Math: make one-dimensional range just from scalar types.

Since Range1D is now used all over Animation, the vector made it very
annoying to use. That's fixed now. This is a backwards-incompatible
change, but I don't expect the 1D range to be used much, mainly because
it was so shitty to use. Generic code that needs a vector can always
cast to it, like this:

    Math::Vector<dimensions, T>{range.min()}

Test for the constructor from pair is no longer accepting pairs of 1D
vectors. I have no idea what I meant by that test case (it's testing the
same thing twice), so I removed one of these.

doc/changelog.dox

@@ -528,6 +528,12 @@ See also:
     working to fail with an assertion. See the new
     @ref Math::Matrix3::rotationShear() and @ref Math::Matrix4::rotationShear()
     accessors for a possible solution.
+-   Since one-dimensional @ref Math::Range is now used on many new places such
+    as the @ref Animation library, its underlying type is just @cpp T @ce
+    instead of @ref Math::Vector "Math::Vector<1, T>" to make it easier to use.
+    This may break rare existing code that was using one-dimensional ranges or
+    generic code that's always expecting a vector type. See
+    @ref Math-Range-generic for possible solutions.
 -   @ref SceneGraph::Camera::setViewport() and @ref SceneGraph::Camera::draw()
     are no longer @cpp virtual @ce functions. If you need to override their
     functionality, simply call the subclass implementation directly instead of

doc/snippets/MagnumMath.cpp

@@ -873,6 +873,19 @@ Debug{} << Math::Vector3<UnsignedShort>{a};  // prints {16968, 48552, 15993}
 /* [Half-usage-vector] */
 }
 
+{
+Range1D range, a, b;
+constexpr UnsignedInt dimensions = 1;
+typedef Float T;
+/* [Range-generic] */
+Math::Vector<dimensions, T> min = range.min(); // works for 1D, 2D and 3D
+
+T c = Math::max<dimensions, T>(a.size(), b.size()).product(); // vector max()
+/* [Range-generic] */
+static_cast<void>(min);
+static_cast<void>(c);
+}
+
 {
 /* [Range-construct-minmax] */
 Vector3 a, b, c;

src/Magnum/Animation/Player.hpp

@@ -250,7 +250,7 @@ template<class T, class K> std::pair<UnsignedInt, K> Player<T, K>::elapsed(const
     T startTime = _startTime;
     T pauseTime = _stopPauseTime;
     State state = _state;
-    const K duration = _duration.size()[0];
+    const K duration = _duration.size();
     const Containers::Optional<std::pair<UnsignedInt, K>> elapsed = Implementation::playerElapsed(duration, _playCount, _scaler, time, startTime, pauseTime, state);
     if(elapsed) return *elapsed;
 
@@ -282,12 +282,12 @@ template<class T, class K> std::pair<UnsignedInt, K> Player<T, K>::elapsed(const
 template<class T, class K> Player<T, K>& Player<T, K>::advance(const T time) {
     /* Get the elapsed time. If we shouldn't advance anything (player already
        stopped / not yet playing, quit */
-    Containers::Optional<std::pair<UnsignedInt, K>> elapsed = Implementation::playerElapsed(_duration.size()[0], _playCount, _scaler, time, _startTime, _stopPauseTime, _state);
+    Containers::Optional<std::pair<UnsignedInt, K>> elapsed = Implementation::playerElapsed(_duration.size(), _playCount, _scaler, time, _startTime, _stopPauseTime, _state);
     if(!elapsed) return *this;
 
     /* Advance all tracks. Properly handle durations that don't start at 0. */
     for(Track& t: _tracks)
-        t.advancer(t.track, _duration.min()[0] + elapsed->second, t.hint, t.destination, t.userCallback, t.userCallbackData);
+        t.advancer(t.track, _duration.min() + elapsed->second, t.hint, t.destination, t.userCallback, t.userCallbackData);
 
     return *this;
 }

src/Magnum/Animation/Test/PlayerCustomTest.cpp

@@ -67,7 +67,7 @@ void PlayerCustomTest::test() {
     player.add(Track, value)
         .play(2000000ull);
 
-    CORRADE_COMPARE(player.duration().size()[0], 24*3);
+    CORRADE_COMPARE(player.duration().size(), 24*3);
 
     /* 1.75 secs in */
     player.advance(3750000ull);

src/Magnum/Animation/Test/PlayerTest.cpp

@@ -1230,7 +1230,7 @@ void PlayerTest::runFor100YearsFloat() {
 
     /* The track must fit an integer number of times into the day for this test
        to work (3 seconds do fit) */
-    CORRADE_COMPARE(player.duration().size()[0], 3.0f);
+    CORRADE_COMPARE(player.duration().size(), 3.0f);
 
     CORRADE_COMPARE(player.state(), State::Playing);
     CORRADE_COMPARE(value, -1.0f);
@@ -1277,7 +1277,7 @@ void PlayerTest::runFor100YearsChrono() {
 
     /* The track must fit an integer number of times into the day for this test
        to work (3 seconds do fit) */
-    CORRADE_COMPARE(player.duration().size()[0], 3.0f);
+    CORRADE_COMPARE(player.duration().size(), 3.0f);
 
     CORRADE_COMPARE(player.state(), State::Playing);
     CORRADE_COMPARE(value, -1.0f);

src/Magnum/GL/AbstractTexture.cpp

@@ -1795,7 +1795,7 @@ template<UnsignedInt dimensions> void AbstractTexture::subImage(const GLint leve
 
     const Math::Vector<dimensions, Int> size = range.size();
     const std::size_t dataSize = Magnum::Implementation::imageDataSizeFor(image, size);
-    const Vector3i paddedOffset = Vector3i::pad(range.min());
+    const Vector3i paddedOffset = Vector3i::pad<dimensions>(range.min());
     const Vector3i paddedSize = Vector3i::pad(size, 1);
 
     /* Reallocate only if needed */
@@ -1818,7 +1818,7 @@ template<UnsignedInt dimensions> void AbstractTexture::subImage(const GLint leve
 
     const Math::Vector<dimensions, Int> size = range.size();
     const std::size_t dataSize = Magnum::Implementation::imageDataSizeFor(image, size);
-    const Vector3i paddedOffset = Vector3i::pad(range.min());
+    const Vector3i paddedOffset = Vector3i::pad<dimensions>(range.min());
     const Vector3i paddedSize = Vector3i::pad(size, 1);
 
     /* Reallocate only if needed */
@@ -1848,7 +1848,7 @@ template<UnsignedInt dimensions> void AbstractTexture::compressedSubImage(const
     createIfNotAlready();
 
     const Math::Vector<dimensions, Int> size = range.size();
-    const Vector3i paddedOffset = Vector3i::pad(range.min());
+    const Vector3i paddedOffset = Vector3i::pad<dimensions>(range.min());
     const Vector3i paddedSize = Vector3i::pad(size, 1);
 
     /* Internal texture format */
@@ -1882,7 +1882,7 @@ template<UnsignedInt dimensions> void AbstractTexture::compressedSubImage(const
     createIfNotAlready();
 
     const Math::Vector<dimensions, Int> size = range.size();
-    const Vector3i paddedOffset = Vector3i::pad(range.min());
+    const Vector3i paddedOffset = Vector3i::pad<dimensions>(range.min());
     const Vector3i paddedSize = Vector3i::pad(size, 1);
 
     /* Internal texture format */

src/Magnum/GL/Renderer.cpp

@@ -40,7 +40,7 @@ Range1D Renderer::lineWidthRange() {
     Range1D& value = state.lineWidthRange;
 
     /* Get the value, if not already cached */
-    if(value.max().isZero())
+    if(!value.max())
         value = state.lineWidthRangeImplementation();
 
     return value;
@@ -55,7 +55,7 @@ Range1D Renderer::lineWidthRangeImplementationDefault() {
 #ifndef MAGNUM_TARGET_GLES
 Range1D Renderer::lineWidthRangeImplementationMesaForwardCompatible() {
     Range1D value = lineWidthRangeImplementationDefault();
-    value.max() = Math::min(1.0f, value.max()[0]);
+    value.max() = Math::min(1.0f, value.max());
     return value;
 }
 #endif

src/Magnum/GL/Test/RendererGLTest.cpp

@@ -55,7 +55,7 @@ void RendererGLTest::maxLineWidth() {
 
     MAGNUM_VERIFY_NO_GL_ERROR();
 
-    Renderer::setLineWidth(lineWidthRange.max()[0]);
+    Renderer::setLineWidth(lineWidthRange.max());
 
     MAGNUM_VERIFY_NO_GL_ERROR();
 }

src/Magnum/Math/Range.h

@@ -37,7 +37,7 @@ namespace Magnum { namespace Math {
 namespace Implementation {
     template<UnsignedInt, class> struct RangeTraits;
 
-    template<class T> struct RangeTraits<1, T> { typedef Vector<1, T> Type; };
+    template<class T> struct RangeTraits<1, T> { typedef T Type; };
     template<class T> struct RangeTraits<2, T> { typedef Vector2<T> Type; };
     template<class T> struct RangeTraits<3, T> { typedef Vector3<T> Type; };
 
@@ -47,9 +47,19 @@ namespace Implementation {
 /**
 @brief N-dimensional range
 
-Axis-aligned line (in 1D), rectangle (in 2D) or cube (in 3D). Minimal
+Axis-aligned line (in 1D), rectangle (in 2D) or cube (in 3D). The minimal
 coordinate is inclusive, maximal exclusive. See @ref Range1D, @ref Range2D and
 @ref Range3D specializations for given dimension count.
+
+@section Math-Range-generic Use in generic code
+
+While @ref Range2D and @ref Range3D have a vector underlying type, @ref Range1D
+is just a scalar. This makes common usage simpler, but may break in generic
+code that expects a vector type for any dimension. Solution is to
+unconditionally cast the value to a vector type or explicitly specify template
+parameters to choose a vector function overload. For example:
+
+@snippet MagnumMath.cpp Range-generic
 */
 template<UnsignedInt dimensions, class T> class Range {
     template<UnsignedInt, class> friend class Range;
@@ -58,8 +68,8 @@ template<UnsignedInt dimensions, class T> class Range {
         /**
          * @brief Underlying vector type
          *
-         * @ref Math::Vector "Vector<1, T>" in 1D, @ref Math::Vector2 "Vector2<T>"
-         * in 2D, @ref Math::Vector3 "Vector3<T>" in 3D.
+         * @cpp T @ce in 1D, @ref Math::Vector2 "Vector2<T>" in 2D,
+         * @ref Math::Vector3 "Vector3<T>" in 3D.
          */
         typedef typename Implementation::RangeTraits<dimensions, T>::Type VectorType;
 
@@ -91,10 +101,10 @@ template<UnsignedInt dimensions, class T> class Range {
          *
          * Construct zero-size range positioned at origin.
          */
-        constexpr /*implicit*/ Range(ZeroInitT = ZeroInit) noexcept: _min{ZeroInit}, _max{ZeroInit} {}
+        constexpr /*implicit*/ Range(ZeroInitT = ZeroInit) noexcept: Range<dimensions, T>{ZeroInit, typename std::conditional<dimensions == 1, void*, ZeroInitT*>::type{}} {}
 
         /** @brief Construct without initializing the contents */
-        explicit Range(NoInitT) noexcept: _min{NoInit}, _max{NoInit} {}
+        explicit Range(NoInitT) noexcept: Range<dimensions, T>{NoInit, typename std::conditional<dimensions == 1, void*, NoInitT*>::type{}} {}
 
         /** @brief Construct a range from minimal and maximal coordinates */
         constexpr /*implicit*/ Range(const VectorType& min, const VectorType& max) noexcept: _min{min}, _max{max} {}
@@ -143,12 +153,10 @@ template<UnsignedInt dimensions, class T> class Range {
         }
 
         /** @brief Equality comparison */
-        constexpr bool operator==(const Range<dimensions, T>& other) const {
-            return _min == other._min && _max == other._max;
-        }
+        bool operator==(const Range<dimensions, T>& other) const;
 
         /** @brief Non-equality comparison */
-        constexpr bool operator!=(const Range<dimensions, T>& other) const {
+        bool operator!=(const Range<dimensions, T>& other) const {
             return !operator==(other);
         }
 
@@ -156,8 +164,12 @@ template<UnsignedInt dimensions, class T> class Range {
          * @brief Raw data
          * @return One-dimensional array of `dimensions`*2 length.
          */
-        T* data() { return _min.data(); }
-        constexpr const T* data() const { return _min.data(); } /**< @overload */
+        T* data() {
+            return dataInternal(typename std::conditional<dimensions == 1, void*, T*>::type{});
+        }
+        constexpr const T* data() const {
+            return dataInternal(typename std::conditional<dimensions == 1, void*, T*>::type{});
+        } /**< @overload */
 
         /**
          * @brief Minimal coordinates (inclusive)
@@ -258,7 +270,8 @@ template<UnsignedInt dimensions, class T> class Range {
          *      @ref min(), @ref max()
          */
         bool contains(const VectorType& b) const {
-            return (b >= _min).all() && (b < _max).all();
+            return (Vector<dimensions, T>{b} >= _min).all() &&
+                   (Vector<dimensions, T>{b} < _max).all();
         }
 
         /**
@@ -276,10 +289,27 @@ template<UnsignedInt dimensions, class T> class Range {
          *      @ref min(), @ref max()
          */
         bool contains(const Range<dimensions, T>& b) const {
-            return (b._min >= _min).all() && (b._max <= _max).all();
+            return (Vector<dimensions, T>{b._min} >= _min).all() &&
+                   (Vector<dimensions, T>{b._max} <= _max).all();
         }
 
     private:
+        /* Called from Range(ZeroInit), either using the ZeroInit constructor
+           (if available) or passing zero directly (for scalar types) */
+        constexpr explicit Range(ZeroInitT, ZeroInitT*) noexcept: _min{ZeroInit}, _max{ZeroInit} {}
+        constexpr explicit Range(ZeroInitT, void*) noexcept: _min{T(0)}, _max{T(0)} {}
+
+        /* Called from Range(NoInit), either using the NoInit constructor (if
+           available) or not doing anything */
+        explicit Range(NoInitT, NoInitT*) noexcept: _min{NoInit}, _max{NoInit} {}
+        explicit Range(NoInitT, void*) noexcept {}
+
+        /* Called from data(), always returning a T* */
+        constexpr const VectorType* dataInternal(void*) const { return &_min; }
+        VectorType* dataInternal(void*) { return &_min; }
+        constexpr const T* dataInternal(T*) const { return _min.data(); }
+        T* dataInternal(T*) { return _min.data(); }
+
         VectorType _min, _max;
 };
 
@@ -693,21 +723,29 @@ are undefined if any range has a negative size.
     @ref Range::max()
 */
 template<UnsignedInt dimensions, class T> inline bool intersects(const Range<dimensions, T>& a, const Range<dimensions, T>& b) {
-    return (a.max() > b.min()).all() && (a.min() < b.max()).all();
+    return (Vector<dimensions, T>{a.max()} > b.min()).all() &&
+           (Vector<dimensions, T>{a.min()} < b.max()).all();
 }
 
 /** @debugoperator{Range} */
 template<UnsignedInt dimensions, class T> Corrade::Utility::Debug& operator<<(Corrade::Utility::Debug& debug, const Range<dimensions, T>& value) {
-    debug << "Range({" << Corrade::Utility::Debug::nospace << value.min()[0];
+    debug << "Range({" << Corrade::Utility::Debug::nospace << Vector<dimensions, T>{value.min()}[0];
     for(UnsignedInt i = 1; i != dimensions; ++i)
-        debug << Corrade::Utility::Debug::nospace << "," << value.min()[i];
+        debug << Corrade::Utility::Debug::nospace << "," << Vector<dimensions, T>{value.min()}[i];
     debug << Corrade::Utility::Debug::nospace << "}, {"
-          << Corrade::Utility::Debug::nospace << value.max()[0];
+          << Corrade::Utility::Debug::nospace << Vector<dimensions, T>{value.max()}[0];
     for(UnsignedInt i = 1; i != dimensions; ++i)
-        debug << Corrade::Utility::Debug::nospace << "," << value.max()[i];
+        debug << Corrade::Utility::Debug::nospace << "," << Vector<dimensions, T>{value.max()}[i];
     return debug << Corrade::Utility::Debug::nospace << "})";
 }
 
+template<UnsignedInt dimensions, class T> inline bool Range<dimensions, T>::operator==(const Range<dimensions, T>& other) const {
+    /* For non-scalar types default implementation of TypeTraits would be used,
+       which is just operator== */
+    return TypeTraits<VectorType>::equals(_min, other._min) &&
+        TypeTraits<VectorType>::equals(_max, other._max);
+}
+
 /* Explicit instantiation for commonly used types */
 #ifndef DOXYGEN_GENERATING_OUTPUT
 extern template MAGNUM_EXPORT Corrade::Utility::Debug& operator<<(Corrade::Utility::Debug&, const Range<1, Float>&);

src/Magnum/Math/Test/RangeTest.cpp

@@ -52,9 +52,9 @@ template<> struct RangeConverter<1, Float, Dim> {
     }
 
     constexpr static Dim to(const Range<1, Float>& other) {
-        return {other.min()[0],
+        return {other.min(),
                 /* Doing it this way to preserve constexpr */
-                other.max()[0] - other.min()[0]};
+                other.max() - other.min()};
     }
 };
 
@@ -113,15 +113,26 @@ struct RangeTest: Corrade::TestSuite::Tester {
     void size();
     void center();
 
+    /* Testing 1D separately because it's a scalar, not vector. The above
+       functions test all dimensions explicitly. */
+
     void translated();
+    void translated1D();
     void padded();
+    void padded1D();
     void scaled();
+    void scaled1D();
     void scaledFromCenter();
+    void scaledFromCenter1D();
 
-    void containsVector();
+    void containsPoint();
+    void containsPoint1D();
     void containsRange();
+    void containsRange1D();
     void intersectIntersects();
+    void intersectIntersects1D();
     void join();
+    void join1D();
 
     void subclassTypes();
     void subclass();
@@ -157,14 +168,22 @@ RangeTest::RangeTest() {
               &RangeTest::center,
 
               &RangeTest::translated,
+              &RangeTest::translated1D,
               &RangeTest::padded,
+              &RangeTest::padded1D,
               &RangeTest::scaled,
+              &RangeTest::scaled1D,
               &RangeTest::scaledFromCenter,
+              &RangeTest::scaledFromCenter1D,
 
-              &RangeTest::containsVector,
+              &RangeTest::containsPoint,
+              &RangeTest::containsPoint1D,
               &RangeTest::containsRange,
+              &RangeTest::containsRange1D,
               &RangeTest::intersectIntersects,
+              &RangeTest::intersectIntersects1D,
               &RangeTest::join,
+              &RangeTest::join1D,
 
               &RangeTest::subclassTypes,
               &RangeTest::subclass,
@@ -255,11 +274,9 @@ void RangeTest::constructPair() {
     Vector2i b{30, 18};
     Vector2i c{20, 25};
 
-    Range1Di bounds1a{Math::minmax<Math::Vector<1, Int>>({a.x(), b.x(), c.x()})};
-    Range1Di bounds1b{std::pair<Math::Vector<1, Int>, Math::Vector<1, Int>>{10, 30}};
+    Range1Di bounds1a{Math::minmax({a.x(), b.x(), c.x()})};
     Range1Di bounds1c{10, 30};
     CORRADE_COMPARE(bounds1a, bounds1c);
-    CORRADE_COMPARE(bounds1b, bounds1c);
 
     Range2Di bounds2a{Math::minmax({a, b, c})};
     Range2Di bounds2b{std::pair<Math::Vector<2, Int>, Math::Vector<2, Int>>{{10, 18}, {30, 25}}};
@@ -372,6 +389,16 @@ void RangeTest::access() {
     constexpr Range2Di crect({34, 23}, {47, 30});
     constexpr Range3Di ccube({34, 23, -17}, {47, 30, 12});
 
+    CORRADE_COMPARE(line.data(), static_cast<void*>(&line));
+    CORRADE_COMPARE(rect.data(), static_cast<void*>(&rect));
+    CORRADE_COMPARE(cube.data(), static_cast<void*>(&cube));
+    constexpr Int lineData = *cline.data();
+    constexpr Int rectData = *crect.data();
+    constexpr Int cubeData = *ccube.data();
+    CORRADE_COMPARE(lineData, 34);
+    CORRADE_COMPARE(rectData, 34);
+    CORRADE_COMPARE(cubeData, 34);
+
     CORRADE_COMPARE(line.min(), 34);
     CORRADE_COMPARE(cline.min(), 34);
     CORRADE_COMPARE(line.max(), 47);
@@ -520,6 +547,14 @@ void RangeTest::translated() {
     CORRADE_COMPARE(a.size(), b.size());
 }
 
+void RangeTest::translated1D() {
+    Range1Di a(34, 47);
+    Range1Di b(17, 30);
+
+    CORRADE_COMPARE(a.translated(-17), b);
+    CORRADE_COMPARE(a.size(), b.size());
+}
+
 void RangeTest::padded() {
     Range2Di a({34, 23}, {47, 30});
     Range2Di b({31, 28}, {50, 25});
@@ -528,6 +563,14 @@ void RangeTest::padded() {
     CORRADE_COMPARE(a.center(), b.center());
 }
 
+void RangeTest::padded1D() {
+    Range1Di a{34, 47};
+    Range1Di b{31, 50};
+
+    CORRADE_COMPARE(a.padded(3), b);
+    CORRADE_COMPARE(a.center(), b.center());
+}
+
 void RangeTest::scaled() {
     Range2Di a({34, 23}, {47, 30});
     Range2Di b({68, -69}, {94, -90});
@@ -536,6 +579,14 @@ void RangeTest::scaled() {
     CORRADE_COMPARE((a.size()*Vector2i{2, -3}), b.size());
 }
 
+void RangeTest::scaled1D() {
+    Range1Di a{34, 47};
+    Range1Di b{68, 94};
+
+    CORRADE_COMPARE(a.scaled(2), b);
+    CORRADE_COMPARE(a.size()*2, b.size());
+}
+
 void RangeTest::scaledFromCenter() {
     Range2Di a{{34, 22}, {48, 30}};
     Range2Di b{{27, 38}, {55, 14}};
@@ -545,7 +596,16 @@ void RangeTest::scaledFromCenter() {
     CORRADE_COMPARE((a.size()*Vector2i{2, -3}), b.size());
 }
 
-void RangeTest::containsVector() {
+void RangeTest::scaledFromCenter1D() {
+    Range1Di a{34, 48};
+    Range1Di b{27, 55};
+
+    CORRADE_COMPARE(a.scaledFromCenter(2), b);
+    CORRADE_COMPARE(a.center(), b.center());
+    CORRADE_COMPARE(a.size()*2, b.size());
+}
+
+void RangeTest::containsPoint() {
     Range2Di a({34, 23}, {47, 30});
 
     CORRADE_VERIFY(a.contains({40, 23}));
@@ -557,6 +617,17 @@ void RangeTest::containsVector() {
     CORRADE_VERIFY(!a.contains({47, 30}));
 }
 
+void RangeTest::containsPoint1D() {
+    Range1Di a{34, 47};
+
+    CORRADE_VERIFY(a.contains(40));
+    CORRADE_VERIFY(!a.contains(33));
+
+    /* Contains a point at min, but not at max */
+    CORRADE_VERIFY(a.contains(34));
+    CORRADE_VERIFY(!a.contains(47));
+}
+
 void RangeTest::containsRange() {
     Range2Di a({34, 23}, {47, 30});
 
@@ -593,6 +664,42 @@ void RangeTest::containsRange() {
     CORRADE_VERIFY(!a.contains(j));
 }
 
+void RangeTest::containsRange1D() {
+    Range1Di a{34, 47};
+
+    /* Contains whole range with a gap, not the other way around */
+    Range1Di b{35, 40};
+    CORRADE_VERIFY(a.contains(b));
+    CORRADE_VERIFY(!b.contains(a));
+
+    /* Contains itself, empty range contains itself as well */
+    Range1Di c;
+    CORRADE_VERIFY(a.contains(a));
+    CORRADE_VERIFY(b.contains(b));
+    CORRADE_VERIFY(c.contains(c));
+
+    /* Contains zero-sized range inside but not outside */
+    Range1Di d{34, 34};
+    Range1Di e{33, 33};
+    Range1Di f{47, 47};
+    Range1Di g{48, 48};
+    CORRADE_VERIFY(a.contains(d));
+    CORRADE_VERIFY(!a.contains(e));
+    CORRADE_VERIFY(a.contains(f));
+    CORRADE_VERIFY(!a.contains(g));
+
+    /* Doesn't contain a range that overlaps */
+    Range1Di h{30, 35};
+    CORRADE_VERIFY(!a.contains(h));
+    CORRADE_VERIFY(!h.contains(a));
+
+    /* Doesn't contain a range touching the edges from the outside */
+    Range1Di i{20, 34};
+    Range1Di j{47, 60};
+    CORRADE_VERIFY(!a.contains(i));
+    CORRADE_VERIFY(!a.contains(j));
+}
+
 void RangeTest::intersectIntersects() {
     Range2Di a({34, 23}, {47, 30});
 
@@ -645,6 +752,48 @@ void RangeTest::intersectIntersects() {
     CORRADE_COMPARE(Math::intersect(l, a), Range2Di{});
 }
 
+void RangeTest::intersectIntersects1D() {
+    Range1Di a(34, 47);
+
+    /* Intersects itself */
+    CORRADE_VERIFY(Math::intersects(a, a));
+    CORRADE_COMPARE(Math::intersect(a, a), a);
+
+    /* Non-empty intersection */
+    Range1Di b{30, 35};
+    Range1Di c{34, 35};
+    CORRADE_VERIFY(Math::intersects(a, b));
+    CORRADE_VERIFY(Math::intersects(b, a));
+    CORRADE_COMPARE(Math::intersect(a, b), c);
+    CORRADE_COMPARE(Math::intersect(b, a), c);
+
+    /* Intersecting with an empty range outside produces a default-constructed range */
+    Range1Di d{130, 130};
+    CORRADE_VERIFY(!Math::intersects(a, d));
+    CORRADE_VERIFY(!Math::intersects(d, a));
+    CORRADE_COMPARE(Math::intersect(a, d), Range1Di{});
+    CORRADE_COMPARE(Math::intersect(d, a), Range1Di{});
+
+    /* Intersecting with an empty range inside produces an empty range */
+    Range1Di e{40, 40};
+    CORRADE_VERIFY(Math::intersects(a, e));
+    CORRADE_VERIFY(Math::intersects(e, a));
+    CORRADE_COMPARE(Math::intersect(a, e), e);
+    CORRADE_COMPARE(Math::intersect(e, a), e);
+
+    /* Doesn't intersect a range touching the edges from the outside */
+    Range1Di i{20, 34};
+    Range1Di j{47, 60};
+    CORRADE_VERIFY(!Math::intersects(a, i));
+    CORRADE_VERIFY(!Math::intersects(a, j));
+    CORRADE_VERIFY(!Math::intersects(i, a));
+    CORRADE_VERIFY(!Math::intersects(j, a));
+    CORRADE_COMPARE(Math::intersect(a, i), Range1Di{});
+    CORRADE_COMPARE(Math::intersect(a, j), Range1Di{});
+    CORRADE_COMPARE(Math::intersect(i, a), Range1Di{});
+    CORRADE_COMPARE(Math::intersect(j, a), Range1Di{});
+}
+
 void RangeTest::join() {
     Range2Di a{{12, 20}, {15, 35}};
     Range2Di b{{10, 25}, {17, 105}};
@@ -657,6 +806,18 @@ void RangeTest::join() {
     CORRADE_COMPARE(Math::join(c, a), a);
 }
 
+void RangeTest::join1D() {
+    Range1Di a{12, 15};
+    Range1Di b{10, 17};
+    Range1Di c{130, 130};
+    Range1Di d{10, 17};
+
+    CORRADE_COMPARE(Math::join(a, b), d);
+    CORRADE_COMPARE(Math::join(b, a), d);
+    CORRADE_COMPARE(Math::join(a, c), a);
+    CORRADE_COMPARE(Math::join(c, a), a);
+}
+
 template<class T> class BasicRect: public Math::Range<2, T> {
     public:
         template<class ...U> constexpr BasicRect(U&&... args): Math::Range<2, T>{args...} {}