Use library to improve lightmap texture packing

CMakeLists.txt

@@ -220,6 +220,7 @@ set( SOURCES
 )
 
 set(THIRDPARTY_SOURCES
+	${CMAKE_SOURCE_DIR}/thirdparty/dp_rect_pack/dp_rect_pack.h
 	${CMAKE_SOURCE_DIR}/thirdparty/miniz/miniz.h
 	${CMAKE_SOURCE_DIR}/thirdparty/miniz/miniz.c
 	${CMAKE_SOURCE_DIR}/thirdparty/vk_mem_alloc/vk_mem_alloc.h
@@ -440,6 +441,7 @@ source_group("Sources\\Lightmap" REGULAR_EXPRESSION "^${CMAKE_CURRENT_SOURCE_DIR
 source_group("Sources\\Models" REGULAR_EXPRESSION "^${CMAKE_CURRENT_SOURCE_DIR}/src/models/.+")
 
 source_group("thirdparty" REGULAR_EXPRESSION "${CMAKE_CURRENT_SOURCE_DIR}/thirdparty/.+")
+source_group("thirdparty\\dp_rect_pack" REGULAR_EXPRESSION "${CMAKE_CURRENT_SOURCE_DIR}/thirdparty/dp_rect_pack/.+")
 source_group("thirdparty\\ShaderCompiler" REGULAR_EXPRESSION "${CMAKE_CURRENT_SOURCE_DIR}/thirdparty/ShaderCompiler/.+")
 source_group("thirdparty\\vk_mem_alloc" REGULAR_EXPRESSION "${CMAKE_CURRENT_SOURCE_DIR}/thirdparty/vk_mem_alloc/.+")
 source_group("thirdparty\\volk" REGULAR_EXPRESSION "${CMAKE_CURRENT_SOURCE_DIR}/thirdparty/volk/.+")

src/lightmap/levelmesh.cpp

@@ -273,135 +273,124 @@ void LevelMesh::CreateTextures()
 {
 	std::vector<Surface*> sortedSurfaces;
 	sortedSurfaces.reserve(surfaces.size());
-	for (auto& surf : surfaces)
+
-		sortedSurfaces.push_back(surf.get());
+	for (auto& surface : surfaces)
-	std::sort(sortedSurfaces.begin(), sortedSurfaces.end(), [](Surface* a, Surface* b) { return a->lightmapDims[1] < b->lightmapDims[1]; });
+	{
+		int sampleWidth = surface->lightmapDims[0];
+		int sampleHeight = surface->lightmapDims[1];
+		vec3* colorSamples = surface->samples.data();
+
+		// SVE redraws the scene for lightmaps, so for optimizations,
+		// tell the engine to ignore this surface if completely black
+		bool bShouldLookupTexture = false;
+		for (int i = 0; i < sampleHeight; i++)
+		{
+			for (int j = 0; j < sampleWidth; j++)
+			{
+				const auto& c = colorSamples[i * sampleWidth + j];
+				if (c.x > 0.0f || c.y > 0.0f || c.z > 0.0f)
+				{
+					bShouldLookupTexture = true;
+					break;
+				}
+			}
+		}
+
+		if (bShouldLookupTexture)
+		{
+			sortedSurfaces.push_back(surface.get());
+		}
+		else
+		{
+			surface->lightmapNum = -1;
+		}
+	}
+
+	std::sort(sortedSurfaces.begin(), sortedSurfaces.end(), [](Surface* a, Surface* b) { return a->lightmapDims[1] != b->lightmapDims[1] ? a->lightmapDims[1] > b->lightmapDims[1] : a->lightmapDims[0] > b->lightmapDims[0]; });
+
+	RectPacker packer(textureWidth, textureHeight, RectPacker::Spacing(0));
 
 	for (Surface* surf : sortedSurfaces)
 	{
-		FinishSurface(surf);
+		FinishSurface(packer, surf);
 	}
 }
 
-void LevelMesh::FinishSurface(Surface* surface)
+void LevelMesh::FinishSurface(RectPacker& packer, Surface* surface)
 {
 	int sampleWidth = surface->lightmapDims[0];
 	int sampleHeight = surface->lightmapDims[1];
 	vec3* colorSamples = surface->samples.data();
 
-	// SVE redraws the scene for lightmaps, so for optimizations,
+	auto result = packer.insert(sampleWidth, sampleHeight);
-	// tell the engine to ignore this surface if completely black
+	int x = result.pos.x, y = result.pos.y;
-	bool bShouldLookupTexture = false;
+	surface->lightmapNum = result.pageIndex;
+
+	while (result.pageIndex >= textures.size())
+	{
+		textures.push_back(std::make_unique<LightmapTexture>(textureWidth, textureHeight));
+	}
+
+	uint16_t* currentTexture = textures[surface->lightmapNum]->Pixels();
+
+	// calculate final texture coordinates
+	for (int i = 0; i < surface->numVerts; i++)
+	{
+		auto& u = surface->lightmapCoords[i].x;
+		auto& v = surface->lightmapCoords[i].y;
+		u = (u + x) / (float)textureWidth;
+		v = (v + y) / (float)textureHeight;
+	}
+
+	surface->lightmapOffs[0] = x;
+	surface->lightmapOffs[1] = y;
+
+#if 1
+	// store results to lightmap texture
+	float weights[9] = { 0.125f, 0.25f, 0.125f, 0.25f, 0.50f, 0.25f, 0.125f, 0.25f, 0.125f };
+	for (int y = 0; y < sampleHeight; y++)
+	{
+		vec3* src = &colorSamples[y * sampleWidth];
+		for (int x = 0; x < sampleWidth; x++)
+		{
+			// gaussian blur with a 3x3 kernel
+			vec3 color = { 0.0f };
+			for (int yy = -1; yy <= 1; yy++)
+			{
+				int yyy = clamp(y + yy, 0, sampleHeight - 1) - y;
+				for (int xx = -1; xx <= 1; xx++)
+				{
+					int xxx = clamp(x + xx, 0, sampleWidth - 1);
+					color += src[yyy * sampleWidth + xxx] * weights[4 + xx + yy * 3];
+				}
+			}
+			color *= 0.5f;
+
+			// get texture offset
+			int offs = ((textureWidth * (y + surface->lightmapOffs[1])) + surface->lightmapOffs[0]) * 3;
+
+			// convert RGB to bytes
+			currentTexture[offs + x * 3 + 0] = floatToHalf(clamp(colorSamples[y * sampleWidth + x].x, -65000.0f, 65000.0f));
+			currentTexture[offs + x * 3 + 1] = floatToHalf(clamp(colorSamples[y * sampleWidth + x].y, -65000.0f, 65000.0f));
+			currentTexture[offs + x * 3 + 2] = floatToHalf(clamp(colorSamples[y * sampleWidth + x].z, -65000.0f, 65000.0f));
+		}
+	}
+#else
+	// store results to lightmap texture
 	for (int i = 0; i < sampleHeight; i++)
 	{
 		for (int j = 0; j < sampleWidth; j++)
 		{
-			const auto& c = colorSamples[i * sampleWidth + j];
+			// get texture offset
-			if (c.x > 0.0f || c.y > 0.0f || c.z > 0.0f)
+			int offs = ((textureWidth * (i + surface->lightmapOffs[1])) + surface->lightmapOffs[0]) * 3;
-			{
+
-				bShouldLookupTexture = true;
+			// convert RGB to bytes
-				break;
+			currentTexture[offs + j * 3 + 0] = floatToHalf(clamp(colorSamples[i * sampleWidth + j].x, -65000.0f, 65000.0f));
-			}
+			currentTexture[offs + j * 3 + 1] = floatToHalf(clamp(colorSamples[i * sampleWidth + j].y, -65000.0f, 65000.0f));
+			currentTexture[offs + j * 3 + 2] = floatToHalf(clamp(colorSamples[i * sampleWidth + j].z, -65000.0f, 65000.0f));
 		}
 	}
-
-	if (bShouldLookupTexture == false)
-	{
-		surface->lightmapNum = -1;
-	}
-	else
-	{
-		int x = 0, y = 0;
-		surface->lightmapNum = AllocTextureRoom(sampleWidth + 2, sampleHeight + 2, &x, &y);
-		x++;
-		y++;
-
-		uint16_t* currentTexture = textures[surface->lightmapNum]->Pixels();
-
-		// calculate final texture coordinates
-		for (int i = 0; i < surface->numVerts; i++)
-		{
-			auto& u = surface->lightmapCoords[i].x;
-			auto& v = surface->lightmapCoords[i].y;
-			u = (u + x) / (float)textureWidth;
-			v = (v + y) / (float)textureHeight;
-		}
-
-		surface->lightmapOffs[0] = x;
-		surface->lightmapOffs[1] = y;
-
-#if 1
-		// store results to lightmap texture
-		float weights[9] = { 0.125f, 0.25f, 0.125f, 0.25f, 0.50f, 0.25f, 0.125f, 0.25f, 0.125f };
-		for (int y = 0; y < sampleHeight; y++)
-		{
-			vec3* src = &colorSamples[y * sampleWidth];
-			for (int x = 0; x < sampleWidth; x++)
-			{
-				// gaussian blur with a 3x3 kernel
-				vec3 color = { 0.0f };
-				for (int yy = -1; yy <= 1; yy++)
-				{
-					int yyy = clamp(y + yy, 0, sampleHeight - 1) - y;
-					for (int xx = -1; xx <= 1; xx++)
-					{
-						int xxx = clamp(x + xx, 0, sampleWidth - 1);
-						color += src[yyy * sampleWidth + xxx] * weights[4 + xx + yy * 3];
-					}
-				}
-				color *= 0.5f;
-
-				// get texture offset
-				int offs = ((textureWidth * (y + surface->lightmapOffs[1])) + surface->lightmapOffs[0]) * 3;
-
-				// convert RGB to bytes
-				currentTexture[offs + x * 3 + 0] = floatToHalf(clamp(colorSamples[y * sampleWidth + x].x, -65000.0f, 65000.0f));
-				currentTexture[offs + x * 3 + 1] = floatToHalf(clamp(colorSamples[y * sampleWidth + x].y, -65000.0f, 65000.0f));
-				currentTexture[offs + x * 3 + 2] = floatToHalf(clamp(colorSamples[y * sampleWidth + x].z, -65000.0f, 65000.0f));
-			}
-		}
-#else
-		// store results to lightmap texture
-		for (int i = 0; i < sampleHeight; i++)
-		{
-			for (int j = 0; j < sampleWidth; j++)
-			{
-				// get texture offset
-				int offs = ((textureWidth * (i + surface->lightmapOffs[1])) + surface->lightmapOffs[0]) * 3;
-
-				// convert RGB to bytes
-				currentTexture[offs + j * 3 + 0] = floatToHalf(clamp(colorSamples[i * sampleWidth + j].x, -65000.0f, 65000.0f));
-				currentTexture[offs + j * 3 + 1] = floatToHalf(clamp(colorSamples[i * sampleWidth + j].y, -65000.0f, 65000.0f));
-				currentTexture[offs + j * 3 + 2] = floatToHalf(clamp(colorSamples[i * sampleWidth + j].z, -65000.0f, 65000.0f));
-			}
-		}
 #endif
-	}
-}
-
-int LevelMesh::AllocTextureRoom(int width, int height, int* x, int* y)
-{
-	int numTextures = textures.size();
-
-	int k;
-	for (k = 0; k < numTextures; ++k)
-	{
-		if (textures[k]->MakeRoomForBlock(width, height, x, y))
-		{
-			break;
-		}
-	}
-
-	if (k == numTextures)
-	{
-		textures.push_back(std::make_unique<LightmapTexture>(textureWidth, textureHeight));
-		if (!textures[k]->MakeRoomForBlock(width, height, x, y))
-		{
-			throw std::runtime_error("Lightmap allocation failed");
-		}
-	}
-
-	return k;
 }
 
 void LevelMesh::CreateLightProbes(FLevel& map)

src/lightmap/levelmesh.h

@@ -37,6 +37,10 @@
 #include "lightmaptexture.h"
 #include "math/mathlib.h"
 
+#include "dp_rect_pack/dp_rect_pack.h"
+
+typedef dp::rect_pack::RectPacker<int> RectPacker;
+
 struct MapSubsectorEx;
 struct IntSector;
 struct IntSideDef;
@@ -118,8 +122,7 @@ private:
 
 	void BuildSurfaceParams(Surface* surface);
 	BBox GetBoundsFromSurface(const Surface* surface);
-	void FinishSurface(Surface* surface);
+	void FinishSurface(RectPacker& packer, Surface* surface);
-	int AllocTextureRoom(int width, int height, int* x, int* y);
 
 	static bool IsDegenerate(const vec3 &v0, const vec3 &v1, const vec3 &v2);
 };

thirdparty/dp_rect_pack/dp_rect_pack.h

@@ -0,0 +1,672 @@
+/*
+ * Rectangle packing library.
+ * v1.1.3
+ *
+ * Copyright (c) 2017-2021 Daniel Plakhotich
+ *
+ * This software is provided 'as-is', without any express or implied
+ * warranty. In no event will the authors be held liable for any damages
+ * arising from the use of this software.
+ *
+ * Permission is granted to anyone to use this software for any purpose,
+ * including commercial applications, and to alter it and redistribute it
+ * freely, subject to the following restrictions:
+ *
+ * 1. The origin of this software must not be misrepresented; you must not
+ *    claim that you wrote the original software. If you use this software
+ *    in a product, an acknowledgement in the product documentation would be
+ *    appreciated but is not required.
+ * 2. Altered source versions must be plainly marked as such, and must not be
+ *    misrepresented as being the original software.
+ * 3. This notice may not be removed or altered from any source distribution.
+ */
+
+
+#ifndef DP_RECT_PACK_H
+#define DP_RECT_PACK_H
+
+#include <cassert>
+#include <cstddef>
+#include <vector>
+
+
+#define DP_RECT_PACK_VERSION_MAJOR 1
+#define DP_RECT_PACK_VERSION_MINOR 1
+#define DP_RECT_PACK_VERSION_PATCH 3
+
+
+namespace dp {
+namespace rect_pack {
+
+
+/**
+ * Status of the RectPacker::InsertResult.
+ *
+ * Only InsertStatus::ok indicates a successful insertion;
+ * all other values are kinds of errors.
+ */
+struct InsertStatus {
+    enum Type {
+        ok,  ///< Successful insertion
+        negativeSize,  ///< Width and/or height is negative
+        zeroSize,  ///< Width and/or height is zero
+
+        /**
+         * Rectangle is too big to fit in a single page.
+         *
+         * Width and/or height of the rectangle exceeds the maximum
+         * size a single page can hold, which is the maximum page size
+         * minus the padding.
+         *
+         * \sa RectPacker::RectPacker()
+         */
+        rectTooBig
+    };
+};
+
+
+// A note on the implementation.
+// The current algorithm is absolutely the same as in version 1.0.0,
+// except that we only keep the leaf nodes of the binary tree. This
+// dramatically improves performance and reduces memory usage, but
+// growDown() and growRight() methods are harder to understand
+// because the leafs insertion order depends on several layers of
+// parent branches that don't physically exist. I added comments to
+// help you visualize what happens, but it will probably be easier
+// to just look at the code of the version 1.0.0.
+
+
+/**
+ * Rectangle packer.
+ *
+ * GeomT is not required to hold negative numbers, and thus can be
+ * an unsigned integer. It's also possible to use a floating-point
+ * or a custom numeric type.
+ *
+ * A custom type for GeomT should support:
+ *     * Implicit construction from an integer >= 0
+ *     * Addition and subtraction (including compound assignment)
+ *     * Comparison
+ *
+ * \tparam GeomT numeric type to use for geometry
+ */
+template<typename GeomT = int>
+class RectPacker {
+public:
+    struct Spacing {
+        GeomT x;  ///< Horizontal spacing
+        GeomT y;  ///< Vertical spacing
+
+        /**
+         * Construct Spacing with the same spacing for both dimensions.
+         */
+        explicit Spacing(GeomT spacing)
+            : x(spacing)
+            , y(spacing)
+        {}
+
+        Spacing(GeomT x, GeomT y)
+            : x(x)
+            , y(y)
+        {}
+    };
+
+    struct Padding {
+        GeomT top;
+        GeomT bottom;
+        GeomT left;
+        GeomT right;
+
+        /**
+         * Construct Padding with the same padding for all sides.
+         */
+        explicit Padding(GeomT padding)
+            : top(padding)
+            , bottom(padding)
+            , left(padding)
+            , right(padding)
+        {}
+
+        Padding(GeomT top, GeomT bottom, GeomT left, GeomT right)
+            : top(top)
+            , bottom(bottom)
+            , left(left)
+            , right(right)
+        {}
+    };
+
+    struct Position {
+        GeomT x;
+        GeomT y;
+
+        Position()
+            : x()
+            , y()
+        {}
+
+        Position(GeomT x, GeomT y)
+            : x(x)
+            , y(y)
+        {}
+    };
+
+    /**
+     * Result returned by RectPacker::insert().
+     */
+    struct InsertResult {
+        /**
+         * Status of the insertion.
+         *
+         * \warning If InsertResult.status is not InsertStatus::ok,
+         *     values of all other fields of InsertResult are undefined.
+         */
+        InsertStatus::Type status;
+
+        /**
+         * Position of the inserted rectangle within the page.
+         */
+        Position pos;
+
+        /**
+         * Index of the page in which the rectangle was inserted.
+         *
+         * \sa getPageSize()
+         */
+        std::size_t pageIndex;
+    };
+
+    /**
+     * RectPacker constructor.
+     *
+     * maxPageWidth and maxPageHeight define the maximum size of
+     * a single page, including the padding. Depending on this limit
+     * and the features of GeomT, a RectPacker can work in multipage
+     * or infinite single-page mode.
+     *
+     * To enable infinite single-page mode, you have two choices,
+     * depending on the properties of GeomT:
+     *     * If GeomT has a physical limit (like any standard integer),
+     *       you can set the maximum size to the maximum positive
+     *       value GeomT can hold.
+     *     * Otherwise, if GeomT is a floating-point type or a custom
+     *       unbounded type, you can set the maximum size to a huge
+     *       value or, if supported by the type, a magic value that
+     *       always bigger than any finite number (like a positive
+     *       infinity for floating-point types).
+     *
+     * If GeomT can hold negative values, the maximum page size, spacing,
+     * and padding will be clamped to 0. Keep in mind that if the
+     * maximum page size is 0, or if the total padding greater or equal
+     * to the maximum page size, pages will have no free space for
+     * rectangles, and all calls to insert() will result in
+     * InsertStatus::rectTooBig.
+     *
+     * \param maxPageWidth maximum width of a page, including
+     *     the horizontal padding
+     * \param maxPageHeight maximum height of a page, including
+     *     the vertical padding
+     * \param rectsSpacing space between rectangles
+     * \param pagePadding space between rectangles and edges of a page
+     */
+    RectPacker(
+        GeomT maxPageWidth, GeomT maxPageHeight,
+        const Spacing& rectsSpacing = Spacing(0),
+        const Padding& pagePadding = Padding(0))
+            : ctx(maxPageWidth, maxPageHeight, rectsSpacing, pagePadding)
+            , pages(1)
+    {}
+
+    /**
+     * Return the current number of pages.
+     *
+     * \returns number of pages (always > 0)
+     */
+    std::size_t getNumPages() const
+    {
+        return pages.size();
+    }
+
+    /**
+     * Return the current size of the page.
+     *
+     * \param pageIndex index of the page in range [0..getNumPages())
+     * \param[out] width width of the page
+     * \param[out] height height of the page
+     *
+     * \sa getNumPages(), InsertResult::pageIndex
+     */
+    void getPageSize(std::size_t pageIndex, GeomT& width, GeomT& height) const
+    {
+        const Size size = pages[pageIndex].getSize(ctx);
+        width = size.w;
+        height = size.h;
+    }
+
+    /**
+     * Insert a rectangle.
+     *
+     * The rectangles you'll feed to insert() should be sorted in
+     * descending order by comparing first by height, then by width.
+     * A comparison function for std::sort may look like the following:
+     * \code
+     *     bool compare(const T& a, const T& b)
+     *     {
+     *         if (a.height != b.height)
+     *             return a.height > b.height;
+     *         else
+     *             return a.width > b.width;
+     *     }
+     * \endcode
+     *
+     * \param width width of the rectangle
+     * \param height height of the rectangle
+     * \returns InsertResult
+     */
+    InsertResult insert(GeomT width, GeomT height);
+private:
+    struct Size {
+        GeomT w;
+        GeomT h;
+
+        Size(GeomT w, GeomT h)
+            : w(w)
+            , h(h)
+        {}
+    };
+
+    struct Context;
+    class Page {
+    public:
+        Page()
+            : nodes()
+            , rootSize(0, 0)
+            , growDownRootBottomIdx(0)
+        {}
+
+        Size getSize(const Context& ctx) const
+        {
+            return Size(
+                ctx.padding.left + rootSize.w + ctx.padding.right,
+                ctx.padding.top + rootSize.h + ctx.padding.bottom);
+        }
+
+        bool insert(Context& ctx, const Size& rect, Position& pos);
+    private:
+        struct Node {
+            Position pos;
+            Size size;
+
+            Node(GeomT x, GeomT y, GeomT w, GeomT h)
+                : pos(x, y)
+                , size(w, h)
+            {}
+        };
+
+        // Leaf nodes of the binary tree in depth-first order
+        std::vector<Node> nodes;
+        Size rootSize;
+        // The index of the first leaf bottom node of the new root
+        // created in growDown(). See the method for more details.
+        std::size_t growDownRootBottomIdx;
+
+        bool tryInsert(Context& ctx, const Size& rect, Position& pos);
+        bool findNode(
+            const Size& rect,
+            std::size_t& nodeIdx, Position& pos) const;
+        void subdivideNode(
+            Context& ctx, std::size_t nodeIdx, const Size& rect);
+        bool tryGrow(Context& ctx, const Size& rect, Position& pos);
+        void growDown(Context& ctx, const Size& rect, Position& pos);
+        void growRight(Context& ctx, const Size& rect, Position& pos);
+    };
+
+    struct Context {
+        Size maxSize;
+        Spacing spacing;
+        Padding padding;
+
+        Context(
+            GeomT maxPageWidth, GeomT maxPageHeight,
+            const Spacing& rectsSpacing, const Padding& pagePadding);
+
+        static void subtractPadding(GeomT& padding, GeomT& size);
+    };
+
+    Context ctx;
+    std::vector<Page> pages;
+};
+
+
+template<typename GeomT>
+typename RectPacker<GeomT>::InsertResult
+RectPacker<GeomT>::insert(GeomT width, GeomT height)
+{
+    InsertResult result;
+
+    if (width < 0 || height < 0) {
+        result.status = InsertStatus::negativeSize;
+        return result;
+    }
+
+    if (width == 0 || height == 0) {
+        result.status = InsertStatus::zeroSize;
+        return result;
+    }
+
+    if (width > ctx.maxSize.w || height > ctx.maxSize.h) {
+        result.status = InsertStatus::rectTooBig;
+        return result;
+    }
+
+    const Size rect(width, height);
+
+    for (std::size_t i = 0; i < pages.size(); ++i)
+        if (pages[i].insert(ctx, rect, result.pos)) {
+            result.status = InsertStatus::ok;
+            result.pageIndex = i;
+            return result;
+        }
+
+    pages.push_back(Page());
+    Page& page = pages.back();
+    page.insert(ctx, rect, result.pos);
+    result.status = InsertStatus::ok;
+    result.pageIndex = pages.size() - 1;
+
+    return result;
+}
+
+
+template<typename GeomT>
+bool RectPacker<GeomT>::Page::insert(
+    Context& ctx, const Size& rect, Position& pos)
+{
+    assert(rect.w > 0);
+    assert(rect.w <= ctx.maxSize.w);
+    assert(rect.h > 0);
+    assert(rect.h <= ctx.maxSize.h);
+
+    // The first insertion should be handled especially since
+    // growRight() and growDown() add spacing between the root
+    // and the inserted rectangle.
+    if (rootSize.w == 0) {
+        rootSize = rect;
+        pos.x = ctx.padding.left;
+        pos.y = ctx.padding.top;
+
+        return true;
+    }
+
+    return tryInsert(ctx, rect, pos) || tryGrow(ctx, rect, pos);
+}
+
+
+template<typename GeomT>
+bool RectPacker<GeomT>::Page::tryInsert(
+    Context& ctx, const Size& rect, Position& pos)
+{
+    std::size_t nodeIdx;
+    if (findNode(rect, nodeIdx, pos)) {
+        subdivideNode(ctx, nodeIdx, rect);
+        return true;
+    }
+
+    return false;
+}
+
+
+template<typename GeomT>
+bool RectPacker<GeomT>::Page::findNode(
+    const Size& rect, std::size_t& nodeIdx, Position& pos) const
+{
+    for (nodeIdx = 0; nodeIdx < nodes.size(); ++nodeIdx) {
+        const Node& node = nodes[nodeIdx];
+        if (rect.w <= node.size.w && rect.h <= node.size.h) {
+            pos = node.pos;
+            return true;
+        }
+    }
+
+    return false;
+}
+
+
+/**
+ * Called after a rectangle was inserted in the top left corner of
+ * a free node to create child nodes from free space, if any.
+ *
+ * The node is first cut horizontally along the rect's bottom,
+ * then vertically along the right edge of the rect. Splitting
+ * that way is crucial for the algorithm to work correctly.
+ *
+ *      +---+
+ *      |   |
+ *  +---+---+
+ *  |       |
+ *  +-------+
+ */
+template<typename GeomT>
+void RectPacker<GeomT>::Page::subdivideNode(
+    Context& ctx, std::size_t nodeIdx, const Size& rect)
+{
+    assert(nodeIdx < nodes.size());
+
+    Node& node = nodes[nodeIdx];
+
+    assert(node.size.w >= rect.w);
+    const GeomT rightW = node.size.w - rect.w;
+    const bool hasSpaceRight = rightW > ctx.spacing.x;
+
+    assert(node.size.h >= rect.h);
+    const GeomT bottomH = node.size.h - rect.h;
+    const bool hasSpaceBelow = bottomH > ctx.spacing.y;
+
+    if (hasSpaceRight) {
+        // Right node replaces the current
+
+        const GeomT bottomX = node.pos.x;
+        const GeomT bottomW = node.size.w;
+
+        node.pos.x += rect.w + ctx.spacing.x;
+        node.size.w = rightW - ctx.spacing.x;
+        node.size.h = rect.h;
+
+        if (hasSpaceBelow) {
+            nodes.insert(
+                nodes.begin() + nodeIdx + 1,
+                Node(
+                    bottomX,
+                    node.pos.y + rect.h + ctx.spacing.y,
+                    bottomW,
+                    bottomH - ctx.spacing.y));
+
+            if (nodeIdx <= growDownRootBottomIdx)
+                ++growDownRootBottomIdx;
+        }
+    } else if (hasSpaceBelow) {
+        // Bottom node replaces the current
+        node.pos.y += rect.h + ctx.spacing.y;
+        node.size.h = bottomH - ctx.spacing.y;
+    } else {
+        nodes.erase(nodes.begin() + nodeIdx);
+        if (nodeIdx < growDownRootBottomIdx)
+            --growDownRootBottomIdx;
+    }
+}
+
+
+template<typename GeomT>
+bool RectPacker<GeomT>::Page::tryGrow(
+    Context& ctx, const Size& rect, Position& pos)
+{
+    assert(ctx.maxSize.w >= rootSize.w);
+    const GeomT freeW = ctx.maxSize.w - rootSize.w;
+    assert(ctx.maxSize.h >= rootSize.h);
+    const GeomT freeH = ctx.maxSize.h - rootSize.h;
+
+    const bool canGrowDown = (
+        freeH >= rect.h && freeH - rect.h >= ctx.spacing.y);
+    const bool mustGrowDown = (
+        canGrowDown
+        && freeW >= ctx.spacing.x
+        && (rootSize.w + ctx.spacing.x
+            >= rootSize.h + rect.h + ctx.spacing.y));
+    if (mustGrowDown) {
+        growDown(ctx, rect, pos);
+        return true;
+    }
+
+    const bool canGrowRight = (
+        freeW >= rect.w && freeW - rect.w >= ctx.spacing.x);
+    if (canGrowRight) {
+        growRight(ctx, rect, pos);
+        return true;
+    }
+
+    if (canGrowDown) {
+        growDown(ctx, rect, pos);
+        return true;
+    }
+
+    return false;
+}
+
+
+template<typename GeomT>
+void RectPacker<GeomT>::Page::growDown(
+    Context& ctx, const Size& rect, Position& pos)
+{
+    assert(ctx.maxSize.h > rootSize.h);
+    assert(ctx.maxSize.h - rootSize.h >= rect.h);
+    assert(ctx.maxSize.h - rootSize.h - rect.h >= ctx.spacing.y);
+
+    pos.x = ctx.padding.left;
+    pos.y = ctx.padding.top + rootSize.h + ctx.spacing.y;
+
+    if (rootSize.w < rect.w) {
+        if (rect.w - rootSize.w > ctx.spacing.x) {
+            // The auxiliary node becomes the right child of the new
+            // root. It contains the current root (bottom child) and
+            // free space at the current root's right (right child).
+            nodes.insert(
+                nodes.begin(),
+                Node(
+                    ctx.padding.left + rootSize.w + ctx.spacing.x,
+                    ctx.padding.top,
+                    rect.w - rootSize.w - ctx.spacing.x,
+                    rootSize.h));
+            ++growDownRootBottomIdx;
+        }
+
+        rootSize.w = rect.w;
+    } else if (rootSize.w - rect.w > ctx.spacing.x) {
+        // Free space at the right of the inserted rect becomes the
+        // right child of the rect's node, which in turn is the
+        // bottom child of the new root.
+        nodes.insert(
+            nodes.begin() + growDownRootBottomIdx,
+            Node(
+                pos.x + rect.w + ctx.spacing.x,
+                pos.y,
+                rootSize.w - rect.w - ctx.spacing.x,
+                rect.h));
+
+        // The inserted node is visited before the node from the next
+        // growDown() since the current new root will be the right
+        // child of the next root.
+        ++growDownRootBottomIdx;
+    }
+
+    rootSize.h += ctx.spacing.y + rect.h;
+}
+
+
+template<typename GeomT>
+void RectPacker<GeomT>::Page::growRight(
+    Context& ctx, const Size& rect, Position& pos)
+{
+    assert(ctx.maxSize.w > rootSize.w);
+    assert(ctx.maxSize.w - rootSize.w >= rect.w);
+    assert(ctx.maxSize.w - rootSize.w - rect.w >= ctx.spacing.x);
+
+    pos.x = ctx.padding.left + rootSize.w + ctx.spacing.x;
+    pos.y = ctx.padding.top;
+
+    if (rootSize.h < rect.h) {
+        if (rect.h - rootSize.h > ctx.spacing.y)
+            // The auxiliary node becomes the bottom child of the
+            // new root. It contains the current root (right child)
+            // and free space at the current root's bottom, if any
+            // (bottom child).
+            nodes.insert(
+                nodes.end(),
+                Node(
+                    ctx.padding.left,
+                    ctx.padding.top + rootSize.h + ctx.spacing.y,
+                    rootSize.w,
+                    rect.h - rootSize.h - ctx.spacing.y));
+
+        rootSize.h = rect.h;
+    } else if (rootSize.h - rect.h > ctx.spacing.y) {
+        // Free space at the bottom of the inserted rect becomes the
+        // bottom child of the rect's node, which in turn is the
+        // right child of the new root node.
+        nodes.insert(
+            nodes.begin(),
+            Node(
+                pos.x,
+                pos.y + rect.h + ctx.spacing.y,
+                rect.w,
+                rootSize.h - rect.h - ctx.spacing.y));
+        ++growDownRootBottomIdx;
+    }
+
+    rootSize.w += ctx.spacing.x + rect.w;
+}
+
+
+template<typename GeomT>
+RectPacker<GeomT>::Context::Context(
+    GeomT maxPageWidth, GeomT maxPageHeight,
+    const Spacing& rectsSpacing, const Padding& pagePadding)
+        : maxSize(maxPageWidth, maxPageHeight)
+        , spacing(rectsSpacing)
+        , padding(pagePadding)
+{
+    if (maxSize.w < 0)
+        maxSize.w = 0;
+    if (maxSize.h < 0)
+        maxSize.h = 0;
+
+    if (spacing.x < 0)
+        spacing.x = 0;
+    if (spacing.y < 0)
+        spacing.y = 0;
+
+    subtractPadding(padding.top, maxSize.h);
+    subtractPadding(padding.bottom, maxSize.h);
+    subtractPadding(padding.left, maxSize.w);
+    subtractPadding(padding.right, maxSize.w);
+}
+
+
+template<typename GeomT>
+void RectPacker<GeomT>::Context::subtractPadding(
+    GeomT& padding, GeomT& size)
+{
+    if (padding < 0)
+        padding = 0;
+    else if (padding < size)
+        size -= padding;
+    else {
+        padding = size;
+        size = 0;
+    }
+}
+
+
+}  // namespace rect_pack
+}  // namespace dp
+
+
+#endif  // DP_RECT_PACK_H