diff --git a/src/AbstractShaderProgram.h b/src/AbstractShaderProgram.h
index 9a28886a0..53b69ce6c 100644
--- a/src/AbstractShaderProgram.h
+++ b/src/AbstractShaderProgram.h
@@ -46,7 +46,7 @@ functions and properties:
  - <strong>%Attribute definitions</strong> with location and type for
    configuring meshes, for example:
 @code
-typedef Attribute<0, Point3D> Position;
+typedef Attribute<0, Vector3> Position;
 typedef Attribute<1, Vector3> Normal;
 typedef Attribute<2, Vector2> TextureCoordinates;
 @endcode
@@ -1371,8 +1371,6 @@ template<std::size_t size_> struct Attribute<Math::Vector<size_, GLdouble>>: Dou
 template<class T> struct Attribute<Math::Vector2<T>>: Attribute<Math::Vector<2, T>> {};
 template<class T> struct Attribute<Math::Vector3<T>>: Attribute<Math::Vector<3, T>> {};
 template<class T> struct Attribute<Math::Vector4<T>>: Attribute<Math::Vector<4, T>> {};
-template<class T> struct Attribute<Math::Point2D<T>>: Attribute<Math::Vector3<T>> {};
-template<class T> struct Attribute<Math::Point3D<T>>: Attribute<Math::Vector4<T>> {};
 template<class T> struct Attribute<Color3<T>>: Attribute<Math::Vector3<T>> {};
 template<class T> struct Attribute<Color4<T>>: Attribute<Math::Vector4<T>> {};
 
diff --git a/src/DebugTools/ObjectRenderer.cpp b/src/DebugTools/ObjectRenderer.cpp
index 137df6a73..3deac8cdc 100644
--- a/src/DebugTools/ObjectRenderer.cpp
+++ b/src/DebugTools/ObjectRenderer.cpp
@@ -33,12 +33,12 @@ template<> struct Renderer<2> {
     inline static ResourceKey indexBuffer() { return {"object2d-indices"}; }
     inline static ResourceKey mesh() { return {"object2d"}; }
 
-    static const std::array<Point2D, 8> positions;
+    static const std::array<Vector2, 8> positions;
     static const std::array<Color3<>, 8> colors;
     static const std::array<std::uint8_t, 12> indices;
 };
 
-const std::array<Point2D, 8> Renderer<2>::positions{{
+const std::array<Vector2, 8> Renderer<2>::positions{{
     { 0.0f,  0.0f},
     { 1.0f,  0.0f}, /* X axis */
     { 0.9f,  0.1f},
@@ -78,12 +78,12 @@ template<> struct Renderer<3> {
     inline static ResourceKey indexBuffer() { return {"object3d-indices"}; }
     inline static ResourceKey mesh() { return {"object3d"}; }
 
-    static const std::array<Point3D, 12> positions;
+    static const std::array<Vector3, 12> positions;
     static const std::array<Color3<>, 12> colors;
     static const std::array<uint8_t, 18> indices;
 };
 
-const std::array<Point3D, 12> Renderer<3>::positions{{
+const std::array<Vector3, 12> Renderer<3>::positions{{
     { 0.0f,  0.0f,  0.0f},
     { 1.0f,  0.0f,  0.0f}, /* X axis */
     { 0.9f,  0.1f,  0.0f},
diff --git a/src/Mesh.h b/src/Mesh.h
index 60edb1c8b..3f2c554f2 100644
--- a/src/Mesh.h
+++ b/src/Mesh.h
@@ -64,7 +64,7 @@ mesh is empty and no draw commands are issued when calling draw().
 // Custom shader, needing only position data
 class MyShader: public AbstractShaderProgram {
     public:
-        typedef Attribute<0, Point3D> Position;
+        typedef Attribute<0, Vector3> Position;
 
     // ...
 };
@@ -72,7 +72,7 @@ Mesh* mesh;
 Buffer* vertexBuffer;
 
 // Fill vertex buffer with position data
-static constexpr Point3D positions[30] = {
+static constexpr Vector3 positions[30] = {
     // ...
 };
 vertexBuffer->setData(positions, Buffer::Usage::StaticDraw);
@@ -109,7 +109,7 @@ mesh->setPrimitive(plane.primitive())
 // Custom shader
 class MyShader: public AbstractShaderProgram {
     public:
-        typedef Attribute<0, Point3D> Position;
+        typedef Attribute<0, Vector3> Position;
 
     // ...
 };
@@ -117,7 +117,7 @@ Buffer *vertexBuffer, *indexBuffer;
 Mesh* mesh;
 
 // Fill vertex buffer with position data
-static constexpr Point3D positions[300] = {
+static constexpr Vector3 positions[300] = {
     // ...
 };
 vertexBuffer->setData(positions, Buffer::Usage::StaticDraw);
diff --git a/src/Text/TextRenderer.cpp b/src/Text/TextRenderer.cpp
index 4e54b86d7..4339d78f5 100644
--- a/src/Text/TextRenderer.cpp
+++ b/src/Text/TextRenderer.cpp
@@ -23,8 +23,6 @@
 #include <Utility/Unicode.h>
 #endif
 
-#include "Math/Point2D.h"
-#include "Math/Point3D.h"
 #include "Context.h"
 #include "Extensions.h"
 #include "Mesh.h"
@@ -151,30 +149,30 @@ template<class T> void createIndices(void* output, const std::uint32_t glyphCoun
     }
 }
 
-template<std::uint8_t dimensions> typename DimensionTraits<dimensions>::PointType point(const Vector2& vec);
+template<std::uint8_t dimensions> typename DimensionTraits<dimensions>::VectorType point(const Vector2& vec);
 
-template<> inline Point2D point<2>(const Vector2& vec) {
-    return swizzle<'x', 'y', '1'>(vec);
+template<> inline Vector2 point<2>(const Vector2& vec) {
+    return vec;
 }
 
-template<> inline Point3D point<3>(const Vector2& vec) {
-    return swizzle<'x', 'y', '0', '1'>(vec);
+template<> inline Vector3 point<3>(const Vector2& vec) {
+    return {vec, 1.0f};
 }
 
 template<std::uint8_t dimensions> struct Vertex {
-    typename DimensionTraits<dimensions>::PointType position;
+    typename DimensionTraits<dimensions>::VectorType position;
     Vector2 texcoords;
 };
 
 }
 
-template<std::uint8_t dimensions> std::tuple<std::vector<typename DimensionTraits<dimensions>::PointType>, std::vector<Vector2>, std::vector<std::uint32_t>, Rectangle> TextRenderer<dimensions>::render(Font& font, GLfloat size, const std::string& text) {
+template<std::uint8_t dimensions> std::tuple<std::vector<typename DimensionTraits<dimensions>::VectorType>, std::vector<Vector2>, std::vector<std::uint32_t>, Rectangle> TextRenderer<dimensions>::render(Font& font, GLfloat size, const std::string& text) {
     TextLayouter layouter(font, size, text);
 
     const std::uint32_t vertexCount = layouter.glyphCount()*4;
 
     /* Output data */
-    std::vector<typename DimensionTraits<dimensions>::PointType> positions;
+    std::vector<typename DimensionTraits<dimensions>::VectorType> positions;
     std::vector<Vector2> texcoords;
     positions.reserve(vertexCount);
     texcoords.reserve(vertexCount);
@@ -210,7 +208,8 @@ template<std::uint8_t dimensions> std::tuple<std::vector<typename DimensionTrait
 
     /* Rendered rectangle */
     Rectangle rectangle;
-    if(layouter.glyphCount()) rectangle = {positions[1].xy(), positions[positions.size()-2].xy()};
+    if(layouter.glyphCount()) rectangle =
+        {swizzle<'x', 'y'>(positions[1]), swizzle<'x', 'y'>(positions[positions.size()-2])};
 
     return std::make_tuple(std::move(positions), std::move(texcoords), std::move(indices), rectangle);
 }
@@ -270,7 +269,8 @@ template<std::uint8_t dimensions> std::tuple<Mesh, Rectangle> TextRenderer<dimen
 
     /* Rendered rectangle */
     Rectangle rectangle;
-    if(layouter.glyphCount()) rectangle = {vertices[1].position.xy(), vertices[vertices.size()-2].position.xy()};
+    if(layouter.glyphCount()) rectangle =
+        {swizzle<'x', 'y'>(vertices[1].position), swizzle<'x', 'y'>(vertices[vertices.size()-2].position)};
 
     /* Configure mesh */
     Mesh mesh;
diff --git a/src/Text/TextRenderer.h b/src/Text/TextRenderer.h
index 89328520c..4c2a1c7f6 100644
--- a/src/Text/TextRenderer.h
+++ b/src/Text/TextRenderer.h
@@ -109,7 +109,7 @@ template<std::uint8_t dimensions> class MAGNUM_TEXT_EXPORT TextRenderer {
          * Returns tuple with vertex positions, texture coordinates, indices
          * and rectangle spanning the rendered text.
          */
-        static std::tuple<std::vector<typename DimensionTraits<dimensions>::PointType>, std::vector<Vector2>, std::vector<std::uint32_t>, Rectangle> render(Font& font, GLfloat size, const std::string& text);
+        static std::tuple<std::vector<typename DimensionTraits<dimensions>::VectorType>, std::vector<Vector2>, std::vector<std::uint32_t>, Rectangle> render(Font& font, GLfloat size, const std::string& text);
 
         /**
          * @brief Render text