Math: make Matrix4::transformPoint() work with projection matrices.

Dividing by w instead of ignoring it.

src/Magnum/Math/Matrix4.h

@@ -447,13 +447,14 @@ template<class T> class Matrix4: public Matrix4x4<T> {
          *
          * Unlike in @ref transformVector(), translation is also involved in
          * the transformation. @f[
-         *      \boldsymbol v' = \boldsymbol M \begin{pmatrix} v_x \\ v_y \\ v_z \\ 1 \end{pmatrix}
+         *      \boldsymbol v' = v''_{xyz} / v''_w ~~~~~~~~~~ \boldsymbol v'' = \begin{pmatrix} v''_x \\ v''_y \\ v''_z \\ v''_w \end{pmatrix} = \boldsymbol M \begin{pmatrix} v_x \\ v_y \\ v_z \\ 1 \end{pmatrix} \\
          * @f]
          * @see @ref DualQuaternion::transformPoint(),
          *      @ref Matrix3::transformPoint()
          */
         Vector3<T> transformPoint(const Vector3<T>& vector) const {
-            return ((*this)*Vector4<T>(vector, T(1))).xyz();
+            const Vector4<T> transformed{(*this)*Vector4<T>(vector, T(1))};
+            return transformed.xyz()/transformed.w();
         }
 
         MAGNUM_RECTANGULARMATRIX_SUBCLASS_IMPLEMENTATION(4, 4, Matrix4<T>)

src/Magnum/Math/Test/Matrix4Test.cpp

@@ -95,6 +95,7 @@ struct Matrix4Test: Corrade::TestSuite::Tester {
     void vectorParts();
     void invertedRigid();
     void transform();
+    void transformProjection();
 
     void debug();
     void configuration();
@@ -143,6 +144,7 @@ Matrix4Test::Matrix4Test() {
               &Matrix4Test::vectorParts,
               &Matrix4Test::invertedRigid,
               &Matrix4Test::transform,
+              &Matrix4Test::transformProjection,
 
               &Matrix4Test::debug,
               &Matrix4Test::configuration});
@@ -546,6 +548,14 @@ void Matrix4Test::transform() {
     CORRADE_COMPARE(a.transformPoint(v), Vector3(3.0f, -4.0f, 9.0f));
 }
 
+void Matrix4Test::transformProjection() {
+    Matrix4 a = Matrix4::perspectiveProjection({2.0f, 2.0f}, 1.0f, 100.0f);
+    Vector3 v{0.0f, 0.0f, -100.0f};
+
+    CORRADE_COMPARE(a.transformVector(v), Vector3(0.0f, 0.0f, 0.0f));
+    CORRADE_COMPARE(a.transformPoint(v), Vector3(0.0f, 0.0f, 1.0f));
+}
+
 void Matrix4Test::lookAt() {
     Matrix4 a = Matrix4::lookAt({0.0f, 0.0f, 0.0f},
                                 {0.0f, 1.0f, 0.0f},