diff --git a/src/AbstractShaderProgram.h b/src/AbstractShaderProgram.h
index 8078c9e6f..2d5b410b9 100644
--- a/src/AbstractShaderProgram.h
+++ b/src/AbstractShaderProgram.h
@@ -41,7 +41,7 @@ functions and properties:
  - <strong>%Attribute location</strong> typedefs defining locations and types
    for attribute binding with Mesh::bindAttribute(), for example:
 @code
-typedef Attribute<0, Vector4> Position;
+typedef Attribute<0, Point3D> Position;
 typedef Attribute<1, Vector3> Normal;
 typedef Attribute<2, Vector2> TextureCoords;
 @endcode
diff --git a/src/Magnum.h b/src/Magnum.h
index 49fe94f59..63bcc00c7 100644
--- a/src/Magnum.h
+++ b/src/Magnum.h
@@ -41,6 +41,8 @@ namespace Magnum {
         template<class> class Vector2;
         template<class> class Vector3;
         template<class> class Vector4;
+        template<class> class Point2D;
+        template<class> class Point3D;
         template<class> class Matrix3;
         template<class> class Matrix4;
 
@@ -62,6 +64,12 @@ typedef Math::Vector3<GLfloat> Vector3;
 /** @brief Four-component floating-point vector */
 typedef Math::Vector4<GLfloat> Vector4;
 
+/** @brief Two-dimensional floating-point homogeneous coordinates */
+typedef Math::Point2D<GLfloat> Point2D;
+
+/** @brief Three-dimensional floating-point homogeneous coordinates */
+typedef Math::Point3D<GLfloat> Point3D;
+
 /** @brief 3x3 floating-point matrix */
 typedef Math::Matrix3<GLfloat> Matrix3;
 
diff --git a/src/Math/CMakeLists.txt b/src/Math/CMakeLists.txt
index edcfe14ac..a92da34c4 100644
--- a/src/Math/CMakeLists.txt
+++ b/src/Math/CMakeLists.txt
@@ -7,6 +7,8 @@ set(MagnumMath_HEADERS
     Matrix.h
     Matrix3.h
     Matrix4.h
+    Point2D.h
+    Point3D.h
     RectangularMatrix.h
     Vector.h
     Vector2.h
diff --git a/src/Math/Point2D.h b/src/Math/Point2D.h
new file mode 100644
index 000000000..953438d51
--- /dev/null
+++ b/src/Math/Point2D.h
@@ -0,0 +1,74 @@
+#ifndef Magnum_Math_Point2D_h
+#define Magnum_Math_Point2D_h
+/*
+    Copyright © 2010, 2011, 2012 Vladimír Vondruš <mosra@centrum.cz>
+
+    This file is part of Magnum.
+
+    Magnum is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License version 3
+    only, as published by the Free Software Foundation.
+
+    Magnum is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License version 3 for more details.
+*/
+
+/** @file
+ * @brief Class Magnum::Math::Point2D
+ */
+
+#include "Vector3.h"
+
+namespace Magnum { namespace Math {
+
+/**
+@brief Two-dimensional homogeneous coordinates
+@tparam T   Data type
+
+Same as Vector3, except that constructors have default value for Z component
+set to one. See also @ref matrix-vector for brief introduction.
+@configurationvalueref{Magnum::Math::Point2D}
+*/
+template<class T> class Point2D: public Vector3<T> {
+    public:
+        /**
+         * @brief Default constructor
+         *
+         * X and Y components are set to zero, Z is set to one.
+         */
+        inline constexpr Point2D(): Vector3<T>(T(0), T(0), T(1)) {}
+
+        /** @brief Copy constructor */
+        inline constexpr Point2D(const RectangularMatrix<1, 3, T>& other): Vector3<T>(other) {}
+
+        /**
+         * @brief Constructor
+         * @param x     X component
+         * @param y     Y component
+         * @param z     Z component
+         */
+        inline constexpr Point2D(T x, T y, T z = T(1)): Vector3<T>(x, y, z) {}
+
+        /**
+         * @brief Constructor
+         * @param xy    Two-component vector
+         * @param z     Z component
+         */
+        inline constexpr Point2D(const Vector<2, T>& xy, T z = T(1)): Vector3<T>(xy, z) {}
+};
+
+/** @debugoperator{Magnum::Math::Point2D} */
+template<class T> Corrade::Utility::Debug operator<<(Corrade::Utility::Debug debug, const Magnum::Math::Point2D<T>& value) {
+    return debug << static_cast<const Magnum::Math::Vector<3, T>&>(value);
+}
+
+}}
+
+namespace Corrade { namespace Utility {
+    /** @configurationvalue{Magnum::Math::Point2D} */
+    template<class T> struct ConfigurationValue<Magnum::Math::Point2D<T>>: public ConfigurationValue<Magnum::Math::Vector<3, T>> {};
+}}
+
+#endif
diff --git a/src/Math/Point3D.h b/src/Math/Point3D.h
new file mode 100644
index 000000000..e92e1e7b1
--- /dev/null
+++ b/src/Math/Point3D.h
@@ -0,0 +1,75 @@
+#ifndef Magnum_Math_Point3D_h
+#define Magnum_Math_Point3D_h
+/*
+    Copyright © 2010, 2011, 2012 Vladimír Vondruš <mosra@centrum.cz>
+
+    This file is part of Magnum.
+
+    Magnum is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License version 3
+    only, as published by the Free Software Foundation.
+
+    Magnum is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License version 3 for more details.
+*/
+
+/** @file
+ * @brief Class Magnum::Math::Point3D
+ */
+
+#include "Vector4.h"
+
+namespace Magnum { namespace Math {
+
+/**
+@brief Three-dimensional homogeneous coordinates
+@tparam T   Data type
+
+Same as Vector4, except that constructors have default value for W component
+set to one. See also @ref matrix-vector for brief introduction.
+@configurationvalueref{Magnum::Math::Point3D}
+*/
+template<class T> class Point3D: public Vector4<T> {
+    public:
+        /**
+         * @brief Default constructor
+         *
+         * X, Y and Z components are set to zero, W is set to one.
+         */
+        inline constexpr Point3D(): Vector4<T>(T(0), T(0), T(0), T(1)) {}
+
+        /** @brief Copy constructor */
+        inline constexpr Point3D(const RectangularMatrix<1, 4, T>& other): Vector4<T>(other) {}
+
+        /**
+         * @brief Constructor
+         * @param x     X component
+         * @param y     Y component
+         * @param z     Z component
+         * @param w     W component
+         */
+        inline constexpr Point3D(T x, T y, T z, T w = T(1)): Vector4<T>(x, y, z, w) {}
+
+        /**
+         * @brief Constructor
+         * @param xyz   Three-component vector
+         * @param w     W component
+         */
+        inline constexpr Point3D(const Vector<3, T>& xyz, T w = T(1)): Vector4<T>(xyz, w) {}
+};
+
+/** @debugoperator{Magnum::Math::Point3D} */
+template<class T> Corrade::Utility::Debug operator<<(Corrade::Utility::Debug debug, const Magnum::Math::Point3D<T>& value) {
+    return debug << static_cast<const Magnum::Math::Vector<4, T>&>(value);
+}
+
+}}
+
+namespace Corrade { namespace Utility {
+    /** @configurationvalue{Magnum::Math::Point3D} */
+    template<class T> struct ConfigurationValue<Magnum::Math::Point3D<T>>: public ConfigurationValue<Magnum::Math::Vector<4, T>> {};
+}}
+
+#endif
diff --git a/src/Math/Test/CMakeLists.txt b/src/Math/Test/CMakeLists.txt
index 8f3690ea8..a62ecefca 100644
--- a/src/Math/Test/CMakeLists.txt
+++ b/src/Math/Test/CMakeLists.txt
@@ -10,6 +10,9 @@ corrade_add_test2(MathVector2Test Vector2Test.cpp)
 corrade_add_test2(MathVector3Test Vector3Test.cpp)
 corrade_add_test2(MathVector4Test Vector4Test.cpp)
 
+corrade_add_test2(MathPoint2DTest Point2DTest.cpp)
+corrade_add_test2(MathPoint3DTest Point3DTest.cpp)
+
 corrade_add_test2(MathMatrixTest MatrixTest.cpp)
 corrade_add_test2(MathMatrix3Test Matrix3Test.cpp)
 corrade_add_test2(MathMatrix4Test Matrix4Test.cpp)
diff --git a/src/Math/Test/Point2DTest.cpp b/src/Math/Test/Point2DTest.cpp
new file mode 100644
index 000000000..64d5540bc
--- /dev/null
+++ b/src/Math/Test/Point2DTest.cpp
@@ -0,0 +1,56 @@
+/*
+    Copyright © 2010, 2011, 2012 Vladimír Vondruš <mosra@centrum.cz>
+
+    This file is part of Magnum.
+
+    Magnum is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License version 3
+    only, as published by the Free Software Foundation.
+
+    Magnum is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License version 3 for more details.
+*/
+
+#include "Point2DTest.h"
+
+#include <sstream>
+
+#include "Point2D.h"
+
+CORRADE_TEST_MAIN(Magnum::Math::Test::Point2DTest)
+
+using namespace std;
+using namespace Corrade::Utility;
+
+namespace Magnum { namespace Math { namespace Test {
+
+typedef Math::Point2D<float> Point2D;
+
+Point2DTest::Point2DTest() {
+    addTests(&Point2DTest::construct,
+             &Point2DTest::debug,
+             &Point2DTest::configuration);
+}
+
+void Point2DTest::construct() {
+    CORRADE_COMPARE(Point2D(), (Vector<3, float>(0.0f, 0.0f, 1.0f)));
+    CORRADE_COMPARE(Point2D(1, 2), (Vector<3, float>(1.0f, 2.0f, 1.0f)));
+    CORRADE_COMPARE(Point2D(Vector<2, float>(1.0f, 2.0f), 3), (Vector<3, float>(1.0f, 2.0f, 3.0f)));
+}
+
+void Point2DTest::debug() {
+    ostringstream o;
+    Debug(&o) << Point2D(0.5f, 15.0f, 1.0f);
+    CORRADE_COMPARE(o.str(), "Vector(0.5, 15, 1)\n");
+}
+
+void Point2DTest::configuration() {
+    Point2D vec(3.0f, 3.125f, 9.55f);
+    string value("3 3.125 9.55");
+    CORRADE_COMPARE(ConfigurationValue<Point2D>::toString(vec), value);
+    CORRADE_COMPARE(ConfigurationValue<Point2D>::fromString(value), vec);
+}
+
+}}}
diff --git a/src/Math/Test/Point2DTest.h b/src/Math/Test/Point2DTest.h
new file mode 100644
index 000000000..39ec72d3b
--- /dev/null
+++ b/src/Math/Test/Point2DTest.h
@@ -0,0 +1,33 @@
+#ifndef Magnum_Math_Test_Point2DTest_h
+#define Magnum_Math_Test_Point2DTest_h
+/*
+    Copyright © 2010, 2011, 2012 Vladimír Vondruš <mosra@centrum.cz>
+
+    This file is part of Magnum.
+
+    Magnum is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License version 3
+    only, as published by the Free Software Foundation.
+
+    Magnum is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License version 3 for more details.
+*/
+
+#include <TestSuite/Tester.h>
+
+namespace Magnum { namespace Math { namespace Test {
+
+class Point2DTest: public Corrade::TestSuite::Tester<Point2DTest> {
+    public:
+        Point2DTest();
+
+        void construct();
+        void debug();
+        void configuration();
+};
+
+}}}
+
+#endif
diff --git a/src/Math/Test/Point3DTest.cpp b/src/Math/Test/Point3DTest.cpp
new file mode 100644
index 000000000..092f5a0f0
--- /dev/null
+++ b/src/Math/Test/Point3DTest.cpp
@@ -0,0 +1,56 @@
+/*
+    Copyright © 2010, 2011, 2012 Vladimír Vondruš <mosra@centrum.cz>
+
+    This file is part of Magnum.
+
+    Magnum is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License version 3
+    only, as published by the Free Software Foundation.
+
+    Magnum is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License version 3 for more details.
+*/
+
+#include "Point3DTest.h"
+
+#include <sstream>
+
+#include "Point3D.h"
+
+CORRADE_TEST_MAIN(Magnum::Math::Test::Point3DTest)
+
+using namespace std;
+using namespace Corrade::Utility;
+
+namespace Magnum { namespace Math { namespace Test {
+
+typedef Math::Point3D<float> Point3D;
+
+Point3DTest::Point3DTest() {
+    addTests(&Point3DTest::construct,
+             &Point3DTest::debug,
+             &Point3DTest::configuration);
+}
+
+void Point3DTest::construct() {
+    CORRADE_COMPARE(Point3D(), Point3D(0.0f, 0.0f, 0.0f, 1.0f));
+    CORRADE_COMPARE(Point3D(1, 2, 3, 4), (Vector<4, float>(1.0f, 2.0f, 3.0f, 4.0f)));
+    CORRADE_COMPARE(Point3D(Vector<3, float>(1.0f, 2.0f, 3.0f), 4), (Vector<4, float>(1.0f, 2.0f, 3.0f, 4.0f)));
+}
+
+void Point3DTest::debug() {
+    ostringstream o;
+    Debug(&o) << Point3D(0.5f, 15.0f, 1.0f, 1.0f);
+    CORRADE_COMPARE(o.str(), "Vector(0.5, 15, 1, 1)\n");
+}
+
+void Point3DTest::configuration() {
+    Point3D vec(3.0f, 3.125f, 9.0f, 9.55f);
+    string value("3 3.125 9 9.55");
+    CORRADE_COMPARE(ConfigurationValue<Point3D>::toString(vec), value);
+    CORRADE_COMPARE(ConfigurationValue<Point3D>::fromString(value), vec);
+}
+
+}}}
diff --git a/src/Math/Test/Point3DTest.h b/src/Math/Test/Point3DTest.h
new file mode 100644
index 000000000..9560e01d5
--- /dev/null
+++ b/src/Math/Test/Point3DTest.h
@@ -0,0 +1,33 @@
+#ifndef Magnum_Math_Test_Point3DTest_h
+#define Magnum_Math_Test_Point3DTest_h
+/*
+    Copyright © 2010, 2011, 2012 Vladimír Vondruš <mosra@centrum.cz>
+
+    This file is part of Magnum.
+
+    Magnum is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License version 3
+    only, as published by the Free Software Foundation.
+
+    Magnum is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License version 3 for more details.
+*/
+
+#include <TestSuite/Tester.h>
+
+namespace Magnum { namespace Math { namespace Test {
+
+class Point3DTest: public Corrade::TestSuite::Tester<Point3DTest> {
+    public:
+        Point3DTest();
+
+        void construct();
+        void debug();
+        void configuration();
+};
+
+}}}
+
+#endif
diff --git a/src/Math/Test/Vector3Test.cpp b/src/Math/Test/Vector3Test.cpp
index 710c60cd0..6ffdc267d 100644
--- a/src/Math/Test/Vector3Test.cpp
+++ b/src/Math/Test/Vector3Test.cpp
@@ -40,6 +40,7 @@ Vector3Test::Vector3Test() {
 }
 
 void Vector3Test::construct() {
+    CORRADE_COMPARE(Vector3(), Vector3(0.0f, 0.0f, 0.0f));
     CORRADE_COMPARE(Vector3(1, 2, 3), (Vector<3, float>(1.0f, 2.0f, 3.0f)));
     CORRADE_COMPARE(Vector3(Vector<2, float>(1.0f, 2.0f), 3), (Vector<3, float>(1.0f, 2.0f, 3.0f)));
 }
diff --git a/src/Math/Test/Vector4Test.cpp b/src/Math/Test/Vector4Test.cpp
index b8765b65b..c12838a20 100644
--- a/src/Math/Test/Vector4Test.cpp
+++ b/src/Math/Test/Vector4Test.cpp
@@ -39,7 +39,7 @@ Vector4Test::Vector4Test() {
 }
 
 void Vector4Test::construct() {
-    CORRADE_COMPARE(Vector4(), Vector4(0.0f, 0.0f, 0.0f, 1.0f));
+    CORRADE_COMPARE(Vector4(), Vector4(0.0f, 0.0f, 0.0f, 0.0f));
     CORRADE_COMPARE(Vector4(1, 2, 3, 4), (Vector<4, float>(1.0f, 2.0f, 3.0f, 4.0f)));
     CORRADE_COMPARE(Vector4(Vector<3, float>(1.0f, 2.0f, 3.0f), 4), (Vector<4, float>(1.0f, 2.0f, 3.0f, 4.0f)));
 }
diff --git a/src/Math/Vector3.h b/src/Math/Vector3.h
index 990a6cba2..79a3a9075 100644
--- a/src/Math/Vector3.h
+++ b/src/Math/Vector3.h
@@ -27,7 +27,8 @@ namespace Magnum { namespace Math {
 @brief Three-component vector
 @tparam T   Data type
 
-See @ref matrix-vector for brief introduction.
+See @ref matrix-vector for brief introduction. See also Point2D for
+homogeneous two-dimensional coordinates.
 @configurationvalueref{Magnum::Math::Vector3}
 */
 template<class T> class Vector3: public Vector<3, T> {
diff --git a/src/Math/Vector4.h b/src/Math/Vector4.h
index 2fc35f9de..0df339f24 100644
--- a/src/Math/Vector4.h
+++ b/src/Math/Vector4.h
@@ -27,16 +27,14 @@ namespace Magnum { namespace Math {
 @brief Four-component vector
 @tparam T   Data type
 
-See @ref matrix-vector for brief introduction.
+See @ref matrix-vector for brief introduction. See also Point3D for
+homogeneous three-dimensional coordinates.
 @configurationvalueref{Magnum::Math::Vector4}
 */
 template<class T> class Vector4: public Vector<4, T> {
     public:
-        /**
-         * @copydoc Vector::Vector
-         * W component is set to one.
-         */
-        inline constexpr Vector4(): Vector<4, T>(T(0), T(0), T(0), T(1)) {}
+        /** @copydoc Vector::Vector() */
+        inline constexpr Vector4() {}
 
         /** @copydoc Vector::Vector(T) */
         inline constexpr explicit Vector4(T value): Vector<4, T>(value, value, value, value) {}
@@ -51,16 +49,14 @@ template<class T> class Vector4: public Vector<4, T> {
          * @param z     Z component
          * @param w     W component
          */
-        inline constexpr Vector4(T x, T y, T z, T w = T(1)): Vector<4, T>(x, y, z, w) {}
+        inline constexpr Vector4(T x, T y, T z, T w): Vector<4, T>(x, y, z, w) {}
 
         /**
          * @brief Constructor
          * @param xyz   Three-component vector
          * @param w     W component
          */
-        /* Not marked as explicit, because conversion from Vector3 to Vector4
-           is fairly common, nearly always with W set to 1 */
-        inline constexpr Vector4(const Vector<3, T>& xyz, T w = T(1)): Vector<4, T>(xyz[0], xyz[1], xyz[2], w) {}
+        inline constexpr Vector4(const Vector<3, T>& xyz, T w): Vector<4, T>(xyz[0], xyz[1], xyz[2], w) {}
 
         inline T& x() { return (*this)[0]; }                /**< @brief X component */
         inline constexpr T x() const { return (*this)[0]; } /**< @overload */
diff --git a/src/MeshTools/CombineIndexedArrays.h b/src/MeshTools/CombineIndexedArrays.h
index 6f4f8f699..25a8cca4e 100644
--- a/src/MeshTools/CombineIndexedArrays.h
+++ b/src/MeshTools/CombineIndexedArrays.h
@@ -106,7 +106,7 @@ of some STL functions like shown below. Also if one index array is shader by
 more than one attribute array, just pass the index array more times. Example:
 @code
 std::vector<unsigned int> vertexIndices;
-std::vector<Vector4> positions;
+std::vector<Point3D> positions;
 std::vector<unsigned int> normalTextureIndices;
 std::vector<Vector3> normals;
 std::vector<Vector2> textureCoordinates;
diff --git a/src/MeshTools/GenerateFlatNormals.cpp b/src/MeshTools/GenerateFlatNormals.cpp
index 50866eb18..5d4868a3b 100644
--- a/src/MeshTools/GenerateFlatNormals.cpp
+++ b/src/MeshTools/GenerateFlatNormals.cpp
@@ -15,14 +15,14 @@
 
 #include "GenerateFlatNormals.h"
 
-#include "Math/Vector4.h"
+#include "Math/Point3D.h"
 #include "MeshTools/Clean.h"
 
 using namespace std;
 
 namespace Magnum { namespace MeshTools {
 
-tuple<vector<unsigned int>, vector<Vector3>> generateFlatNormals(const vector<unsigned int>& indices, const vector<Vector4>& positions) {
+tuple<vector<unsigned int>, vector<Vector3>> generateFlatNormals(const vector<unsigned int>& indices, const vector<Point3D>& positions) {
     CORRADE_ASSERT(!(indices.size()%3), "MeshTools::generateFlatNormals(): index count is not divisible by 3!", (tuple<vector<unsigned int>, vector<Vector3>>()));
 
     /* Create normal for every triangle (assuming counterclockwise winding) */
diff --git a/src/MeshTools/GenerateFlatNormals.h b/src/MeshTools/GenerateFlatNormals.h
index 48f289e19..bdbcca05a 100644
--- a/src/MeshTools/GenerateFlatNormals.h
+++ b/src/MeshTools/GenerateFlatNormals.h
@@ -38,7 +38,7 @@ For each face generates one normal vector, removes duplicates before
 returning. Example usage:
 @code
 std::vector<unsigned int> vertexIndices;
-std::vector<Vector4> positions;
+std::vector<Point3D> positions;
 
 std::vector<unsigned int> normalIndices;
 std::vector<Vector3> normals;
@@ -50,7 +50,7 @@ use the same indices.
 @attention Index count must be divisible by 3, otherwise zero length result
     is generated.
 */
-std::tuple<std::vector<unsigned int>, std::vector<Vector3>> MESHTOOLS_EXPORT generateFlatNormals(const std::vector<unsigned int>& indices, const std::vector<Vector4>& positions);
+std::tuple<std::vector<unsigned int>, std::vector<Vector3>> MESHTOOLS_EXPORT generateFlatNormals(const std::vector<unsigned int>& indices, const std::vector<Point3D>& positions);
 
 }}
 
diff --git a/src/MeshTools/Test/GenerateFlatNormalsTest.cpp b/src/MeshTools/Test/GenerateFlatNormalsTest.cpp
index 8cf127a46..1de255976 100644
--- a/src/MeshTools/Test/GenerateFlatNormalsTest.cpp
+++ b/src/MeshTools/Test/GenerateFlatNormalsTest.cpp
@@ -17,7 +17,7 @@
 
 #include <sstream>
 
-#include "Math/Vector4.h"
+#include "Math/Point3D.h"
 #include "MeshTools/GenerateFlatNormals.h"
 
 CORRADE_TEST_MAIN(Magnum::MeshTools::Test::GenerateFlatNormalsTest)
diff --git a/src/Physics/AxisAlignedBox.cpp b/src/Physics/AxisAlignedBox.cpp
index b0ef33339..30ad3551b 100644
--- a/src/Physics/AxisAlignedBox.cpp
+++ b/src/Physics/AxisAlignedBox.cpp
@@ -16,11 +16,12 @@
 #include "AxisAlignedBox.h"
 
 #include "Math/Matrix4.h"
+#include "Math/Point3D.h"
 
 namespace Magnum { namespace Physics {
 
 void AxisAlignedBox::applyTransformation(const Matrix4& transformation) {
-    _transformedPosition = (transformation*Vector4(_position)).xyz();
+    _transformedPosition = (transformation*Point3D(_position)).xyz();
     _transformedSize = transformation.rotationScaling()*_size;
 }
 
diff --git a/src/Physics/Capsule.cpp b/src/Physics/Capsule.cpp
index 3f7936901..b6d175f7d 100644
--- a/src/Physics/Capsule.cpp
+++ b/src/Physics/Capsule.cpp
@@ -18,6 +18,7 @@
 #include "Math/Constants.h"
 #include "Math/Math.h"
 #include "Math/Matrix4.h"
+#include "Math/Point3D.h"
 #include "Math/Geometry/Distance.h"
 #include "Point.h"
 #include "Sphere.h"
@@ -27,8 +28,8 @@ using namespace Magnum::Math::Geometry;
 namespace Magnum { namespace Physics {
 
 void Capsule::applyTransformation(const Matrix4& transformation) {
-    _transformedA = (transformation*Vector4(_a)).xyz();
-    _transformedB = (transformation*Vector4(_b)).xyz();
+    _transformedA = (transformation*Point3D(_a)).xyz();
+    _transformedB = (transformation*Point3D(_b)).xyz();
     float scaling = (transformation.rotationScaling()*Vector3(1/Math::Constants<float>::sqrt3())).length();
     _transformedRadius = scaling*_radius;
 }
diff --git a/src/Physics/Line.cpp b/src/Physics/Line.cpp
index 010cf5c37..3dec9a602 100644
--- a/src/Physics/Line.cpp
+++ b/src/Physics/Line.cpp
@@ -16,12 +16,13 @@
 #include "Line.h"
 
 #include "Math/Matrix4.h"
+#include "Math/Point3D.h"
 
 namespace Magnum { namespace Physics {
 
 void Line::applyTransformation(const Matrix4& transformation) {
-    _transformedA = (transformation*Vector4(_a)).xyz();
-    _transformedB = (transformation*Vector4(_b)).xyz();
+    _transformedA = (transformation*Point3D(_a)).xyz();
+    _transformedB = (transformation*Point3D(_b)).xyz();
 }
 
 }}
diff --git a/src/Physics/Plane.cpp b/src/Physics/Plane.cpp
index 5ca9d49c3..124b28ccf 100644
--- a/src/Physics/Plane.cpp
+++ b/src/Physics/Plane.cpp
@@ -18,6 +18,7 @@
 #include <limits>
 
 #include "Math/Matrix4.h"
+#include "Math/Point3D.h"
 #include "Math/Geometry/Intersection.h"
 #include "LineSegment.h"
 
@@ -27,7 +28,7 @@ using namespace Magnum::Math::Geometry;
 namespace Magnum { namespace Physics {
 
 void Plane::applyTransformation(const Matrix4& transformation) {
-    _transformedPosition = (transformation*Vector4(_position)).xyz();
+    _transformedPosition = (transformation*Point3D(_position)).xyz();
     _transformedNormal = transformation.rotation()*_normal;
 }
 
diff --git a/src/Physics/Point.cpp b/src/Physics/Point.cpp
index eef45829f..6ec43579b 100644
--- a/src/Physics/Point.cpp
+++ b/src/Physics/Point.cpp
@@ -16,11 +16,12 @@
 #include "Point.h"
 
 #include "Math/Matrix4.h"
+#include "Math/Point3D.h"
 
 namespace Magnum { namespace Physics {
 
 void Point::applyTransformation(const Matrix4& transformation) {
-    _transformedPosition = (transformation*Vector4(_position)).xyz();
+    _transformedPosition = (transformation*Point3D(_position)).xyz();
 }
 
 }}
diff --git a/src/Physics/Sphere.cpp b/src/Physics/Sphere.cpp
index 54a656168..f3b0579b1 100644
--- a/src/Physics/Sphere.cpp
+++ b/src/Physics/Sphere.cpp
@@ -18,6 +18,7 @@
 #include "Math/Constants.h"
 #include "Math/Math.h"
 #include "Math/Matrix4.h"
+#include "Math/Point3D.h"
 #include "Math/Geometry/Distance.h"
 #include "LineSegment.h"
 #include "Point.h"
@@ -27,7 +28,7 @@ using namespace Magnum::Math::Geometry;
 namespace Magnum { namespace Physics {
 
 void Sphere::applyTransformation(const Matrix4& transformation) {
-    _transformedPosition = (transformation*Vector4(_position)).xyz();
+    _transformedPosition = (transformation*Point3D(_position)).xyz();
     float scaling = (transformation.rotationScaling()*Vector3(1/Math::Constants<float>::sqrt3())).length();
     _transformedRadius = scaling*_radius;
 }
diff --git a/src/Primitives/Capsule.cpp b/src/Primitives/Capsule.cpp
index 11fa8f9f0..c65c87d36 100644
--- a/src/Primitives/Capsule.cpp
+++ b/src/Primitives/Capsule.cpp
@@ -16,13 +16,13 @@
 #include "Capsule.h"
 
 #include "Math/Constants.h"
-#include "Math/Vector4.h"
+#include "Math/Point3D.h"
 
 using namespace std;
 
 namespace Magnum { namespace Primitives {
 
-Capsule::Capsule(unsigned int hemisphereRings, unsigned int cylinderRings, unsigned int segments, GLfloat length, TextureCoords textureCoords): MeshData("", Mesh::Primitive::Triangles, new vector<unsigned int>, {new vector<Vector4>()}, {new vector<Vector3>()}, textureCoords == TextureCoords::Generate ? vector<vector<Vector2>*>{new vector<Vector2>()} : vector<vector<Vector2>*>()), segments(segments), textureCoords(textureCoords) {
+Capsule::Capsule(unsigned int hemisphereRings, unsigned int cylinderRings, unsigned int segments, GLfloat length, TextureCoords textureCoords): MeshData("", Mesh::Primitive::Triangles, new vector<unsigned int>, {new vector<Point3D>()}, {new vector<Vector3>()}, textureCoords == TextureCoords::Generate ? vector<vector<Vector2>*>{new vector<Vector2>()} : vector<vector<Vector2>*>()), segments(segments), textureCoords(textureCoords) {
     CORRADE_ASSERT(hemisphereRings >= 1 && cylinderRings >= 1 && segments >= 3, "Capsule must have at least one hemisphere ring, one cylinder ring and three segments", );
 
     GLfloat height = 2.0f+length;
@@ -50,7 +50,7 @@ Capsule::Capsule(unsigned int hemisphereRings, unsigned int cylinderRings, unsig
     topFaceRing();
 }
 
-Capsule::Capsule(unsigned int segments, TextureCoords textureCoords): MeshData("", Mesh::Primitive::Triangles, new std::vector<unsigned int>, {new std::vector<Vector4>()}, {new std::vector<Vector3>()}, textureCoords == TextureCoords::Generate ? std::vector<std::vector<Vector2>*>{new std::vector<Vector2>()} : std::vector<std::vector<Vector2>*>()), segments(segments), textureCoords(textureCoords) {}
+Capsule::Capsule(unsigned int segments, TextureCoords textureCoords): MeshData("", Mesh::Primitive::Triangles, new std::vector<unsigned int>, {new std::vector<Point3D>()}, {new std::vector<Vector3>()}, textureCoords == TextureCoords::Generate ? std::vector<std::vector<Vector2>*>{new std::vector<Vector2>()} : std::vector<std::vector<Vector2>*>()), segments(segments), textureCoords(textureCoords) {}
 
 void Capsule::capVertex(GLfloat y, GLfloat normalY, GLfloat textureCoordsV) {
     positions(0)->push_back({0.0f, y, 0.0f});
diff --git a/src/Primitives/Cube.cpp b/src/Primitives/Cube.cpp
index c524fb77e..ec1917c5f 100644
--- a/src/Primitives/Cube.cpp
+++ b/src/Primitives/Cube.cpp
@@ -15,7 +15,7 @@
 
 #include "Cube.h"
 
-#include "Math/Vector4.h"
+#include "Math/Point3D.h"
 
 using namespace std;
 
@@ -34,7 +34,7 @@ Cube::Cube(): MeshData("", Mesh::Primitive::Triangles, new vector<unsigned int>{
     2, 6, 7,
     4, 1, 5,
     4, 0, 1
-}, {new vector<Vector4>}, {new vector<Vector3>{
+}, {new vector<Point3D>}, {new vector<Vector3>{
     {-1.0f, -1.0f, -1.0f},
     { 1.0f, -1.0f, -1.0f},
     {-1.0f,  1.0f, -1.0f},
diff --git a/src/Primitives/Cylinder.cpp b/src/Primitives/Cylinder.cpp
index 30a031538..709c7dfb9 100644
--- a/src/Primitives/Cylinder.cpp
+++ b/src/Primitives/Cylinder.cpp
@@ -16,7 +16,6 @@
 #include "Cylinder.h"
 
 #include "Math/Constants.h"
-#include "Math/Vector4.h"
 
 using namespace std;
 
diff --git a/src/Primitives/Icosphere.cpp b/src/Primitives/Icosphere.cpp
index 436937906..100858b8f 100644
--- a/src/Primitives/Icosphere.cpp
+++ b/src/Primitives/Icosphere.cpp
@@ -42,7 +42,7 @@ Icosphere<0>::Icosphere(): MeshData("", Mesh::Primitive::Triangles, new vector<u
     7, 1, 0,
     3, 9, 8,
     4, 8, 0
-}, {new vector<Vector4>}, {new vector<Vector3>{
+}, {new vector<Point3D>}, {new vector<Vector3>{
     Vector3(0, -0.525731f, 0.850651f),
     Vector3(0.850651f, 0, 0.525731f),
     Vector3(0.850651f, 0, -0.525731f),
diff --git a/src/Primitives/Plane.cpp b/src/Primitives/Plane.cpp
index 6db0eec5c..74d9a2054 100644
--- a/src/Primitives/Plane.cpp
+++ b/src/Primitives/Plane.cpp
@@ -15,13 +15,13 @@
 
 #include "Plane.h"
 
-#include "Math/Vector4.h"
+#include "Math/Point3D.h"
 
 using namespace std;
 
 namespace Magnum { namespace Primitives {
 
-Plane::Plane(): MeshData("", Mesh::Primitive::TriangleStrip, nullptr, {new vector<Vector4>{
+Plane::Plane(): MeshData("", Mesh::Primitive::TriangleStrip, nullptr, {new vector<Point3D>{
     {1.0f, -1.0f, 0.0f},
     {1.0f, 1.0f, 0.0f},
     {-1.0f, -1.0f, 0.0f},
diff --git a/src/Primitives/Test/CapsuleTest.cpp b/src/Primitives/Test/CapsuleTest.cpp
index 45e16738f..7d95515c3 100644
--- a/src/Primitives/Test/CapsuleTest.cpp
+++ b/src/Primitives/Test/CapsuleTest.cpp
@@ -20,7 +20,7 @@
 
 #include <TestSuite/Compare/Container.h>
 
-#include "Math/Vector4.h"
+#include "Math/Point3D.h"
 #include "Primitives/Capsule.h"
 
 using namespace std;
@@ -38,7 +38,7 @@ CapsuleTest::CapsuleTest() {
 void CapsuleTest::withoutTextureCoords() {
     Capsule capsule(2, 2, 3, 1.0f);
 
-    CORRADE_COMPARE_AS(*capsule.positions(0), (vector<Vector4>{
+    CORRADE_COMPARE_AS(*capsule.positions(0), (vector<Point3D>{
         {0.0f, -1.5f, 0.0f},
 
         {0.0f, -1.20711f, 0.707107f},
@@ -103,7 +103,7 @@ void CapsuleTest::withoutTextureCoords() {
 void CapsuleTest::withTextureCoords() {
     Capsule capsule(2, 2, 3, 1.0f, Capsule::TextureCoords::Generate);
 
-    CORRADE_COMPARE_AS(*capsule.positions(0), (vector<Vector4>{
+    CORRADE_COMPARE_AS(*capsule.positions(0), (vector<Point3D>{
         {0.0f, -1.5f, 0.0f},
 
         {0.0f, -1.20711f, 0.707107f},
diff --git a/src/Primitives/Test/CylinderTest.cpp b/src/Primitives/Test/CylinderTest.cpp
index 43efb5845..cb94fa6d7 100644
--- a/src/Primitives/Test/CylinderTest.cpp
+++ b/src/Primitives/Test/CylinderTest.cpp
@@ -17,7 +17,7 @@
 
 #include <TestSuite/Compare/Container.h>
 
-#include "Math/Vector4.h"
+#include "Math/Point3D.h"
 #include "Primitives/Cylinder.h"
 
 using namespace std;
@@ -35,7 +35,7 @@ CylinderTest::CylinderTest() {
 void CylinderTest::withoutAnything() {
     Cylinder cylinder(2, 3, 3.0f);
 
-    CORRADE_COMPARE_AS(*cylinder.positions(0), (vector<Vector4>{
+    CORRADE_COMPARE_AS(*cylinder.positions(0), (vector<Point3D>{
         {0.0f, -1.5f, 1.0f},
         {0.866025f, -1.5f, -0.5f},
         {-0.866025f, -1.5f, -0.5f},
@@ -72,7 +72,7 @@ void CylinderTest::withoutAnything() {
 void CylinderTest::withTextureCoordsAndCaps() {
     Cylinder cylinder(2, 3, 3.0f, Cylinder::Flag::GenerateTextureCoords|Cylinder::Flag::CapEnds);
 
-    CORRADE_COMPARE_AS(*cylinder.positions(0), (vector<Vector4>{
+    CORRADE_COMPARE_AS(*cylinder.positions(0), (vector<Point3D>{
         {0.0f, -1.5f, 0.0f},
 
         {0.0f, -1.5f, 1.0f},
diff --git a/src/Primitives/Test/UVSphereTest.cpp b/src/Primitives/Test/UVSphereTest.cpp
index 269c52419..cff3f77b9 100644
--- a/src/Primitives/Test/UVSphereTest.cpp
+++ b/src/Primitives/Test/UVSphereTest.cpp
@@ -17,7 +17,7 @@
 
 #include <TestSuite/Compare/Container.h>
 
-#include "Math/Vector4.h"
+#include "Math/Point3D.h"
 #include "Primitives/UVSphere.h"
 
 using namespace std;
@@ -35,7 +35,7 @@ UVSphereTest::UVSphereTest() {
 void UVSphereTest::withoutTextureCoords() {
     UVSphere sphere(3, 3);
 
-    CORRADE_COMPARE_AS(*sphere.positions(0), (vector<Vector4>{
+    CORRADE_COMPARE_AS(*sphere.positions(0), (vector<Point3D>{
         {0.0f, -1.0f, 0.0f},
 
         {0.0f, -0.5f, 0.866025f},
@@ -73,7 +73,7 @@ void UVSphereTest::withoutTextureCoords() {
 void UVSphereTest::withTextureCoords() {
     UVSphere sphere(3, 3, UVSphere::TextureCoords::Generate);
 
-    CORRADE_COMPARE_AS(*sphere.positions(0), (vector<Vector4>{
+    CORRADE_COMPARE_AS(*sphere.positions(0), (vector<Point3D>{
         {0.0f, -1.0f, 0.0f},
 
         {0.0f, -0.5f, 0.866025f},
diff --git a/src/SceneGraph/Light.h b/src/SceneGraph/Light.h
index 3e604f584..74070122c 100644
--- a/src/SceneGraph/Light.h
+++ b/src/SceneGraph/Light.h
@@ -19,6 +19,7 @@
  * @brief Class Magnum::SceneGraph::Light
  */
 
+#include "Math/Point3D.h"
 #include "Object.h"
 
 namespace Magnum { namespace SceneGraph {
@@ -39,7 +40,7 @@ class SCENEGRAPH_EXPORT Light: public Object3D {
         /**
          * @brief Light position relative to root object (scene)
          */
-        inline Vector4 position() {
+        inline Point3D position() {
             setClean();
             return _position;
         }
@@ -51,7 +52,7 @@ class SCENEGRAPH_EXPORT Light: public Object3D {
         void clean(const Matrix4& absoluteTransformation);
 
     private:
-        Vector4 _position;
+        Point3D _position;
 };
 
 }}
diff --git a/src/Shaders/PhongShader.h b/src/Shaders/PhongShader.h
index a27b5d047..a6dd5c6dc 100644
--- a/src/Shaders/PhongShader.h
+++ b/src/Shaders/PhongShader.h
@@ -33,7 +33,7 @@ namespace Magnum { namespace Shaders {
 */
 class SHADERS_EXPORT PhongShader: public AbstractShaderProgram {
     public:
-        typedef Attribute<0, Vector4> Position; /**< @brief Vertex position */
+        typedef Attribute<0, Point3D> Position; /**< @brief Vertex position */
         typedef Attribute<1, Vector3> Normal;   /**< @brief Normal direction */
 
         /** @brief Constructor */
diff --git a/src/Trade/MeshData.h b/src/Trade/MeshData.h
index daf4f3cfa..d3b19bb2e 100644
--- a/src/Trade/MeshData.h
+++ b/src/Trade/MeshData.h
@@ -21,6 +21,7 @@
 
 #include <string>
 
+#include "Math/Point3D.h"
 #include "Mesh.h"
 
 namespace Magnum { namespace Trade {
@@ -50,7 +51,7 @@ class MAGNUM_EXPORT MeshData {
          * @param textureCoords2D   Array with two-dimensional texture
          *      coordinate arrays or empty array
          */
-        inline MeshData(const std::string& name, Mesh::Primitive primitive, std::vector<unsigned int>* indices, std::vector<std::vector<Vector4>*> positions, std::vector<std::vector<Vector3>*> normals, std::vector<std::vector<Vector2>*> textureCoords2D): _name(name), _primitive(primitive), _indices(indices), _positions(positions), _normals(normals), _textureCoords2D(textureCoords2D) {}
+        inline MeshData(const std::string& name, Mesh::Primitive primitive, std::vector<unsigned int>* indices, std::vector<std::vector<Point3D>*> positions, std::vector<std::vector<Vector3>*> normals, std::vector<std::vector<Vector2>*> textureCoords2D): _name(name), _primitive(primitive), _indices(indices), _positions(positions), _normals(normals), _textureCoords2D(textureCoords2D) {}
 
         /** @brief Destructor */
         ~MeshData();
@@ -77,8 +78,8 @@ class MAGNUM_EXPORT MeshData {
          * @return Positions or nullptr if there is no vertex array with given
          *      ID.
          */
-        inline std::vector<Vector4>* positions(unsigned int id) { return _positions[id]; }
-        inline const std::vector<Vector4>* positions(unsigned int id) const { return _positions[id]; } /**< @overload */
+        inline std::vector<Point3D>* positions(unsigned int id) { return _positions[id]; }
+        inline const std::vector<Point3D>* positions(unsigned int id) const { return _positions[id]; } /**< @overload */
 
         /** @brief Count of normal arrays */
         inline unsigned int normalArrayCount() const { return _normals.size(); }
@@ -108,7 +109,7 @@ class MAGNUM_EXPORT MeshData {
         std::string _name;
         Mesh::Primitive _primitive;
         std::vector<unsigned int>* _indices;
-        std::vector<std::vector<Vector4>*> _positions;
+        std::vector<std::vector<Point3D>*> _positions;
         std::vector<std::vector<Vector3>*> _normals;
         std::vector<std::vector<Vector2>*> _textureCoords2D;
 };
diff --git a/src/TypeTraits.h b/src/TypeTraits.h
index 00d590078..5b15c9832 100644
--- a/src/TypeTraits.h
+++ b/src/TypeTraits.h
@@ -242,6 +242,8 @@ template<class T, size_t vectorSize> struct TypeTraits<Math::Vector<vectorSize,
 template<class T> struct TypeTraits<Math::Vector2<T>>: public TypeTraits<Math::Vector<2, T>> {};
 template<class T> struct TypeTraits<Math::Vector3<T>>: public TypeTraits<Math::Vector<3, T>> {};
 template<class T> struct TypeTraits<Math::Vector4<T>>: public TypeTraits<Math::Vector<4, T>> {};
+template<class T> struct TypeTraits<Math::Point2D<T>>: public TypeTraits<Math::Vector<3, T>> {};
+template<class T> struct TypeTraits<Math::Point3D<T>>: public TypeTraits<Math::Vector<4, T>> {};
 template<class T> struct TypeTraits<Color3<T>>: public TypeTraits<Math::Vector<3, T>> {};
 template<class T> struct TypeTraits<Color4<T>>: public TypeTraits<Math::Vector<4, T>> {};