diff --git a/Libraries/LibGfx/DisjointRectSet.cpp b/Libraries/LibGfx/DisjointRectSet.cpp
index 2ca643b85b..b68f4cab05 100644
--- a/Libraries/LibGfx/DisjointRectSet.cpp
+++ b/Libraries/LibGfx/DisjointRectSet.cpp
@@ -28,16 +28,17 @@
 
 namespace Gfx {
 
-void DisjointRectSet::add(const IntRect& new_rect)
+bool DisjointRectSet::add_no_shatter(const IntRect& new_rect)
 {
+    if (new_rect.is_empty())
+        return false;
     for (auto& rect : m_rects) {
         if (rect.contains(new_rect))
-            return;
+            return false;
     }
 
     m_rects.append(new_rect);
-    if (m_rects.size() > 1)
-        shatter();
+    return true;
 }
 
 void DisjointRectSet::shatter()
@@ -72,4 +73,113 @@ void DisjointRectSet::shatter()
     } while (pass_had_intersections);
 }
 
+void DisjointRectSet::move_by(int dx, int dy)
+{
+    for (auto& r : m_rects)
+        r.move_by(dx, dy);
+}
+
+bool DisjointRectSet::contains(const IntRect& rect) const
+{
+    if (is_empty() || rect.is_empty())
+        return false;
+
+    // TODO: This could use some optimization
+    DisjointRectSet remainder(rect);
+    for (auto& r : m_rects) {
+        auto shards = remainder.shatter(r);
+        if (shards.is_empty())
+            return true;
+        remainder = move(shards);
+    }
+    return false;
+}
+
+bool DisjointRectSet::intersects(const IntRect& rect) const
+{
+    for (auto& r : m_rects) {
+        if (r.intersects(rect))
+            return true;
+    }
+    return false;
+}
+
+bool DisjointRectSet::intersects(const DisjointRectSet& rects) const
+{
+    if (this == &rects)
+        return true;
+
+    for (auto& r : m_rects) {
+        for (auto& r2 : rects.m_rects) {
+            if (r.intersects(r2))
+                return true;
+        }
+    }
+    return false;
+}
+
+DisjointRectSet DisjointRectSet::intersected(const IntRect& rect) const
+{
+    DisjointRectSet intersected_rects;
+    intersected_rects.m_rects.ensure_capacity(m_rects.capacity());
+    for (auto& r : m_rects) {
+        auto intersected_rect = r.intersected(rect);
+        if (!intersected_rect.is_empty())
+            intersected_rects.m_rects.append(intersected_rect);
+    }
+    // Since there should be no overlaps, we don't need to call shatter()
+    return intersected_rects;
+}
+
+DisjointRectSet DisjointRectSet::intersected(const DisjointRectSet& rects) const
+{
+    if (&rects == this)
+        return clone();
+    if (is_empty() || rects.is_empty())
+        return {};
+
+    DisjointRectSet intersected_rects;
+    intersected_rects.m_rects.ensure_capacity(m_rects.capacity());
+    for (auto& r : m_rects) {
+        for (auto& r2 : rects.m_rects) {
+            auto intersected_rect = r.intersected(r2);
+            if (!intersected_rect.is_empty())
+                intersected_rects.m_rects.append(intersected_rect);
+        }
+    }
+    // Since there should be no overlaps, we don't need to call shatter()
+    return intersected_rects;
+}
+
+DisjointRectSet DisjointRectSet::shatter(const IntRect& hammer) const
+{
+    if (hammer.is_empty())
+        return clone();
+
+    DisjointRectSet shards;
+    for (auto& rect : m_rects) {
+        for (auto& shard : rect.shatter(hammer))
+            shards.add_no_shatter(shard);
+    }
+    // Since there should be no overlaps, we don't need to call shatter()
+    return shards;
+}
+
+DisjointRectSet DisjointRectSet::shatter(const DisjointRectSet& hammer) const
+{
+    if (this == &hammer)
+        return {};
+    if (hammer.is_empty() || !intersects(hammer))
+        return clone();
+
+    // TODO: This could use some optimization
+    auto shards = clone();
+    for (auto& hammer_rect : hammer.m_rects) {
+        auto shattered = shards.shatter(hammer_rect);
+        shards = move(shattered);
+    }
+    // Since there should be no overlaps, we don't need to call shatter()
+    return shards;
+}
+
 }
diff --git a/Libraries/LibGfx/DisjointRectSet.h b/Libraries/LibGfx/DisjointRectSet.h
index 5844d7bf75..a54ce44ce3 100644
--- a/Libraries/LibGfx/DisjointRectSet.h
+++ b/Libraries/LibGfx/DisjointRectSet.h
@@ -27,20 +27,119 @@
 #pragma once
 
 #include <AK/Vector.h>
+#include <LibGfx/Point.h>
 #include <LibGfx/Rect.h>
 
 namespace Gfx {
 
 class DisjointRectSet {
 public:
-    DisjointRectSet() {}
-    ~DisjointRectSet() {}
-    DisjointRectSet(DisjointRectSet&& other)
-        : m_rects(move(other.m_rects))
+    DisjointRectSet(const DisjointRectSet&) = delete;
+    DisjointRectSet& operator=(const DisjointRectSet&) = delete;
+
+    DisjointRectSet() { }
+    ~DisjointRectSet() { }
+
+    DisjointRectSet(const IntRect& rect)
     {
+        m_rects.append(rect);
     }
 
-    void add(const IntRect&);
+    DisjointRectSet(DisjointRectSet&&) = default;
+    DisjointRectSet& operator=(DisjointRectSet&&) = default;
+
+    DisjointRectSet clone() const
+    {
+        DisjointRectSet rects;
+        rects.m_rects = m_rects;
+        return rects;
+    }
+
+    void move_by(int dx, int dy);
+    void move_by(const IntPoint& delta)
+    {
+        move_by(delta.x(), delta.y());
+    }
+
+    void add(const IntRect& rect)
+    {
+        if (add_no_shatter(rect) && m_rects.size() > 1)
+            shatter();
+    }
+
+    template<typename Container>
+    void add_many(const Container& rects)
+    {
+        bool added = false;
+        for (const auto& rect : rects) {
+            if (add_no_shatter(rect))
+                added = true;
+        }
+        if (added && m_rects.size() > 1)
+            shatter();
+    }
+
+    void add(const DisjointRectSet& rect_set)
+    {
+        if (this == &rect_set)
+            return;
+        if (m_rects.is_empty()) {
+            m_rects = rect_set.m_rects;
+        } else {
+            add_many(rect_set.rects());
+        }
+    }
+
+    DisjointRectSet shatter(const IntRect&) const;
+    DisjointRectSet shatter(const DisjointRectSet& hammer) const;
+
+    bool contains(const IntRect&) const;
+    bool intersects(const IntRect&) const;
+    bool intersects(const DisjointRectSet&) const;
+    DisjointRectSet intersected(const IntRect&) const;
+    DisjointRectSet intersected(const DisjointRectSet&) const;
+
+    template<typename Function>
+    IterationDecision for_each_intersected(const IntRect& rect, Function f) const
+    {
+        if (is_empty() || rect.is_empty())
+            return IterationDecision::Continue;
+        for (auto& r : m_rects) {
+            auto intersected_rect = r.intersected(rect);
+            if (intersected_rect.is_empty())
+                continue;
+            IterationDecision decision = f(intersected_rect);
+            if (decision != IterationDecision::Continue)
+                return decision;
+        }
+        return IterationDecision::Continue;
+    }
+
+    template<typename Function>
+    IterationDecision for_each_intersected(const DisjointRectSet& rects, Function f) const
+    {
+        if (is_empty() || rects.is_empty())
+            return IterationDecision::Continue;
+        if (this == &rects) {
+            for (auto& r : m_rects) {
+                IterationDecision decision = f(r);
+                if (decision != IterationDecision::Continue)
+                    return decision;
+            }
+        } else {
+            for (auto& r : m_rects) {
+                for (auto& r2 : rects.m_rects) {
+                    auto intersected_rect = r.intersected(r2);
+                    if (intersected_rect.is_empty())
+                        continue;
+                    IterationDecision decision = f(intersected_rect);
+                    if (decision != IterationDecision::Continue)
+                        return decision;
+                }
+            }
+        }
+        return IterationDecision::Continue;
+    }
 
     bool is_empty() const { return m_rects.is_empty(); }
     size_t size() const { return m_rects.size(); }
@@ -48,8 +147,10 @@ public:
     void clear() { m_rects.clear(); }
     void clear_with_capacity() { m_rects.clear_with_capacity(); }
     const Vector<IntRect, 32>& rects() const { return m_rects; }
+    Vector<IntRect, 32> take_rects() { return move(m_rects); }
 
 private:
+    bool add_no_shatter(const IntRect&);
     void shatter();
 
     Vector<IntRect, 32> m_rects;