diff --git a/src/Primitives/Capsule.cpp b/src/Primitives/Capsule.cpp
index edd224a53..94b6b8e5d 100644
--- a/src/Primitives/Capsule.cpp
+++ b/src/Primitives/Capsule.cpp
@@ -16,11 +16,11 @@
 #include "Capsule.h"
 
 #include "Math/Functions.h"
-#include "Math/Point3D.h"
+#include "Math/Vector3.h"
 
 namespace Magnum { namespace Primitives {
 
-Capsule::Capsule(std::uint32_t hemisphereRings, std::uint32_t cylinderRings, std::uint32_t segments, GLfloat length, TextureCoords textureCoords): MeshData3D(Mesh::Primitive::Triangles, new std::vector<std::uint32_t>, {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) {
+Capsule::Capsule(std::uint32_t hemisphereRings, std::uint32_t cylinderRings, std::uint32_t segments, GLfloat length, TextureCoords textureCoords): MeshData3D(Mesh::Primitive::Triangles, new std::vector<std::uint32_t>, {new std::vector<Vector3>()}, {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) {
     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;
@@ -48,7 +48,7 @@ Capsule::Capsule(std::uint32_t hemisphereRings, std::uint32_t cylinderRings, std
     topFaceRing();
 }
 
-Capsule::Capsule(std::uint32_t segments, TextureCoords textureCoords): MeshData3D(Mesh::Primitive::Triangles, new std::vector<std::uint32_t>, {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) {}
+Capsule::Capsule(std::uint32_t segments, TextureCoords textureCoords): MeshData3D(Mesh::Primitive::Triangles, new std::vector<std::uint32_t>, {new std::vector<Vector3>()}, {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/Crosshair.cpp b/src/Primitives/Crosshair.cpp
index 26b323d65..e38084498 100644
--- a/src/Primitives/Crosshair.cpp
+++ b/src/Primitives/Crosshair.cpp
@@ -15,22 +15,21 @@
 
 #include "Crosshair.h"
 
-#include "Math/Point2D.h"
-#include "Math/Point3D.h"
+#include "Math/Vector3.h"
 #include "Trade/MeshData2D.h"
 #include "Trade/MeshData3D.h"
 
 namespace Magnum { namespace Primitives {
 
 Trade::MeshData2D Crosshair2D::wireframe() {
-    return Trade::MeshData2D(Mesh::Primitive::Lines, nullptr, {new std::vector<Point2D>{
+    return Trade::MeshData2D(Mesh::Primitive::Lines, nullptr, {new std::vector<Vector2>{
         {-1.0f,  0.0f}, {1.0f, 0.0f},
         { 0.0f, -1.0f}, {0.0f, 1.0f}
     }}, {});
 }
 
 Trade::MeshData3D Crosshair3D::wireframe() {
-    return Trade::MeshData3D(Mesh::Primitive::Lines, nullptr, {new std::vector<Point3D>{
+    return Trade::MeshData3D(Mesh::Primitive::Lines, nullptr, {new std::vector<Vector3>{
         {-1.0f,  0.0f,  0.0f}, {1.0f, 0.0f, 0.0f},
         { 0.0f, -1.0f,  0.0f}, {0.0f, 1.0f, 0.0f},
         { 0.0f,  0.0f, -1.0f}, {0.0f, 0.0f, 1.0f}
diff --git a/src/Primitives/Cube.cpp b/src/Primitives/Cube.cpp
index 51d5a4c02..6c63afdc6 100644
--- a/src/Primitives/Cube.cpp
+++ b/src/Primitives/Cube.cpp
@@ -15,7 +15,7 @@
 
 #include "Cube.h"
 
-#include "Math/Point3D.h"
+#include "Math/Vector3.h"
 #include "Trade/MeshData3D.h"
 
 namespace Magnum { namespace Primitives {
@@ -28,7 +28,7 @@ Trade::MeshData3D Cube::solid() {
         12, 13, 14, 12, 14, 15, /* -Z */
         16, 17, 18, 16, 18, 19, /* -Y */
         20, 21, 22, 20, 22, 23  /* -X */
-    }, {new std::vector<Point3D>{
+    }, {new std::vector<Vector3>{
         {-1.0f, -1.0f,  1.0f},
         { 1.0f, -1.0f,  1.0f},
         { 1.0f,  1.0f,  1.0f}, /* +Z */
@@ -97,7 +97,7 @@ Trade::MeshData3D Cube::wireframe() {
         4, 5, 5, 6, 6, 7, 7, 4, /* -Z */
         1, 5, 2, 6,             /* +X */
         0, 4, 3, 7              /* -X */
-    }, {new std::vector<Point3D>{
+    }, {new std::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 406ecbd24..8b47b67f4 100644
--- a/src/Primitives/Cylinder.cpp
+++ b/src/Primitives/Cylinder.cpp
@@ -16,7 +16,7 @@
 #include "Cylinder.h"
 
 #include "Math/Functions.h"
-#include "Math/Point3D.h"
+#include "Math/Vector3.h"
 
 namespace Magnum { namespace Primitives {
 
diff --git a/src/Primitives/Icosphere.cpp b/src/Primitives/Icosphere.cpp
index 0be978c15..f7e003ba3 100644
--- a/src/Primitives/Icosphere.cpp
+++ b/src/Primitives/Icosphere.cpp
@@ -15,7 +15,7 @@
 
 #include "Icosphere.h"
 
-#include "Math/Point3D.h"
+#include "Math/Vector3.h"
 
 namespace Magnum { namespace Primitives {
 
@@ -40,7 +40,7 @@ Icosphere<0>::Icosphere(): MeshData3D(Mesh::Primitive::Triangles, new std::vecto
     7, 1, 0,
     3, 9, 8,
     4, 8, 0
-}, {new std::vector<Point3D>}, {new std::vector<Vector3>{
+}, {new std::vector<Vector3>}, {new std::vector<Vector3>{
     {0.0f, -0.525731f, 0.850651f},
     {0.850651f, 0.0f, 0.525731f},
     {0.850651f, 0.0f, -0.525731f},
@@ -54,8 +54,7 @@ Icosphere<0>::Icosphere(): MeshData3D(Mesh::Primitive::Triangles, new std::vecto
     {0.0f, 0.525731f, -0.850651f},
     {0.0f, 0.525731f, 0.850651f}
 }}, {}) {
-    positions(0)->reserve(normals(0)->size());
-    for(auto i: *normals(0)) positions(0)->push_back(Point3D(i));
+    positions(0)->assign(normals(0)->begin(), normals(0)->end());
 }
 
 }}
diff --git a/src/Primitives/Icosphere.h b/src/Primitives/Icosphere.h
index 4f24331d6..79f5583e3 100644
--- a/src/Primitives/Icosphere.h
+++ b/src/Primitives/Icosphere.h
@@ -64,9 +64,7 @@ template<std::size_t subdivisions> class Icosphere {
                 });
 
             MeshTools::clean(*indices(), *normals(0));
-            positions(0)->clear();
-            positions(0)->reserve(normals(0)->size());
-            for(auto i: *normals(0)) positions(0)->push_back(Point3D(i));
+            positions(0)->assign(normals(0)->begin(), normals(0)->end());
         }
 };
 
diff --git a/src/Primitives/Plane.cpp b/src/Primitives/Plane.cpp
index 8bcd58c4c..3bf69aca2 100644
--- a/src/Primitives/Plane.cpp
+++ b/src/Primitives/Plane.cpp
@@ -15,13 +15,13 @@
 
 #include "Plane.h"
 
-#include "Math/Point3D.h"
+#include "Math/Vector3.h"
 #include "Trade/MeshData3D.h"
 
 namespace Magnum { namespace Primitives {
 
 Trade::MeshData3D Plane::solid() {
-    return Trade::MeshData3D(Mesh::Primitive::TriangleStrip, nullptr, {new std::vector<Point3D>{
+    return Trade::MeshData3D(Mesh::Primitive::TriangleStrip, nullptr, {new std::vector<Vector3>{
         {1.0f, -1.0f, 0.0f},
         {1.0f, 1.0f, 0.0f},
         {-1.0f, -1.0f, 0.0f},
@@ -35,7 +35,7 @@ Trade::MeshData3D Plane::solid() {
 }
 
 Trade::MeshData3D Plane::wireframe() {
-    return Trade::MeshData3D(Mesh::Primitive::LineLoop, nullptr, {new std::vector<Point3D>{
+    return Trade::MeshData3D(Mesh::Primitive::LineLoop, nullptr, {new std::vector<Vector3>{
         {-1.0f, -1.0f, 0.0f},
         {1.0f, -1.0f, 0.0f},
         {1.0f, 1.0f, 0.0f},
diff --git a/src/Primitives/Square.cpp b/src/Primitives/Square.cpp
index fe2dcd971..9a20cc4d0 100644
--- a/src/Primitives/Square.cpp
+++ b/src/Primitives/Square.cpp
@@ -15,13 +15,13 @@
 
 #include "Square.h"
 
-#include "Math/Point2D.h"
+#include "Math/Vector2.h"
 #include "Trade/MeshData2D.h"
 
 namespace Magnum { namespace Primitives {
 
 Trade::MeshData2D Square::solid() {
-    return Trade::MeshData2D(Mesh::Primitive::TriangleStrip, nullptr, {new std::vector<Point2D>{
+    return Trade::MeshData2D(Mesh::Primitive::TriangleStrip, nullptr, {new std::vector<Vector2>{
         {1.0f, -1.0f},
         {1.0f, 1.0f},
         {-1.0f, -1.0f},
@@ -30,7 +30,7 @@ Trade::MeshData2D Square::solid() {
 }
 
 Trade::MeshData2D Square::wireframe() {
-    return Trade::MeshData2D(Mesh::Primitive::LineLoop, nullptr, {new std::vector<Point2D>{
+    return Trade::MeshData2D(Mesh::Primitive::LineLoop, nullptr, {new std::vector<Vector2>{
         {-1.0f, -1.0f},
         {1.0f, -1.0f},
         {1.0f, 1.0f},
diff --git a/src/Primitives/Test/CapsuleTest.cpp b/src/Primitives/Test/CapsuleTest.cpp
index a39871d77..84177dc4a 100644
--- a/src/Primitives/Test/CapsuleTest.cpp
+++ b/src/Primitives/Test/CapsuleTest.cpp
@@ -19,7 +19,7 @@
 #include <TestSuite/Tester.h>
 #include <TestSuite/Compare/Container.h>
 
-#include "Math/Point3D.h"
+#include "Math/Vector3.h"
 #include "Primitives/Capsule.h"
 
 using Corrade::TestSuite::Compare::Container;
@@ -42,7 +42,7 @@ CapsuleTest::CapsuleTest() {
 void CapsuleTest::withoutTextureCoords() {
     Capsule capsule(2, 2, 3, 1.0f);
 
-    CORRADE_COMPARE_AS(*capsule.positions(0), (std::vector<Point3D>{
+    CORRADE_COMPARE_AS(*capsule.positions(0), (std::vector<Vector3>{
         {0.0f, -1.5f, 0.0f},
 
         {0.0f, -1.20711f, 0.707107f},
@@ -107,7 +107,7 @@ void CapsuleTest::withoutTextureCoords() {
 void CapsuleTest::withTextureCoords() {
     Capsule capsule(2, 2, 3, 1.0f, Capsule::TextureCoords::Generate);
 
-    CORRADE_COMPARE_AS(*capsule.positions(0), (std::vector<Point3D>{
+    CORRADE_COMPARE_AS(*capsule.positions(0), (std::vector<Vector3>{
         {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 dd951d8e5..5e847a984 100644
--- a/src/Primitives/Test/CylinderTest.cpp
+++ b/src/Primitives/Test/CylinderTest.cpp
@@ -16,7 +16,7 @@
 #include <TestSuite/Tester.h>
 #include <TestSuite/Compare/Container.h>
 
-#include "Math/Point3D.h"
+#include "Math/Vector3.h"
 #include "Primitives/Cylinder.h"
 
 using Corrade::TestSuite::Compare::Container;
@@ -39,7 +39,7 @@ CylinderTest::CylinderTest() {
 void CylinderTest::withoutAnything() {
     Cylinder cylinder(2, 3, 3.0f);
 
-    CORRADE_COMPARE_AS(*cylinder.positions(0), (std::vector<Point3D>{
+    CORRADE_COMPARE_AS(*cylinder.positions(0), (std::vector<Vector3>{
         {0.0f, -1.5f, 1.0f},
         {0.866025f, -1.5f, -0.5f},
         {-0.866025f, -1.5f, -0.5f},
@@ -76,7 +76,7 @@ void CylinderTest::withoutAnything() {
 void CylinderTest::withTextureCoordsAndCaps() {
     Cylinder cylinder(2, 3, 3.0f, Cylinder::Flag::GenerateTextureCoords|Cylinder::Flag::CapEnds);
 
-    CORRADE_COMPARE_AS(*cylinder.positions(0), (std::vector<Point3D>{
+    CORRADE_COMPARE_AS(*cylinder.positions(0), (std::vector<Vector3>{
         {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 20c88f625..494a6f4d0 100644
--- a/src/Primitives/Test/UVSphereTest.cpp
+++ b/src/Primitives/Test/UVSphereTest.cpp
@@ -16,7 +16,7 @@
 #include <TestSuite/Tester.h>
 #include <TestSuite/Compare/Container.h>
 
-#include "Math/Point3D.h"
+#include "Math/Vector3.h"
 #include "Primitives/UVSphere.h"
 
 using Corrade::TestSuite::Compare::Container;
@@ -39,7 +39,7 @@ UVSphereTest::UVSphereTest() {
 void UVSphereTest::withoutTextureCoords() {
     UVSphere sphere(3, 3);
 
-    CORRADE_COMPARE_AS(*sphere.positions(0), (std::vector<Point3D>{
+    CORRADE_COMPARE_AS(*sphere.positions(0), (std::vector<Vector3>{
         {0.0f, -1.0f, 0.0f},
 
         {0.0f, -0.5f, 0.866025f},
@@ -77,7 +77,7 @@ void UVSphereTest::withoutTextureCoords() {
 void UVSphereTest::withTextureCoords() {
     UVSphere sphere(3, 3, UVSphere::TextureCoords::Generate);
 
-    CORRADE_COMPARE_AS(*sphere.positions(0), (std::vector<Point3D>{
+    CORRADE_COMPARE_AS(*sphere.positions(0), (std::vector<Vector3>{
         {0.0f, -1.0f, 0.0f},
 
         {0.0f, -0.5f, 0.866025f},
diff --git a/src/Trade/MeshData2D.cpp b/src/Trade/MeshData2D.cpp
index b143396bb..810fc0c96 100644
--- a/src/Trade/MeshData2D.cpp
+++ b/src/Trade/MeshData2D.cpp
@@ -15,7 +15,7 @@
 
 #include "MeshData2D.h"
 
-#include "Math/Point2D.h"
+#include "Math/Vector2.h"
 
 namespace Magnum { namespace Trade {
 
diff --git a/src/Trade/MeshData2D.h b/src/Trade/MeshData2D.h
index c41ae1697..85f6ea7d3 100644
--- a/src/Trade/MeshData2D.h
+++ b/src/Trade/MeshData2D.h
@@ -47,7 +47,7 @@ class MAGNUM_EXPORT MeshData2D {
          * @param textureCoords2D   Array with two-dimensional texture
          *      coordinate arrays or empty array
          */
-        inline MeshData2D(Mesh::Primitive primitive, std::vector<std::uint32_t>* indices, std::vector<std::vector<Point2D>*> positions, std::vector<std::vector<Vector2>*> textureCoords2D): _primitive(primitive), _indices(indices), _positions(positions), _textureCoords2D(textureCoords2D) {}
+        inline MeshData2D(Mesh::Primitive primitive, std::vector<std::uint32_t>* indices, std::vector<std::vector<Vector2>*> positions, std::vector<std::vector<Vector2>*> textureCoords2D): _primitive(primitive), _indices(indices), _positions(positions), _textureCoords2D(textureCoords2D) {}
 
         /** @brief Move constructor */
         MeshData2D(MeshData2D&&) = default;
@@ -77,8 +77,8 @@ class MAGNUM_EXPORT MeshData2D {
          * @return Positions or nullptr if there is no vertex array with given
          *      ID.
          */
-        inline std::vector<Point2D>* positions(std::uint32_t id) { return _positions[id]; }
-        inline const std::vector<Point2D>* positions(std::uint32_t id) const { return _positions[id]; } /**< @overload */
+        inline std::vector<Vector2>* positions(std::uint32_t id) { return _positions[id]; }
+        inline const std::vector<Vector2>* positions(std::uint32_t id) const { return _positions[id]; } /**< @overload */
 
         /** @brief Count of 2D texture coordinate arrays */
         inline std::uint32_t textureCoords2DArrayCount() const { return _textureCoords2D.size(); }
@@ -95,7 +95,7 @@ class MAGNUM_EXPORT MeshData2D {
     private:
         Mesh::Primitive _primitive;
         std::vector<std::uint32_t>* _indices;
-        std::vector<std::vector<Point2D>*> _positions;
+        std::vector<std::vector<Vector2>*> _positions;
         std::vector<std::vector<Vector2>*> _textureCoords2D;
 };
 
diff --git a/src/Trade/MeshData3D.cpp b/src/Trade/MeshData3D.cpp
index e76968720..bfca98c39 100644
--- a/src/Trade/MeshData3D.cpp
+++ b/src/Trade/MeshData3D.cpp
@@ -15,7 +15,7 @@
 
 #include "MeshData3D.h"
 
-#include "Math/Point3D.h"
+#include "Math/Vector3.h"
 
 namespace Magnum { namespace Trade {
 
diff --git a/src/Trade/MeshData3D.h b/src/Trade/MeshData3D.h
index eed0c1650..17a1ac802 100644
--- a/src/Trade/MeshData3D.h
+++ b/src/Trade/MeshData3D.h
@@ -48,7 +48,7 @@ class MAGNUM_EXPORT MeshData3D {
          * @param textureCoords2D   Array with two-dimensional texture
          *      coordinate arrays or empty array
          */
-        inline MeshData3D(Mesh::Primitive primitive, std::vector<std::uint32_t>* indices, std::vector<std::vector<Point3D>*> positions, std::vector<std::vector<Vector3>*> normals, std::vector<std::vector<Vector2>*> textureCoords2D): _primitive(primitive), _indices(indices), _positions(positions), _normals(normals), _textureCoords2D(textureCoords2D) {}
+        inline MeshData3D(Mesh::Primitive primitive, std::vector<std::uint32_t>* indices, std::vector<std::vector<Vector3>*> positions, std::vector<std::vector<Vector3>*> normals, std::vector<std::vector<Vector2>*> textureCoords2D): _primitive(primitive), _indices(indices), _positions(positions), _normals(normals), _textureCoords2D(textureCoords2D) {}
 
         /** @brief Move constructor */
         MeshData3D(MeshData3D&&) = default;
@@ -78,8 +78,8 @@ class MAGNUM_EXPORT MeshData3D {
          * @return Positions or nullptr if there is no vertex array with given
          *      ID.
          */
-        inline std::vector<Point3D>* positions(std::uint32_t id) { return _positions[id]; }
-        inline const std::vector<Point3D>* positions(std::uint32_t id) const { return _positions[id]; } /**< @overload */
+        inline std::vector<Vector3>* positions(std::uint32_t id) { return _positions[id]; }
+        inline const std::vector<Vector3>* positions(std::uint32_t id) const { return _positions[id]; } /**< @overload */
 
         /** @brief Count of normal arrays */
         inline std::uint32_t normalArrayCount() const { return _normals.size(); }
@@ -108,7 +108,7 @@ class MAGNUM_EXPORT MeshData3D {
     private:
         Mesh::Primitive _primitive;
         std::vector<std::uint32_t>* _indices;
-        std::vector<std::vector<Point3D>*> _positions;
+        std::vector<std::vector<Vector3>*> _positions;
         std::vector<std::vector<Vector3>*> _normals;
         std::vector<std::vector<Vector2>*> _textureCoords2D;
 };