diff --git a/src/Magnum/Trade/MeshData.cpp b/src/Magnum/Trade/MeshData.cpp
index f1e458bb9..cb930b30d 100644
--- a/src/Magnum/Trade/MeshData.cpp
+++ b/src/Magnum/Trade/MeshData.cpp
@@ -28,6 +28,7 @@
 #include <Corrade/Utility/Algorithms.h>
 
 #include "Magnum/Math/Color.h"
+#include "Magnum/Math/PackingBatch.h"
 #include "Magnum/Trade/Implementation/arrayUtilities.h"
 
 namespace Magnum { namespace Trade {
@@ -365,10 +366,39 @@ void MeshData::positions2DInto(const Containers::StridedArrayView1D<Vector2> des
     CORRADE_ASSERT(destination.size() == _vertexCount, "Trade::MeshData::positions2DInto(): expected a view with" << _vertexCount << "elements but got" << destination.size(), );
     const MeshAttributeData& attribute = _attributes[attributeId];
 
+    const auto destination2f = Containers::arrayCast<2, Float>(destination);
+
     /* Copy 2D positions as-is, for 3D positions ignore Z */
     if(attribute._format == VertexFormat::Vector2 ||
        attribute._format == VertexFormat::Vector3)
         Utility::copy(Containers::arrayCast<const Vector2>(attribute._data), destination);
+    else if(attribute._format == VertexFormat::Vector2h ||
+            attribute._format == VertexFormat::Vector3h)
+        Math::unpackHalfInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2ub ||
+            attribute._format == VertexFormat::Vector3ub)
+        Math::castInto(Containers::arrayCast<2, const UnsignedByte>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2b ||
+            attribute._format == VertexFormat::Vector3b)
+        Math::castInto(Containers::arrayCast<2, const Byte>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2us ||
+            attribute._format == VertexFormat::Vector3us)
+        Math::castInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2s ||
+            attribute._format == VertexFormat::Vector3s)
+        Math::castInto(Containers::arrayCast<2, const Short>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2ubNormalized ||
+            attribute._format == VertexFormat::Vector3ubNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const UnsignedByte>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2bNormalized ||
+            attribute._format == VertexFormat::Vector3bNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const Byte>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2usNormalized ||
+            attribute._format == VertexFormat::Vector3usNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2sNormalized ||
+            attribute._format == VertexFormat::Vector3sNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const Short>(attribute._data, 2), destination2f);
     else CORRADE_ASSERT_UNREACHABLE(); /* LCOV_EXCL_LINE */
 }
 
@@ -384,19 +414,71 @@ void MeshData::positions3DInto(const Containers::StridedArrayView1D<Vector3> des
     CORRADE_ASSERT(destination.size() == _vertexCount, "Trade::MeshData::positions3DInto(): expected a view with" << _vertexCount << "elements but got" << destination.size(), );
     const MeshAttributeData& attribute = _attributes[attributeId];
 
-    /* For 2D positions copy the XY part to the first two components and then
-       fill the Z with a single value */
-    if(attribute._format == VertexFormat::Vector2) {
+    const Containers::StridedArrayView2D<Float> destination2f = Containers::arrayCast<2, Float>(Containers::arrayCast<Vector2>(destination));
+    const Containers::StridedArrayView2D<Float> destination3f = Containers::arrayCast<2, Float>(destination);
+
+    /* For 2D positions copy the XY part to the first two components */
+    if(attribute._format == VertexFormat::Vector2)
         Utility::copy(Containers::arrayCast<const Vector2>(attribute._data),
                       Containers::arrayCast<Vector2>(destination));
+    else if(attribute._format == VertexFormat::Vector2h)
+        Math::unpackHalfInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2ub)
+        Math::castInto(Containers::arrayCast<2, const UnsignedByte>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2b)
+        Math::castInto(Containers::arrayCast<2, const Byte>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2us)
+        Math::castInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2s)
+        Math::castInto(Containers::arrayCast<2, const Short>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2ubNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const UnsignedByte>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2bNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const Byte>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2usNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2sNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const Short>(attribute._data, 2), destination2f);
+
+    /* Copy 3D positions as-is */
+    else if(attribute._format == VertexFormat::Vector3)
+        Utility::copy(Containers::arrayCast<const Vector3>(attribute._data), destination);
+    else if(attribute._format == VertexFormat::Vector3h)
+        Math::unpackHalfInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 3), destination3f);
+    else if(attribute._format == VertexFormat::Vector3ub)
+        Math::castInto(Containers::arrayCast<2, const UnsignedByte>(attribute._data, 3), destination3f);
+    else if(attribute._format == VertexFormat::Vector3b)
+        Math::castInto(Containers::arrayCast<2, const Byte>(attribute._data, 3), destination3f);
+    else if(attribute._format == VertexFormat::Vector3us)
+        Math::castInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 3), destination3f);
+    else if(attribute._format == VertexFormat::Vector3s)
+        Math::castInto(Containers::arrayCast<2, const Short>(attribute._data, 3), destination3f);
+    else if(attribute._format == VertexFormat::Vector3ubNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const UnsignedByte>(attribute._data, 3), destination3f);
+    else if(attribute._format == VertexFormat::Vector3bNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const Byte>(attribute._data, 3), destination3f);
+    else if(attribute._format == VertexFormat::Vector3usNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 3), destination3f);
+    else if(attribute._format == VertexFormat::Vector3sNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const Short>(attribute._data, 3), destination3f);
+    else CORRADE_ASSERT_UNREACHABLE(); /* LCOV_EXCL_LINE */
+
+    /* For 2D positions finally fill the Z with a single value */
+    if(attribute._format == VertexFormat::Vector2 ||
+       attribute._format == VertexFormat::Vector2h ||
+       attribute._format == VertexFormat::Vector2ub ||
+       attribute._format == VertexFormat::Vector2b ||
+       attribute._format == VertexFormat::Vector2us ||
+       attribute._format == VertexFormat::Vector2s ||
+       attribute._format == VertexFormat::Vector2ubNormalized ||
+       attribute._format == VertexFormat::Vector2bNormalized ||
+       attribute._format == VertexFormat::Vector2usNormalized ||
+       attribute._format == VertexFormat::Vector2sNormalized) {
         constexpr Float z[1]{0.0f};
         Utility::copy(
             Containers::stridedArrayView(z).broadcasted<0>(_vertexCount),
-            Containers::arrayCast<2, Float>(destination).transposed<0, 1>()[2]);
-    /* Copy 3D positions as-is */
-    } else if(attribute._format == VertexFormat::Vector3) {
-        Utility::copy(Containers::arrayCast<const Vector3>(attribute._data), destination);
-    } else CORRADE_ASSERT_UNREACHABLE(); /* LCOV_EXCL_LINE */
+            destination3f.transposed<0, 1>()[2]);
+    }
 }
 
 Containers::Array<Vector3> MeshData::positions3DAsArray(const UnsignedInt id) const {
@@ -411,8 +493,16 @@ void MeshData::normalsInto(const Containers::StridedArrayView1D<Vector3> destina
     CORRADE_ASSERT(destination.size() == _vertexCount, "Trade::MeshData::normalsInto(): expected a view with" << _vertexCount << "elements but got" << destination.size(), );
     const MeshAttributeData& attribute = _attributes[attributeId];
 
+    const auto destination3f = Containers::arrayCast<2, Float>(destination);
+
     if(attribute._format == VertexFormat::Vector3)
         Utility::copy(Containers::arrayCast<const Vector3>(attribute._data), destination);
+    else if(attribute._format == VertexFormat::Vector3h)
+        Math::unpackHalfInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 3), destination3f);
+    else if(attribute._format == VertexFormat::Vector3bNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const Byte>(attribute._data, 3), destination3f);
+    else if(attribute._format == VertexFormat::Vector3sNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const Short>(attribute._data, 3), destination3f);
     else CORRADE_ASSERT_UNREACHABLE(); /* LCOV_EXCL_LINE */
 }
 
@@ -428,8 +518,28 @@ void MeshData::textureCoordinates2DInto(const Containers::StridedArrayView1D<Vec
     CORRADE_ASSERT(destination.size() == _vertexCount, "Trade::MeshData::textureCoordinates2DInto(): expected a view with" << _vertexCount << "elements but got" << destination.size(), );
     const MeshAttributeData& attribute = _attributes[attributeId];
 
+    const auto destination2f = Containers::arrayCast<2, Float>(destination);
+
     if(attribute._format == VertexFormat::Vector2)
         Utility::copy(Containers::arrayCast<const Vector2>(attribute._data), destination);
+    else if(attribute._format == VertexFormat::Vector2h)
+        Math::unpackHalfInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2ub)
+        Math::castInto(Containers::arrayCast<2, const UnsignedByte>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2b)
+        Math::castInto(Containers::arrayCast<2, const Byte>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2us)
+        Math::castInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2s)
+        Math::castInto(Containers::arrayCast<2, const Short>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2ubNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const UnsignedByte>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2bNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const Byte>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2usNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 2), destination2f);
+    else if(attribute._format == VertexFormat::Vector2sNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const Short>(attribute._data, 2), destination2f);
     else CORRADE_ASSERT_UNREACHABLE(); /* LCOV_EXCL_LINE */
 }
 
@@ -445,20 +555,43 @@ void MeshData::colorsInto(const Containers::StridedArrayView1D<Color4> destinati
     CORRADE_ASSERT(destination.size() == _vertexCount, "Trade::MeshData::colorsInto(): expected a view with" << _vertexCount << "elements but got" << destination.size(), );
     const MeshAttributeData& attribute = _attributes[attributeId];
 
+    const Containers::StridedArrayView2D<Float> destination3f = Containers::arrayCast<2, Float>(Containers::arrayCast<Vector3>(destination));
+    const Containers::StridedArrayView2D<Float> destination4f = Containers::arrayCast<2, Float>(destination);
+
     /* For three-component colors copy the RGB part to the first three
-       components and then fill the alpha with a single value */
-    if(attribute._format == VertexFormat::Vector3) {
+       components */
+    if(attribute._format == VertexFormat::Vector3)
         Utility::copy(Containers::arrayCast<const Vector3>(attribute._data),
                       Containers::arrayCast<Vector3>(destination));
-        constexpr Float alpha[1]{1.0f};
-        Utility::copy(
-            Containers::stridedArrayView(alpha).broadcasted<0>(_vertexCount),
-            Containers::arrayCast<2, Float>(destination).transposed<0, 1>()[3]);
+    else if(attribute._format == VertexFormat::Vector3h)
+        Math::unpackHalfInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 3), destination3f);
+    else if(attribute._format == VertexFormat::Vector3ubNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const UnsignedByte>(attribute._data, 3), destination3f);
+    else if(attribute._format == VertexFormat::Vector3usNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 3), destination3f);
+
     /* Copy four-component colors as-is */
-    } else if(attribute._format == VertexFormat::Vector4) {
+    else if(attribute._format == VertexFormat::Vector4)
         Utility::copy(Containers::arrayCast<const Vector4>(attribute._data),
                       Containers::arrayCast<Vector4>(destination));
-    } else CORRADE_ASSERT_UNREACHABLE(); /* LCOV_EXCL_LINE */
+    else if(attribute._format == VertexFormat::Vector4h)
+        Math::unpackHalfInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 4), destination4f);
+    else if(attribute._format == VertexFormat::Vector4ubNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const UnsignedByte>(attribute._data, 4), destination4f);
+    else if(attribute._format == VertexFormat::Vector4usNormalized)
+        Math::unpackInto(Containers::arrayCast<2, const UnsignedShort>(attribute._data, 4), destination4f);
+    else CORRADE_ASSERT_UNREACHABLE(); /* LCOV_EXCL_LINE */
+
+    /* For three-component colors finally fill the alpha with a single value */
+    if(attribute._format == VertexFormat::Vector3 ||
+       attribute._format == VertexFormat::Vector3h ||
+       attribute._format == VertexFormat::Vector3ubNormalized ||
+       attribute._format == VertexFormat::Vector3usNormalized) {
+        constexpr Float alpha[1]{1.0f};
+        Utility::copy(
+            Containers::stridedArrayView(alpha).broadcasted<0>(_vertexCount),
+            destination4f.transposed<0, 1>()[3]);
+    }
 }
 
 Containers::Array<Color4> MeshData::colorsAsArray(const UnsignedInt id) const {
diff --git a/src/Magnum/Trade/MeshData.h b/src/Magnum/Trade/MeshData.h
index 3409e5ddc..468458483 100644
--- a/src/Magnum/Trade/MeshData.h
+++ b/src/Magnum/Trade/MeshData.h
@@ -55,37 +55,54 @@ enum class MeshAttribute: UnsignedShort {
        AbstractImporter::meshAttributeForName()) */
 
     /**
-     * Position. Type is usually @ref Magnum::Vector2 "Vector2" for 2D and
-     * @ref Magnum::Vector3 "Vector3" for 3D. Corresponds to
-     * @ref Shaders::Generic::Position.
-     * @see @ref VertexFormat::Vector2, @ref VertexFormat::Vector3,
-     *      @ref MeshData::positions2DAsArray(),
+     * Position. Type is usually @ref VertexFormat::Vector2 for 2D and
+     * @ref VertexFormat::Vector3 for 3D, but can be also any of
+     * @ref VertexFormat::Vector2h, @ref VertexFormat::Vector3h,
+     * @ref VertexFormat::Vector2ub, @ref VertexFormat::Vector2ubNormalized,
+     * @ref VertexFormat::Vector2b, @ref VertexFormat::Vector2bNormalized,
+     * @ref VertexFormat::Vector2us, @ref VertexFormat::Vector2usNormalized,
+     * @ref VertexFormat::Vector2s, @ref VertexFormat::Vector2sNormalized,
+     * @ref VertexFormat::Vector3ub, @ref VertexFormat::Vector3ubNormalized,
+     * @ref VertexFormat::Vector3b, @ref VertexFormat::Vector3bNormalized,
+     * @ref VertexFormat::Vector3us, @ref VertexFormat::Vector3usNormalized,
+     * @ref VertexFormat::Vector3s or @ref VertexFormat::Vector3sNormalized.
+     * Corresponds to @ref Shaders::Generic::Position.
+     * @see @ref MeshData::positions2DAsArray(),
      *      @ref MeshData::positions3DAsArray()
      */
     Position = 1,
 
     /**
-     * Normal. Type is usually @ref Magnum::Vector3 "Vector3". Corresponds to
+     * Normal. Type is usually @ref VertexFormat::Vector3, but can be also
+     * @ref VertexFormat::Vector3h. @ref VertexFormat::Vector3bNormalized or
+     * @ref VertexFormat::Vector3sNormalized. Corresponds to
      * @ref Shaders::Generic::Normal.
-     * @see @ref VertexFormat::Vector3, @ref MeshData::normalsAsArray()
+     * @see @ref MeshData::normalsAsArray()
      */
     Normal,
 
     /**
-     * Texture coordinates. Type is usually @ref Magnum::Vector2 "Vector2" for
-     * 2D coordinates. Corresponds to @ref Shaders::Generic::TextureCoordinates.
-     * @see @ref VertexFormat::Vector2,
-     *      @ref MeshData::textureCoordinates2DAsArray()
+     * Texture coordinates. Type is usually @ref VertexFormat::Vector2 for
+     * 2D coordinates, but can be also any of @ref VertexFormat::Vector2h,
+     * @ref VertexFormat::Vector2ub, @ref VertexFormat::Vector2ubNormalized,
+     * @ref VertexFormat::Vector2b, @ref VertexFormat::Vector2bNormalized,
+     * @ref VertexFormat::Vector2us, @ref VertexFormat::Vector2usNormalized,
+     * @ref VertexFormat::Vector2s or @ref VertexFormat::Vector2sNormalized.
+     * Corresponds to @ref Shaders::Generic::TextureCoordinates.
+     * @see @ref MeshData::textureCoordinates2DAsArray()
      */
     TextureCoordinates,
 
     /**
-     * Vertex color. Type is usually @ref Magnum::Vector3 "Vector3" or
-     * @ref Magnum::Vector4 "Vector4" (or @ref Color3 / @ref Color4).
-     * Corresponds to @ref Shaders::Generic::Color3 or
-     * @ref Shaders::Generic::Color4.
-     * @see @ref VertexFormat::Vector3, @ref VertexFormat::Vector4,
-     *      @ref MeshData::colorsAsArray()
+     * Vertex color. Type is usually @ref VertexFormat::Vector3 or
+     * @ref VertexFormat::Vector4, but can be also any of
+     * @ref VertexFormat::Vector3h, @ref VertexFormat::Vector4h,
+     * @ref VertexFormat::Vector3ubNormalized,
+     * @ref VertexFormat::Vector3usNormalized,
+     * @ref VertexFormat::Vector4ubNormalized or
+     * @ref VertexFormat::Vector4usNormalized. Corresponds to
+     * @ref Shaders::Generic::Color3 or @ref Shaders::Generic::Color4.
+     * @see @ref MeshData::colorsAsArray()
      */
     Color,
 
@@ -261,6 +278,27 @@ class MAGNUM_TRADE_EXPORT MeshAttributeData {
          *
          * Detects @ref VertexFormat based on @p T and calls
          * @ref MeshAttributeData(MeshAttribute, VertexFormat, const Containers::StridedArrayView1D<const void>&).
+         * For most types known by Magnum, the detected @ref VertexFormat is of
+         * the same name as the type (so e.g. @ref Magnum::Vector3ui "Vector3ui"
+         * gets recognized as @ref VertexFormat::Vector3ui), with the
+         * following exceptions:
+         *
+         * -    @ref Color3ub is recognized as
+         *      @ref VertexFormat::Vector3ubNormalized
+         * -    @ref Color3us is recognized as
+         *      @ref VertexFormat::Vector3usNormalized
+         * -    @ref Color4ub is recognized as
+         *      @ref VertexFormat::Vector4ubNormalized
+         * -    @ref Color4us is recognized as
+         *      @ref VertexFormat::Vector4usNormalized
+         *
+         * This also means that if you have a @ref Magnum::Vector2s "Vector2s",
+         * for example, and want to pick a
+         * @ref VertexFormat::Vector2sNormalized instead of the
+         * (autodetected) @ref VertexFormat::Vector2s, you need to specify
+         * it explicitly --- there's no way the library can infer this from the
+         * type alone, except for the color types above (which are generally
+         * always normalized).
          */
         template<class T> constexpr explicit MeshAttributeData(MeshAttribute name, const Containers::StridedArrayView1D<T>& data) noexcept;
 
@@ -1164,6 +1202,7 @@ namespace Implementation {
     template<> constexpr MeshIndexType meshIndexTypeFor<UnsignedShort>() { return MeshIndexType::UnsignedShort; }
     template<> constexpr MeshIndexType meshIndexTypeFor<UnsignedInt>() { return MeshIndexType::UnsignedInt; }
 
+    /* Implicit mapping from a format to enum (1:1) */
     template<class T> constexpr VertexFormat vertexFormatFor() {
         /* C++ why there isn't an obvious way to do such a thing?! */
         static_assert(sizeof(T) == 0, "unsupported attribute type");
@@ -1173,6 +1212,8 @@ namespace Implementation {
     #define _c(format) \
         template<> constexpr VertexFormat vertexFormatFor<format>() { return VertexFormat::format; }
     _c(Float)
+    _c(Half)
+    _c(Double)
     _c(UnsignedByte)
     _c(Byte)
     _c(UnsignedShort)
@@ -1180,28 +1221,128 @@ namespace Implementation {
     _c(UnsignedInt)
     _c(Int)
     _c(Vector2)
+    _c(Vector2h)
+    _c(Vector2d)
+    _c(Vector2ub)
+    _c(Vector2b)
+    _c(Vector2us)
+    _c(Vector2s)
+    _c(Vector2ui)
+    _c(Vector2i)
     _c(Vector3)
+    _c(Vector3h)
+    _c(Vector3d)
+    _c(Vector3ub)
+    _c(Vector3b)
+    _c(Vector3us)
+    _c(Vector3s)
+    _c(Vector3ui)
+    _c(Vector3i)
     _c(Vector4)
+    _c(Vector4h)
+    _c(Vector4d)
+    _c(Vector4ub)
+    _c(Vector4b)
+    _c(Vector4us)
+    _c(Vector4s)
+    _c(Vector4ui)
+    _c(Vector4i)
     #undef _c
     #endif
     template<> constexpr VertexFormat vertexFormatFor<Color3>() { return VertexFormat::Vector3; }
+    template<> constexpr VertexFormat vertexFormatFor<Color3h>() { return VertexFormat::Vector3h; }
+    template<> constexpr VertexFormat vertexFormatFor<Color3ub>() { return VertexFormat::Vector3ubNormalized; }
+    template<> constexpr VertexFormat vertexFormatFor<Color3us>() { return VertexFormat::Vector3usNormalized; }
     template<> constexpr VertexFormat vertexFormatFor<Color4>() { return VertexFormat::Vector4; }
+    template<> constexpr VertexFormat vertexFormatFor<Color4h>() { return VertexFormat::Vector4h; }
+    template<> constexpr VertexFormat vertexFormatFor<Color4ub>() { return VertexFormat::Vector4ubNormalized; }
+    template<> constexpr VertexFormat vertexFormatFor<Color4us>() { return VertexFormat::Vector4usNormalized; }
+
+    /* Check if enum is compatible with a format (1:n). Mostly just 1:1 mapping
+       tho, so reusing vertexFormatFor(), with a few exceptions. */
+    template<class T> constexpr bool isVertexFormatCompatible(VertexFormat type) {
+        return vertexFormatFor<T>() == type;
+    }
+    #ifndef DOXYGEN_GENERATING_OUTPUT
+    #define _c(format_)                                                     \
+        template<> constexpr bool isVertexFormatCompatible<format_>(VertexFormat format) { \
+            return format == VertexFormat::format_ ||                       \
+                   format == VertexFormat::format_ ## Normalized;           \
+        }
+    _c(UnsignedByte)
+    _c(Byte)
+    _c(UnsignedShort)
+    _c(Short)
+    _c(Vector2ub)
+    _c(Vector2b)
+    _c(Vector2us)
+    _c(Vector2s)
+    _c(Vector3ub)
+    _c(Vector3b)
+    _c(Vector3us)
+    _c(Vector3s)
+    _c(Vector4ub)
+    _c(Vector4b)
+    _c(Vector4us)
+    _c(Vector4s)
+    /* For Color[34]u[sb] we expect the format to be normalized, which is
+       handled by vertexFormatFor() properly already */
+    #undef _c
+    #endif
     /* LCOV_EXCL_STOP */
 }
 #endif
 
 constexpr MeshAttributeData::MeshAttributeData(const MeshAttribute name, const VertexFormat format, const Containers::StridedArrayView1D<const void>& data, std::nullptr_t) noexcept:
     _name{name},  _format{format}, _data{(CORRADE_CONSTEXPR_ASSERT(
+        /* Double formats intentionally not supported for any builtin attributes
+           right now -- only for custom formats */
         (name == MeshAttribute::Position &&
             (format == VertexFormat::Vector2 ||
-             format == VertexFormat::Vector3)) ||
+             format == VertexFormat::Vector2h ||
+             format == VertexFormat::Vector2ub ||
+             format == VertexFormat::Vector2ubNormalized ||
+             format == VertexFormat::Vector2b ||
+             format == VertexFormat::Vector2bNormalized ||
+             format == VertexFormat::Vector2us ||
+             format == VertexFormat::Vector2usNormalized ||
+             format == VertexFormat::Vector2s ||
+             format == VertexFormat::Vector2sNormalized ||
+             format == VertexFormat::Vector3 ||
+             format == VertexFormat::Vector3h ||
+             format == VertexFormat::Vector3ub ||
+             format == VertexFormat::Vector3ubNormalized ||
+             format == VertexFormat::Vector3b ||
+             format == VertexFormat::Vector3bNormalized ||
+             format == VertexFormat::Vector3us ||
+             format == VertexFormat::Vector3usNormalized ||
+             format == VertexFormat::Vector3s ||
+             format == VertexFormat::Vector3sNormalized)) ||
         (name == MeshAttribute::Normal &&
-            (format == VertexFormat::Vector3)) ||
+            (format == VertexFormat::Vector3 ||
+             format == VertexFormat::Vector3h ||
+             format == VertexFormat::Vector3bNormalized ||
+             format == VertexFormat::Vector3sNormalized)) ||
         (name == MeshAttribute::Color &&
             (format == VertexFormat::Vector3 ||
-             format == VertexFormat::Vector4)) ||
+             format == VertexFormat::Vector3h ||
+             format == VertexFormat::Vector3ubNormalized ||
+             format == VertexFormat::Vector3usNormalized ||
+             format == VertexFormat::Vector4 ||
+             format == VertexFormat::Vector4h ||
+             format == VertexFormat::Vector4ubNormalized ||
+             format == VertexFormat::Vector4usNormalized)) ||
         (name == MeshAttribute::TextureCoordinates &&
-            (format == VertexFormat::Vector2)) ||
+            (format == VertexFormat::Vector2 ||
+             format == VertexFormat::Vector2h ||
+             format == VertexFormat::Vector2ub ||
+             format == VertexFormat::Vector2ubNormalized ||
+             format == VertexFormat::Vector2b ||
+             format == VertexFormat::Vector2bNormalized ||
+             format == VertexFormat::Vector2us ||
+             format == VertexFormat::Vector2usNormalized ||
+             format == VertexFormat::Vector2s ||
+             format == VertexFormat::Vector2sNormalized)) ||
         isMeshAttributeCustom(name) /* can be any format */,
         "Trade::MeshAttributeData:" << format << "is not a valid format for" << name), data)}
     {}
@@ -1233,7 +1374,7 @@ template<class T> Containers::StridedArrayView1D<const T> MeshData::attribute(Un
     #ifdef CORRADE_GRACEFUL_ASSERT /* Sigh. Brittle. Better idea? */
     if(!data.stride()[1]) return {};
     #endif
-    CORRADE_ASSERT(Implementation::vertexFormatFor<T>() == _attributes[id]._format,
+    CORRADE_ASSERT(Implementation::isVertexFormatCompatible<T>(_attributes[id]._format),
         "Trade::MeshData::attribute(): improper type requested for" << _attributes[id]._name << "of format" << _attributes[id]._format, nullptr);
     return Containers::arrayCast<1, const T>(data);
 }
@@ -1243,7 +1384,7 @@ template<class T> Containers::StridedArrayView1D<T> MeshData::mutableAttribute(U
     #ifdef CORRADE_GRACEFUL_ASSERT /* Sigh. Brittle. Better idea? */
     if(!data.stride()[1]) return {};
     #endif
-    CORRADE_ASSERT(Implementation::vertexFormatFor<T>() == _attributes[id]._format,
+    CORRADE_ASSERT(Implementation::isVertexFormatCompatible<T>(_attributes[id]._format),
         "Trade::MeshData::mutableAttribute(): improper type requested for" << _attributes[id]._name << "of format" << _attributes[id]._format, nullptr);
     return Containers::arrayCast<1, T>(data);
 }
@@ -1256,7 +1397,7 @@ template<class T> Containers::StridedArrayView1D<const T> MeshData::attribute(Me
     #ifndef CORRADE_NO_ASSERT
     const UnsignedInt attributeId = attributeFor(name, id);
     #endif
-    CORRADE_ASSERT(Implementation::vertexFormatFor<T>() == _attributes[attributeId]._format,
+    CORRADE_ASSERT(Implementation::isVertexFormatCompatible<T>(_attributes[attributeId]._format),
         "Trade::MeshData::attribute(): improper type requested for" << _attributes[attributeId]._name << "of format" << _attributes[attributeId]._format, nullptr);
     return Containers::arrayCast<1, const T>(data);
 }
@@ -1269,8 +1410,8 @@ template<class T> Containers::StridedArrayView1D<T> MeshData::mutableAttribute(M
     #ifndef CORRADE_NO_ASSERT
     const UnsignedInt attributeId = attributeFor(name, id);
     #endif
-    CORRADE_ASSERT(Implementation::vertexFormatFor<T>() == _attributes[attributeId]._format,
-        "Trade::MeshData::mutableAttribute(): improper type requested for" << _attributes[attributeId]._name << "of type" << _attributes[attributeId]._format, nullptr);
+    CORRADE_ASSERT(Implementation::isVertexFormatCompatible<T>(_attributes[attributeId]._format),
+        "Trade::MeshData::mutableAttribute(): improper type requested for" << _attributes[attributeId]._name << "of format" << _attributes[attributeId]._format, nullptr);
     return Containers::arrayCast<1, T>(data);
 }
 
diff --git a/src/Magnum/Trade/Test/MeshDataTest.cpp b/src/Magnum/Trade/Test/MeshDataTest.cpp
index 8d42f8bb6..cde87476e 100644
--- a/src/Magnum/Trade/Test/MeshDataTest.cpp
+++ b/src/Magnum/Trade/Test/MeshDataTest.cpp
@@ -29,6 +29,7 @@
 #include <Corrade/Utility/DebugStl.h>
 
 #include "Magnum/Math/Color.h"
+#include "Magnum/Math/Half.h"
 #include "Magnum/Trade/MeshData.h"
 
 namespace Magnum { namespace Trade { namespace Test { namespace {
@@ -96,14 +97,28 @@ struct MeshDataTest: TestSuite::Tester {
     template<class T> void indicesAsArray();
     void indicesIntoArrayInvalidSize();
     template<class T> void positions2DAsArray();
+    template<class T> void positions2DAsArrayPackedUnsigned();
+    template<class T> void positions2DAsArrayPackedSigned();
+    template<class T> void positions2DAsArrayPackedUnsignedNormalized();
+    template<class T> void positions2DAsArrayPackedSignedNormalized();
     void positions2DIntoArrayInvalidSize();
     template<class T> void positions3DAsArray();
+    template<class T> void positions3DAsArrayPackedUnsigned();
+    template<class T> void positions3DAsArrayPackedSigned();
+    template<class T> void positions3DAsArrayPackedUnsignedNormalized();
+    template<class T> void positions3DAsArrayPackedSignedNormalized();
     void positions3DIntoArrayInvalidSize();
     template<class T> void normalsAsArray();
+    template<class T> void normalsAsArrayPackedSignedNormalized();
     void normalsIntoArrayInvalidSize();
     template<class T> void textureCoordinates2DAsArray();
+    template<class T> void textureCoordinates2DAsArrayPackedUnsigned();
+    template<class T> void textureCoordinates2DAsArrayPackedSigned();
+    template<class T> void textureCoordinates2DAsArrayPackedUnsignedNormalized();
+    template<class T> void textureCoordinates2DAsArrayPackedSignedNormalized();
     void textureCoordinates2DIntoArrayInvalidSize();
     template<class T> void colorsAsArray();
+    template<class T> void colorsAsArrayPackedUnsignedNormalized();
     void colorsIntoArrayInvalidSize();
 
     void mutableAccessNotAllowed();
@@ -202,17 +217,71 @@ MeshDataTest::MeshDataTest() {
               &MeshDataTest::indicesAsArray<UnsignedInt>,
               &MeshDataTest::indicesIntoArrayInvalidSize,
               &MeshDataTest::positions2DAsArray<Vector2>,
+              &MeshDataTest::positions2DAsArray<Vector2h>,
               &MeshDataTest::positions2DAsArray<Vector3>,
+              &MeshDataTest::positions2DAsArray<Vector3h>,
+              &MeshDataTest::positions2DAsArrayPackedUnsigned<Vector2ub>,
+              &MeshDataTest::positions2DAsArrayPackedUnsigned<Vector2us>,
+              &MeshDataTest::positions2DAsArrayPackedUnsigned<Vector3ub>,
+              &MeshDataTest::positions2DAsArrayPackedUnsigned<Vector3us>,
+              &MeshDataTest::positions2DAsArrayPackedSigned<Vector2b>,
+              &MeshDataTest::positions2DAsArrayPackedSigned<Vector2s>,
+              &MeshDataTest::positions2DAsArrayPackedSigned<Vector3b>,
+              &MeshDataTest::positions2DAsArrayPackedSigned<Vector3s>,
+              &MeshDataTest::positions2DAsArrayPackedUnsignedNormalized<Vector2ub>,
+              &MeshDataTest::positions2DAsArrayPackedUnsignedNormalized<Vector2us>,
+              &MeshDataTest::positions2DAsArrayPackedUnsignedNormalized<Vector3ub>,
+              &MeshDataTest::positions2DAsArrayPackedUnsignedNormalized<Vector3us>,
+              &MeshDataTest::positions2DAsArrayPackedSignedNormalized<Vector2b>,
+              &MeshDataTest::positions2DAsArrayPackedSignedNormalized<Vector2s>,
+              &MeshDataTest::positions2DAsArrayPackedSignedNormalized<Vector3b>,
+              &MeshDataTest::positions2DAsArrayPackedSignedNormalized<Vector3s>,
               &MeshDataTest::positions2DIntoArrayInvalidSize,
               &MeshDataTest::positions3DAsArray<Vector2>,
+              &MeshDataTest::positions3DAsArray<Vector2h>,
               &MeshDataTest::positions3DAsArray<Vector3>,
+              &MeshDataTest::positions3DAsArray<Vector3h>,
+              &MeshDataTest::positions3DAsArrayPackedUnsigned<Vector2ub>,
+              &MeshDataTest::positions3DAsArrayPackedUnsigned<Vector2us>,
+              &MeshDataTest::positions3DAsArrayPackedUnsigned<Vector3ub>,
+              &MeshDataTest::positions3DAsArrayPackedUnsigned<Vector3us>,
+              &MeshDataTest::positions3DAsArrayPackedSigned<Vector2b>,
+              &MeshDataTest::positions3DAsArrayPackedSigned<Vector2s>,
+              &MeshDataTest::positions3DAsArrayPackedSigned<Vector3b>,
+              &MeshDataTest::positions3DAsArrayPackedSigned<Vector3s>,
+              &MeshDataTest::positions3DAsArrayPackedUnsignedNormalized<Vector2ub>,
+              &MeshDataTest::positions3DAsArrayPackedUnsignedNormalized<Vector2us>,
+              &MeshDataTest::positions3DAsArrayPackedUnsignedNormalized<Vector3ub>,
+              &MeshDataTest::positions3DAsArrayPackedUnsignedNormalized<Vector3us>,
+              &MeshDataTest::positions3DAsArrayPackedSignedNormalized<Vector2b>,
+              &MeshDataTest::positions3DAsArrayPackedSignedNormalized<Vector2s>,
+              &MeshDataTest::positions3DAsArrayPackedSignedNormalized<Vector3b>,
+              &MeshDataTest::positions3DAsArrayPackedSignedNormalized<Vector3s>,
               &MeshDataTest::positions3DIntoArrayInvalidSize,
               &MeshDataTest::normalsAsArray<Vector3>,
+              &MeshDataTest::normalsAsArray<Vector3h>,
+              &MeshDataTest::normalsAsArrayPackedSignedNormalized<Vector3b>,
+              &MeshDataTest::normalsAsArrayPackedSignedNormalized<Vector3s>,
               &MeshDataTest::normalsIntoArrayInvalidSize,
               &MeshDataTest::textureCoordinates2DAsArray<Vector2>,
+              &MeshDataTest::textureCoordinates2DAsArray<Vector2h>,
+              &MeshDataTest::textureCoordinates2DAsArrayPackedUnsigned<Vector2ub>,
+              &MeshDataTest::textureCoordinates2DAsArrayPackedUnsigned<Vector2us>,
+              &MeshDataTest::textureCoordinates2DAsArrayPackedSigned<Vector2b>,
+              &MeshDataTest::textureCoordinates2DAsArrayPackedSigned<Vector2s>,
+              &MeshDataTest::textureCoordinates2DAsArrayPackedUnsignedNormalized<Vector2ub>,
+              &MeshDataTest::textureCoordinates2DAsArrayPackedUnsignedNormalized<Vector2us>,
+              &MeshDataTest::textureCoordinates2DAsArrayPackedSignedNormalized<Vector2b>,
+              &MeshDataTest::textureCoordinates2DAsArrayPackedSignedNormalized<Vector2s>,
               &MeshDataTest::textureCoordinates2DIntoArrayInvalidSize,
               &MeshDataTest::colorsAsArray<Color3>,
+              &MeshDataTest::colorsAsArray<Color3h>,
               &MeshDataTest::colorsAsArray<Color4>,
+              &MeshDataTest::colorsAsArray<Color4h>,
+              &MeshDataTest::colorsAsArrayPackedUnsignedNormalized<Color3ub>,
+              &MeshDataTest::colorsAsArrayPackedUnsignedNormalized<Color3us>,
+              &MeshDataTest::colorsAsArrayPackedUnsignedNormalized<Color4ub>,
+              &MeshDataTest::colorsAsArrayPackedUnsignedNormalized<Color4us>,
               &MeshDataTest::colorsIntoArrayInvalidSize,
 
               &MeshDataTest::mutableAccessNotAllowed,
@@ -1290,9 +1359,25 @@ template<class> struct NameTraits;
         static const char* name() { return #format; }                       \
     };
 _c(Vector2)
+_c(Vector2h)
+_c(Vector2ub)
+_c(Vector2b)
+_c(Vector2us)
+_c(Vector2s)
 _c(Vector3)
+_c(Vector3h)
+_c(Vector3ub)
+_c(Vector3b)
+_c(Vector3us)
+_c(Vector3s)
 _c(Color3)
+_c(Color3h)
+_c(Color3ub)
+_c(Color3us)
 _c(Color4)
+_c(Color4h)
+_c(Color4ub)
+_c(Color4us)
 #undef _c
 
 template<class T> void MeshDataTest::indicesAsArray() {
@@ -1324,12 +1409,13 @@ void MeshDataTest::indicesIntoArrayInvalidSize() {
 
 template<class T> void MeshDataTest::positions2DAsArray() {
     setTestCaseTemplateName(NameTraits<T>::name());
+    typedef typename T::Type U;
 
     Containers::Array<char> vertexData{3*sizeof(T)};
     auto positionsView = Containers::arrayCast<T>(vertexData);
-    positionsView[0] = T::pad(Vector2{2.0f, 1.0f});
-    positionsView[1] = T::pad(Vector2{0.0f, -1.0f});
-    positionsView[2] = T::pad(Vector2{-2.0f, 3.0f});
+    positionsView[0] = T::pad(Math::Vector2<U>{U(2.0f), U(1.0f)});
+    positionsView[1] = T::pad(Math::Vector2<U>{U(0.0f), U(-1.0f)});
+    positionsView[2] = T::pad(Math::Vector2<U>{U(-2.0f), U(3.0f)});
 
     MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Position, positionsView}}};
     CORRADE_COMPARE_AS(data.positions2DAsArray(),
@@ -1337,6 +1423,70 @@ template<class T> void MeshDataTest::positions2DAsArray() {
         TestSuite::Compare::Container);
 }
 
+template<class T> void MeshDataTest::positions2DAsArrayPackedUnsigned() {
+    setTestCaseTemplateName(NameTraits<T>::name());
+
+    Containers::Array<char> vertexData{3*sizeof(T)};
+    auto positionsView = Containers::arrayCast<T>(vertexData);
+    positionsView[0] = T::pad(Math::Vector2<typename T::Type>{2, 1});
+    positionsView[1] = T::pad(Math::Vector2<typename T::Type>{0, 15});
+    positionsView[2] = T::pad(Math::Vector2<typename T::Type>{22, 3});
+
+    MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Position, positionsView}}};
+    CORRADE_COMPARE_AS(data.positions2DAsArray(),
+        Containers::arrayView<Vector2>({{2.0f, 1.0f}, {0.0f, 15.0f}, {22.0f, 3.0f}}),
+        TestSuite::Compare::Container);
+}
+
+template<class T> void MeshDataTest::positions2DAsArrayPackedSigned() {
+    setTestCaseTemplateName(NameTraits<T>::name());
+
+    Containers::Array<char> vertexData{3*sizeof(T)};
+    auto positionsView = Containers::arrayCast<T>(vertexData);
+    positionsView[0] = T::pad(Math::Vector2<typename T::Type>{2, 1});
+    positionsView[1] = T::pad(Math::Vector2<typename T::Type>{0, -15});
+    positionsView[2] = T::pad(Math::Vector2<typename T::Type>{-22, 3});
+
+    MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Position, positionsView}}};
+    CORRADE_COMPARE_AS(data.positions2DAsArray(),
+        Containers::arrayView<Vector2>({{2.0f, 1.0f}, {0.0f, -15.0f}, {-22.0f, 3.0f}}),
+        TestSuite::Compare::Container);
+}
+
+template<class T> void MeshDataTest::positions2DAsArrayPackedUnsignedNormalized() {
+    setTestCaseTemplateName(NameTraits<T>::name());
+
+    Containers::Array<char> vertexData{2*sizeof(T)};
+    auto positionsView = Containers::arrayCast<T>(vertexData);
+    positionsView[0] = T::pad(Math::Vector2<typename T::Type>{Math::pack<typename T::Type>(1.0f), 0});
+    positionsView[1] = T::pad(Math::Vector2<typename T::Type>{0, Math::pack<typename T::Type>(1.0f)});
+
+    MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Position,
+        /* Assuming the normalized enum is always after the non-normalized */
+        VertexFormat(UnsignedInt(Implementation::vertexFormatFor<T>()) + 1),
+        positionsView}}};
+    CORRADE_COMPARE_AS(data.positions2DAsArray(),
+        Containers::arrayView<Vector2>({{1.0f, 0.0f}, {0.0f, 1.0f}}),
+        TestSuite::Compare::Container);
+}
+
+template<class T> void MeshDataTest::positions2DAsArrayPackedSignedNormalized() {
+    setTestCaseTemplateName(NameTraits<T>::name());
+
+    Containers::Array<char> vertexData{2*sizeof(T)};
+    auto positionsView = Containers::arrayCast<T>(vertexData);
+    positionsView[0] = T::pad(Math::Vector2<typename T::Type>{Math::pack<typename T::Type>(1.0f), 0});
+    positionsView[1] = T::pad(Math::Vector2<typename T::Type>{0, Math::pack<typename T::Type>(-1.0f)});
+
+    MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Position,
+        /* Assuming the normalized enum is always after the non-normalized */
+        VertexFormat(UnsignedInt(Implementation::vertexFormatFor<T>()) + 1),
+        positionsView}}};
+    CORRADE_COMPARE_AS(data.positions2DAsArray(),
+        Containers::arrayView<Vector2>({{1.0f, 0.0f}, {0.0f, -1.0f}}),
+        TestSuite::Compare::Container);
+}
+
 void MeshDataTest::positions2DIntoArrayInvalidSize() {
     Containers::Array<char> vertexData{3*sizeof(Vector2)};
     MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Position, Containers::arrayCast<Vector2>(vertexData)}}};
@@ -1351,18 +1501,91 @@ void MeshDataTest::positions2DIntoArrayInvalidSize() {
 
 template<class T> void MeshDataTest::positions3DAsArray() {
     setTestCaseTemplateName(NameTraits<T>::name());
+    typedef typename T::Type U;
+
+    Containers::Array<char> vertexData{3*sizeof(T)};
+    auto positionsView = Containers::arrayCast<T>(vertexData);
+    /* Needs to be sufficiently representable to have the test work also for
+       half floats */
+    positionsView[0] = T::pad(Math::Vector3<U>{U(2.0f), U(1.0f), U(0.75f)});
+    positionsView[1] = T::pad(Math::Vector3<U>{U(0.0f), U(-1.0f), U(1.25f)});
+    positionsView[2] = T::pad(Math::Vector3<U>{U(-2.0f), U(3.0f), U(2.5f)});
+
+    MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Position, positionsView}}};
+    CORRADE_COMPARE_AS(data.positions3DAsArray(), Containers::arrayView<Vector3>({
+        Vector3::pad(Math::Vector<T::Size, Float>::pad(Vector3{2.0f, 1.0f, 0.75f})),
+        Vector3::pad(Math::Vector<T::Size, Float>::pad(Vector3{0.0f, -1.0f, 1.25f})),
+        Vector3::pad(Math::Vector<T::Size, Float>::pad(Vector3{-2.0f, 3.0f, 2.5f}))
+    }), TestSuite::Compare::Container);
+}
+
+template<class T> void MeshDataTest::positions3DAsArrayPackedUnsigned() {
+    setTestCaseTemplateName(NameTraits<T>::name());
 
     Containers::Array<char> vertexData{3*sizeof(T)};
     auto positionsView = Containers::arrayCast<T>(vertexData);
-    positionsView[0] = T::pad(Vector3{2.0f, 1.0f, 0.3f});
-    positionsView[1] = T::pad(Vector3{0.0f, -1.0f, 1.1f});
-    positionsView[2] = T::pad(Vector3{-2.0f, 3.0f, 2.2f});
+    positionsView[0] = T::pad(Math::Vector3<typename T::Type>{2, 1, 135});
+    positionsView[1] = T::pad(Math::Vector3<typename T::Type>{0, 15, 2});
+    positionsView[2] = T::pad(Math::Vector3<typename T::Type>{22, 3, 192});
 
     MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Position, positionsView}}};
     CORRADE_COMPARE_AS(data.positions3DAsArray(), Containers::arrayView<Vector3>({
-        Vector3::pad(T::pad(Vector3{2.0f, 1.0f, 0.3f})),
-        Vector3::pad(T::pad(Vector3{0.0f, -1.0f, 1.1f})),
-        Vector3::pad(T::pad(Vector3{-2.0f, 3.0f, 2.2f}))
+        Vector3::pad(Math::Vector<T::Size, Float>::pad(Vector3{2.0f, 1.0f, 135.0f})),
+        Vector3::pad(Math::Vector<T::Size, Float>::pad(Vector3{0.0f, 15.0f, 2.0f})),
+        Vector3::pad(Math::Vector<T::Size, Float>::pad(Vector3{22.0f, 3.0f, 192.0f}))
+    }), TestSuite::Compare::Container);
+}
+
+template<class T> void MeshDataTest::positions3DAsArrayPackedSigned() {
+    setTestCaseTemplateName(NameTraits<T>::name());
+
+    Containers::Array<char> vertexData{3*sizeof(T)};
+    auto positionsView = Containers::arrayCast<T>(vertexData);
+    positionsView[0] = T::pad(Math::Vector3<typename T::Type>{2, 1, -117});
+    positionsView[1] = T::pad(Math::Vector3<typename T::Type>{0, -15, 2});
+    positionsView[2] = T::pad(Math::Vector3<typename T::Type>{-22, 3, 86});
+
+    MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Position, positionsView}}};
+    CORRADE_COMPARE_AS(data.positions3DAsArray(), Containers::arrayView<Vector3>({
+        Vector3::pad(Math::Vector<T::Size, Float>::pad(Vector3{2.0f, 1.0f, -117.0f})),
+        Vector3::pad(Math::Vector<T::Size, Float>::pad(Vector3{0.0f, -15.0f, 2.0f})),
+        Vector3::pad(Math::Vector<T::Size, Float>::pad(Vector3{-22.0f, 3.0f, 86.0f}))
+    }), TestSuite::Compare::Container);
+}
+
+template<class T> void MeshDataTest::positions3DAsArrayPackedUnsignedNormalized() {
+    setTestCaseTemplateName(NameTraits<T>::name());
+
+    Containers::Array<char> vertexData{2*sizeof(T)};
+    auto positionsView = Containers::arrayCast<T>(vertexData);
+    positionsView[0] = T::pad(Math::Vector3<typename T::Type>{Math::pack<typename T::Type>(1.0f), 0, Math::pack<typename T::Type>(1.0f)});
+    positionsView[1] = T::pad(Math::Vector3<typename T::Type>{0, Math::pack<typename T::Type>(1.0f), 0});
+
+    MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Position,
+        /* Assuming the normalized enum is always after the non-normalized */
+        VertexFormat(UnsignedInt(Implementation::vertexFormatFor<T>()) + 1),
+        positionsView}}};
+    CORRADE_COMPARE_AS(data.positions3DAsArray(), Containers::arrayView<Vector3>({
+        Vector3::pad(Math::Vector<T::Size, Float>::pad(Vector3{1.0f, 0.0f, 1.0f})),
+        Vector3::pad(Math::Vector<T::Size, Float>::pad(Vector3{0.0f, 1.0f, 0.0f}))
+    }), TestSuite::Compare::Container);
+}
+
+template<class T> void MeshDataTest::positions3DAsArrayPackedSignedNormalized() {
+    setTestCaseTemplateName(NameTraits<T>::name());
+
+    Containers::Array<char> vertexData{2*sizeof(T)};
+    auto positionsView = Containers::arrayCast<T>(vertexData);
+    positionsView[0] = T::pad(Math::Vector3<typename T::Type>{Math::pack<typename T::Type>(1.0f), 0, Math::pack<typename T::Type>(1.0f)});
+    positionsView[1] = T::pad(Math::Vector3<typename T::Type>{0, Math::pack<typename T::Type>(-1.0f), 0});
+
+    MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Position,
+        /* Assuming the normalized enum is always after the non-normalized */
+        VertexFormat(UnsignedInt(Implementation::vertexFormatFor<T>()) + 1),
+        positionsView}}};
+    CORRADE_COMPARE_AS(data.positions3DAsArray(), Containers::arrayView<Vector3>({
+        Vector3::pad(Math::Vector<T::Size, Float>::pad(Vector3{1.0f, 0.0f, 1.0f})),
+        Vector3::pad(Math::Vector<T::Size, Float>::pad(Vector3{0.0f, -1.0f, 0.0f}))
     }), TestSuite::Compare::Container);
 }
 
@@ -1380,16 +1603,36 @@ void MeshDataTest::positions3DIntoArrayInvalidSize() {
 
 template<class T> void MeshDataTest::normalsAsArray() {
     setTestCaseTemplateName(NameTraits<T>::name());
+    typedef typename T::Type U;
 
     Containers::Array<char> vertexData{3*sizeof(T)};
     auto normalsView = Containers::arrayCast<T>(vertexData);
-    normalsView[0] = {2.0f, 1.0f, 0.3f};
-    normalsView[1] = {0.0f, -1.0f, 1.1f};
-    normalsView[2] = {-2.0f, 3.0f, 2.2f};
+    /* Needs to be sufficiently representable to have the test work also for
+       half floats */
+    normalsView[0] = {U(2.0f), U(1.0f), U(0.75f)};
+    normalsView[1] = {U(0.0f), U(-1.0f), U(1.25f)};
+    normalsView[2] = {U(-2.0f), U(3.0f), U(2.5f)};
 
     MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Normal, normalsView}}};
     CORRADE_COMPARE_AS(data.normalsAsArray(), Containers::arrayView<Vector3>({
-        {2.0f, 1.0f, 0.3f}, {0.0f, -1.0f, 1.1f}, {-2.0f, 3.0f, 2.2f},
+        {2.0f, 1.0f, 0.75f}, {0.0f, -1.0f, 1.25f}, {-2.0f, 3.0f, 2.5f},
+    }), TestSuite::Compare::Container);
+}
+
+template<class T> void MeshDataTest::normalsAsArrayPackedSignedNormalized() {
+    setTestCaseTemplateName(NameTraits<T>::name());
+
+    Containers::Array<char> vertexData{2*sizeof(T)};
+    auto normalsView = Containers::arrayCast<T>(vertexData);
+    normalsView[0] = {Math::pack<typename T::Type>(1.0f), 0, Math::pack<typename T::Type>(1.0f)};
+    normalsView[1] = {0, Math::pack<typename T::Type>(-1.0f), 0};
+
+    MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Normal,
+        /* Assuming the normalized enum is always after the non-normalized */
+        VertexFormat(UnsignedInt(Implementation::vertexFormatFor<T>()) + 1),
+        normalsView}}};
+    CORRADE_COMPARE_AS(data.normalsAsArray(), Containers::arrayView<Vector3>({
+        {1.0f, 0.0f, 1.0f}, {0.0f, -1.0f, 0.0f}
     }), TestSuite::Compare::Container);
 }
 
@@ -1407,12 +1650,13 @@ void MeshDataTest::normalsIntoArrayInvalidSize() {
 
 template<class T> void MeshDataTest::textureCoordinates2DAsArray() {
     setTestCaseTemplateName(NameTraits<T>::name());
+    typedef typename T::Type U;
 
     Containers::Array<char> vertexData{3*sizeof(T)};
     auto textureCoordinatesView = Containers::arrayCast<T>(vertexData);
-    textureCoordinatesView[0] = {2.0f, 1.0f};
-    textureCoordinatesView[1] = {0.0f, -1.0f};
-    textureCoordinatesView[2] = {-2.0f, 3.0f};
+    textureCoordinatesView[0] = {U(2.0f), U(1.0f)};
+    textureCoordinatesView[1] = {U(0.0f), U(-1.0f)};
+    textureCoordinatesView[2] = {U(-2.0f), U(3.0f)};
 
     MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::TextureCoordinates, textureCoordinatesView}}};
     CORRADE_COMPARE_AS(data.textureCoordinates2DAsArray(), Containers::arrayView<Vector2>({
@@ -1420,6 +1664,70 @@ template<class T> void MeshDataTest::textureCoordinates2DAsArray() {
     }), TestSuite::Compare::Container);
 }
 
+template<class T> void MeshDataTest::textureCoordinates2DAsArrayPackedUnsigned() {
+    setTestCaseTemplateName(NameTraits<T>::name());
+
+    Containers::Array<char> vertexData{3*sizeof(T)};
+    auto textureCoordinatesView = Containers::arrayCast<T>(vertexData);
+    textureCoordinatesView[0] = {2, 1};
+    textureCoordinatesView[1] = {0, 15};
+    textureCoordinatesView[2] = {22, 3};
+
+    MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::TextureCoordinates, textureCoordinatesView}}};
+    CORRADE_COMPARE_AS(data.textureCoordinates2DAsArray(),
+        Containers::arrayView<Vector2>({{2.0f, 1.0f}, {0.0f, 15.0f}, {22.0f, 3.0f}}),
+        TestSuite::Compare::Container);
+}
+
+template<class T> void MeshDataTest::textureCoordinates2DAsArrayPackedSigned() {
+    setTestCaseTemplateName(NameTraits<T>::name());
+
+    Containers::Array<char> vertexData{3*sizeof(T)};
+    auto textureCoordinatesView = Containers::arrayCast<T>(vertexData);
+    textureCoordinatesView[0] = {2, 1};
+    textureCoordinatesView[1] = {0, -15};
+    textureCoordinatesView[2] = {-22, 3};
+
+    MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::TextureCoordinates, textureCoordinatesView}}};
+    CORRADE_COMPARE_AS(data.textureCoordinates2DAsArray(),
+        Containers::arrayView<Vector2>({{2.0f, 1.0f}, {0.0f, -15.0f}, {-22.0f, 3.0f}}),
+        TestSuite::Compare::Container);
+}
+
+template<class T> void MeshDataTest::textureCoordinates2DAsArrayPackedUnsignedNormalized() {
+    setTestCaseTemplateName(NameTraits<T>::name());
+
+    Containers::Array<char> vertexData{2*sizeof(T)};
+    auto textureCoordinatesView = Containers::arrayCast<T>(vertexData);
+    textureCoordinatesView[0] = {Math::pack<typename T::Type>(1.0f), 0};
+    textureCoordinatesView[1] = {0, Math::pack<typename T::Type>(1.0f)};
+
+    MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::TextureCoordinates,
+        /* Assuming the normalized enum is always after the non-normalized */
+        VertexFormat(UnsignedInt(Implementation::vertexFormatFor<T>()) + 1),
+        textureCoordinatesView}}};
+    CORRADE_COMPARE_AS(data.textureCoordinates2DAsArray(),
+        Containers::arrayView<Vector2>({{1.0f, 0.0f}, {0.0f, 1.0f}}),
+        TestSuite::Compare::Container);
+}
+
+template<class T> void MeshDataTest::textureCoordinates2DAsArrayPackedSignedNormalized() {
+    setTestCaseTemplateName(NameTraits<T>::name());
+
+    Containers::Array<char> vertexData{2*sizeof(T)};
+    auto textureCoordinatesView = Containers::arrayCast<T>(vertexData);
+    textureCoordinatesView[0] = {Math::pack<typename T::Type>(1.0f), 0};
+    textureCoordinatesView[1] = {0, Math::pack<typename T::Type>(-1.0f)};
+
+    MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::TextureCoordinates,
+        /* Assuming the normalized enum is always after the non-normalized */
+        VertexFormat(UnsignedInt(Implementation::vertexFormatFor<T>()) + 1),
+        textureCoordinatesView}}};
+    CORRADE_COMPARE_AS(data.textureCoordinates2DAsArray(),
+        Containers::arrayView<Vector2>({{1.0f, 0.0f}, {0.0f, -1.0f}}),
+        TestSuite::Compare::Container);
+}
+
 void MeshDataTest::textureCoordinates2DIntoArrayInvalidSize() {
     Containers::Array<char> vertexData{3*sizeof(Vector2)};
     MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::TextureCoordinates, Containers::arrayCast<Vector2>(vertexData)}}};
@@ -1434,16 +1742,34 @@ void MeshDataTest::textureCoordinates2DIntoArrayInvalidSize() {
 
 template<class T> void MeshDataTest::colorsAsArray() {
     setTestCaseTemplateName(NameTraits<T>::name());
+    typedef typename T::Type U;
 
     Containers::Array<char> vertexData{3*sizeof(T)};
     auto colorsView = Containers::arrayCast<T>(vertexData);
-    colorsView[0] = 0xff3366_rgbf;
-    colorsView[1] = 0x99aacc_rgbf;
-    colorsView[2] = 0x3377ff_rgbf;
+    /* Can't use e.g. 0xff3366_rgbf because that's not representable in
+       half-floats */
+    colorsView[0] = {U(2.0f), U(1.0f), U(0.75f)};
+    colorsView[1] = {U(0.0f), U(-1.0f), U(1.25f)};
+    colorsView[2] = {U(-2.0f), U(3.0f), U(2.5f)};
+
+    MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Color, colorsView}}};
+    CORRADE_COMPARE_AS(data.colorsAsArray(), Containers::arrayView<Color4>({
+        {2.0f, 1.0f, 0.75f}, {0.0f, -1.0f, 1.25f}, {-2.0f, 3.0f, 2.5f},
+    }), TestSuite::Compare::Container);
+}
+
+template<class T> void MeshDataTest::colorsAsArrayPackedUnsignedNormalized() {
+    setTestCaseTemplateName(NameTraits<T>::name());
+
+    Containers::Array<char> vertexData{2*sizeof(T)};
+    auto colorsView = Containers::arrayCast<T>(vertexData);
+    colorsView[0] = T::pad(Math::Color4<typename T::Type>{Math::pack<typename T::Type>(1.0f), 0, Math::pack<typename T::Type>(1.0f), 0});
+    colorsView[1] = T::pad(Math::Color4<typename T::Type>{0, Math::pack<typename T::Type>(1.0f), 0, Math::pack<typename T::Type>(1.0f)});
 
     MeshData data{MeshPrimitive::Points, std::move(vertexData), {MeshAttributeData{MeshAttribute::Color, colorsView}}};
     CORRADE_COMPARE_AS(data.colorsAsArray(), Containers::arrayView<Color4>({
-        0xff3366_rgbf, 0x99aacc_rgbf, 0x3377ff_rgbf
+        Color4::pad(Math::Vector<T::Size, Float>::pad(Vector4{1.0f, 0.0f, 1.0f, 0.0f}), 1.0f),
+        Color4::pad(Math::Vector<T::Size, Float>::pad(Vector4{0.0f, 1.0f, 0.0f, 1.0f}), 1.0f)
     }), TestSuite::Compare::Container);
 }