Math: added Matrix4::lookAt().

src/Magnum/Math/Matrix4.h

@@ -224,6 +224,15 @@ template<class T> class Matrix4: public Matrix4x4<T> {
             return perspectiveProjection(Vector2<T>(xyScale, xyScale/aspectRatio), near, far);
         }
 
+        /**
+         * @brief Matrix oriented towards a specific point
+         * @param eye       Location to place the matrix
+         * @param target    Location towards which the matrix is oriented
+         * @param up        Vector as a guide of which way is up (should not be
+         *      the same direction as `target - eye`)
+         */
+        static Matrix4<T> lookAt(const Vector3<T>& eye, const Vector3<T>& target, const Vector3<T>& up);
+
         /**
          * @brief Create matrix from rotation/scaling part and translation part
          * @param rotationScaling   Rotation/scaling part (upper-left 3x3
@@ -528,6 +537,17 @@ template<class T> Matrix4<T> Matrix4<T>::perspectiveProjection(const Vector2<T>&
             {       T(0),        T(0), T(2)*far*near*zScale,  T(0)}};
 }
 
+template<class T> Matrix4<T> Matrix4<T>::lookAt(const Vector3<T>& eye, const Vector3<T>& target, const Vector3<T>& up) {
+    const Vector3<T> backward = (eye - target).normalized();
+    const Vector3<T> right = Vector3<T>::cross(up, backward).normalized();
+    const Vector3<T> realUp = Vector3<T>::cross(backward, right);
+
+    return {{   right, T(0)},
+            {  realUp, T(0)},
+            {backward, T(0)},
+            {     eye, T(1)}};
+}
+
 template<class T> inline Matrix3x3<T> Matrix4<T>::rotation() const {
     CORRADE_ASSERT(TypeTraits<T>::equals((*this)[0].xyz().dot(), (*this)[1].xyz().dot()) &&
                    TypeTraits<T>::equals((*this)[1].xyz().dot(), (*this)[2].xyz().dot()),

src/Magnum/Math/Test/Matrix4Test.cpp

@@ -85,6 +85,8 @@ struct Matrix4Test: Corrade::TestSuite::Tester {
     void orthographicProjection();
     void perspectiveProjection();
     void perspectiveProjectionFov();
+    void lookAt();
+
     void fromParts();
     void rotationScalingPart();
     void rotationNormalizedPart();
@@ -131,6 +133,8 @@ Matrix4Test::Matrix4Test() {
               &Matrix4Test::orthographicProjection,
               &Matrix4Test::perspectiveProjection,
               &Matrix4Test::perspectiveProjectionFov,
+              &Matrix4Test::lookAt,
+
               &Matrix4Test::fromParts,
               &Matrix4Test::rotationScalingPart,
               &Matrix4Test::rotationNormalizedPart,
@@ -507,6 +511,44 @@ void Matrix4Test::transform() {
     CORRADE_COMPARE(a.transformPoint(v), Vector3(3.0f, -4.0f, 9.0f));
 }
 
+void Matrix4Test::lookAt() {
+    Matrix4 a = Matrix4::lookAt({0.0f, 0.0f, 0.0f},
+                                {0.0f, 1.0f, 0.0f},
+                                {0.0f, 0.0f, 1.0f});
+    CORRADE_VERIFY(a.isRigidTransformation());
+    CORRADE_COMPARE(a, Matrix4({1.0f,  0.0f, 0.0f, 0.0f},
+                               {0.0f,  0.0f, 1.0f, 0.0f},
+                               {0.0f, -1.0f, 0.0f, 0.0f},
+                               {0.0f,  0.0f, 0.0f, 1.0f}));
+
+    Matrix4 b = Matrix4::lookAt({100.0f, 200.0f, 300.0f},
+                                {  0.0f,   0.0f,   0.0f},
+                                {  0.0f,   1.0f,   0.0f});
+    CORRADE_VERIFY(b.isRigidTransformation());
+    CORRADE_COMPARE(b, Matrix4({ 0.948683f,      0.0f, -0.316228f, 0.0f},
+                               {-0.169031f, 0.845154f, -0.507093f, 0.0f},
+                               { 0.267261f, 0.534522f,  0.801784f, 0.0f},
+                               {    100.0f,    200.0f,     300.0f, 1.0f}));
+
+    Matrix4 c = Matrix4::lookAt({3.0f, 0.0f, 0.0f},
+                                {0.0f, 4.0f, 5.0f},
+                                {0.0f, 0.0f, 1.0f});
+    CORRADE_VERIFY(c.isRigidTransformation());
+    CORRADE_COMPARE(c, Matrix4({     0.8f,       0.6f,       0.0f, 0.0f},
+                               {0.424264f, -0.565685f,  0.707107f, 0.0f},
+                               {0.424264f, -0.565685f, -0.707107f, 0.0f},
+                               {     3.0f,       0.0f,       0.0f, 1.0f}));
+
+    Matrix4 d = Matrix4::lookAt({ 0.0f, 3.0f,  0.0f},
+                                {-5.0f, 0.0f, -4.0f},
+                                { 0.0f, 1.0f,  0.0f});
+    CORRADE_VERIFY(d.isRigidTransformation());
+    CORRADE_COMPARE(d, Matrix4({ 0.624695f,      0.0f, -0.780869f, 0.0f},
+                               {-0.331295f, 0.905539f, -0.265036f, 0.0f},
+                               { 0.707107f, 0.424264f,  0.565685f, 0.0f},
+                               {      0.0f,      3.0f,       0.0f, 1.0f}));
+}
+
 void Matrix4Test::debug() {
     Matrix4 m({3.0f,  5.0f, 8.0f, 4.0f},
               {4.0f,  4.0f, 7.0f, 3.0f},