x \\
+        Z & = & \dfrac{Y}{y}(1 - x - y)
+    \end{array}
+@f]
+@see @ref xyzToXyY(), @ref Color3::fromXyz(), @ref Color3::toXyz()
+*/
+template<class T> inline Vector3<T> xyYToXyz(const Vector3<T>& xyY) {
+    return {xyY[0]*xyY[2]/xyY[1], xyY[2], (T(1) - xyY[0] - xyY[1])*xyY[2]/xyY[1]};
+}
+
+/** @relatesalso Color3
+@brief Convert color from CIE XYZ representation to CIE xyY
+
+@f[
+    \begin{array}{rcl}
+        x & = & \dfrac{X}{X + Y + Z} \\
+        y & = & \dfrac{Y}{X + Y + Z}
+    \end{array}
+@f]
+@see @ref xyYToXyz(), @ref Color3::fromXyz(), @ref Color3::toXyz()
+*/
+template<class T> inline Vector3<T> xyzToXyY(const Vector3<T>& xyz) {
+    return {xyz.xy()/xyz.sum(), xyz.y()};
+}
+
 #ifndef DOXYGEN_GENERATING_OUTPUT
 MAGNUM_VECTORn_OPERATOR_IMPLEMENTATION(4, Color4)
 #endif

src/Magnum/Math/Test/ColorTest.cpp

@@ -99,6 +99,7 @@ struct ColorTest: Corrade::TestSuite::Tester {
 
     void xyz();
     void fromXyzDefaultAlpha();
+    void xyY();
 
     void swizzleType();
     void debug();
@@ -150,6 +151,7 @@ ColorTest::ColorTest() {
 
               &ColorTest::xyz,
               &ColorTest::fromXyzDefaultAlpha,
+              &ColorTest::xyY,
 
               &ColorTest::swizzleType,
               &ColorTest::debug,
@@ -749,6 +751,15 @@ void ColorTest::fromXyzDefaultAlpha() {
         (Math::Color4<UnsignedShort>{52883, 22095, 339, 65535}));
 }
 
+void ColorTest::xyY() {
+    /* Verified using http://www.easyrgb.com/index.php?X=CALC */
+    Vector3 xyz{0.454279f, 0.413092f, 0.0607124f};
+    Vector3 xyY{0.489481f, 0.445102f, 0.413092f};
+
+    CORRADE_COMPARE(xyzToXyY(xyz), xyY);
+    CORRADE_COMPARE(xyYToXyz(xyY), xyz);
+}
+
 void ColorTest::swizzleType() {
     constexpr Color3 origColor3;
     constexpr Color4ub origColor4;