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643 lines
19 KiB
C++
643 lines
19 KiB
C++
/** @file GuillotineBinPack.cpp
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@author Jukka Jylänki
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@brief Implements different bin packer algorithms that use the GUILLOTINE data structure.
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This work is released to Public Domain, do whatever you want with it.
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*/
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#include <cassert>
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#include <limits.h>
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#include "templates.h"
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#include "GuillotineBinPack.h"
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using namespace std;
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GuillotineBinPack::GuillotineBinPack()
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:binWidth(0),
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binHeight(0)
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{
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}
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GuillotineBinPack::GuillotineBinPack(int width, int height)
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{
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Init(width, height);
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}
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void GuillotineBinPack::Init(int width, int height)
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{
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binWidth = width;
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binHeight = height;
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#ifdef _DEBUG
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disjointRects.Clear();
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#endif
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// Clear any memory of previously packed rectangles.
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usedRectangles.Clear();
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// We start with a single big free rectangle that spans the whole bin.
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Rect n;
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n.x = 0;
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n.y = 0;
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n.width = width;
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n.height = height;
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freeRectangles.Clear();
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freeRectangles.Push(n);
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}
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void GuillotineBinPack::Insert(TArray<RectSize> &rects, TArray<Rect> &dst, bool merge,
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FreeRectChoiceHeuristic rectChoice, GuillotineSplitHeuristic splitMethod)
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{
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dst.Clear();
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// Remember variables about the best packing choice we have made so far during the iteration process.
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int bestFreeRect = 0;
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int bestRect = 0;
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bool bestFlipped = false;
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// Pack rectangles one at a time until we have cleared the rects array of all rectangles.
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// rects will get destroyed in the process.
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while(rects.Size() > 0)
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{
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// Stores the penalty score of the best rectangle placement - bigger=worse, smaller=better.
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int bestScore = INT_MAX;
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for(unsigned i = 0; i < freeRectangles.Size(); ++i)
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{
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for(unsigned j = 0; j < rects.Size(); ++j)
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{
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// If this rectangle is a perfect match, we pick it instantly.
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if (rects[j].width == freeRectangles[i].width && rects[j].height == freeRectangles[i].height)
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{
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bestFreeRect = i;
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bestRect = j;
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bestFlipped = false;
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bestScore = INT_MIN;
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i = freeRectangles.Size(); // Force a jump out of the outer loop as well - we got an instant fit.
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break;
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}
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// If flipping this rectangle is a perfect match, pick that then.
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else if (rects[j].height == freeRectangles[i].width && rects[j].width == freeRectangles[i].height)
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{
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bestFreeRect = i;
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bestRect = j;
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bestFlipped = true;
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bestScore = INT_MIN;
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i = freeRectangles.Size(); // Force a jump out of the outer loop as well - we got an instant fit.
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break;
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}
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// Try if we can fit the rectangle upright.
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else if (rects[j].width <= freeRectangles[i].width && rects[j].height <= freeRectangles[i].height)
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{
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int score = ScoreByHeuristic(rects[j].width, rects[j].height, freeRectangles[i], rectChoice);
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if (score < bestScore)
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{
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bestFreeRect = i;
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bestRect = j;
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bestFlipped = false;
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bestScore = score;
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}
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}
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// If not, then perhaps flipping sideways will make it fit?
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else if (rects[j].height <= freeRectangles[i].width && rects[j].width <= freeRectangles[i].height)
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{
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int score = ScoreByHeuristic(rects[j].height, rects[j].width, freeRectangles[i], rectChoice);
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if (score < bestScore)
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{
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bestFreeRect = i;
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bestRect = j;
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bestFlipped = true;
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bestScore = score;
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}
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}
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}
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}
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// If we didn't manage to find any rectangle to pack, abort.
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if (bestScore == INT_MAX)
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return;
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// Otherwise, we're good to go and do the actual packing.
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Rect newNode;
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newNode.x = freeRectangles[bestFreeRect].x;
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newNode.y = freeRectangles[bestFreeRect].y;
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newNode.width = rects[bestRect].width;
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newNode.height = rects[bestRect].height;
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if (bestFlipped)
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std::swap(newNode.width, newNode.height);
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// Remove the free space we lost in the bin.
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SplitFreeRectByHeuristic(freeRectangles[bestFreeRect], newNode, splitMethod);
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freeRectangles.Delete(bestFreeRect);
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// Remove the rectangle we just packed from the input list.
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rects.Delete(bestRect);
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// Perform a Rectangle Merge step if desired.
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if (merge)
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MergeFreeList();
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// Remember the new used rectangle.
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usedRectangles.Push(newNode);
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// Check that we're really producing correct packings here.
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#ifdef _DEBUG
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assert(disjointRects.Add(newNode) == true);
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#endif
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}
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}
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/// @return True if r fits inside freeRect (possibly rotated).
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bool Fits(const RectSize &r, const Rect &freeRect)
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{
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return (r.width <= freeRect.width && r.height <= freeRect.height) ||
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(r.height <= freeRect.width && r.width <= freeRect.height);
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}
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/// @return True if r fits perfectly inside freeRect, i.e. the leftover area is 0.
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bool FitsPerfectly(const RectSize &r, const Rect &freeRect)
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{
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return (r.width == freeRect.width && r.height == freeRect.height) ||
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(r.height == freeRect.width && r.width == freeRect.height);
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}
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/*
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// A helper function for GUILLOTINE-MAXFITTING. Counts how many rectangles fit into the given rectangle
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// after it has been split.
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void CountNumFitting(const Rect &freeRect, int width, int height, const TArray<RectSize> &rects,
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int usedRectIndex, bool splitHorizontal, int &score1, int &score2)
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{
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const int w = freeRect.width - width;
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const int h = freeRect.height - height;
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Rect bottom;
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bottom.x = freeRect.x;
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bottom.y = freeRect.y + height;
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bottom.height = h;
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Rect right;
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right.x = freeRect.x + width;
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right.y = freeRect.y;
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right.width = w;
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if (splitHorizontal)
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{
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bottom.width = freeRect.width;
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right.height = height;
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}
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else // Split vertically
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{
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bottom.width = width;
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right.height = freeRect.height;
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}
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int fitBottom = 0;
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int fitRight = 0;
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for(size_t i = 0; i < rects.size(); ++i)
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if (i != usedRectIndex)
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{
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if (FitsPerfectly(rects[i], bottom))
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fitBottom |= 0x10000000;
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if (FitsPerfectly(rects[i], right))
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fitRight |= 0x10000000;
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if (Fits(rects[i], bottom))
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++fitBottom;
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if (Fits(rects[i], right))
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++fitRight;
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}
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score1 = min(fitBottom, fitRight);
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score2 = max(fitBottom, fitRight);
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}
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*/
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/*
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// Implements GUILLOTINE-MAXFITTING, an experimental heuristic that's really cool but didn't quite work in practice.
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void GuillotineBinPack::InsertMaxFitting(TArray<RectSize> &rects, TArray<Rect> &dst, bool merge,
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FreeRectChoiceHeuristic rectChoice, GuillotineSplitHeuristic splitMethod)
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{
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dst.clear();
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int bestRect = 0;
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bool bestFlipped = false;
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bool bestSplitHorizontal = false;
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// Pick rectangles one at a time and pack the one that leaves the most choices still open.
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while(rects.size() > 0 && freeRectangles.size() > 0)
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{
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int bestScore1 = -1;
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int bestScore2 = -1;
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///\todo Different sort predicates.
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clb::sort::QuickSort(&freeRectangles[0], freeRectangles.size(), CompareRectShortSide);
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Rect &freeRect = freeRectangles[0];
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for(size_t j = 0; j < rects.size(); ++j)
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{
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int score1;
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int score2;
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if (rects[j].width == freeRect.width && rects[j].height == freeRect.height)
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{
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bestRect = j;
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bestFlipped = false;
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bestScore1 = bestScore2 = std::numeric_limits<int>::max();
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break;
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}
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else if (rects[j].width <= freeRect.width && rects[j].height <= freeRect.height)
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{
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CountNumFitting(freeRect, rects[j].width, rects[j].height, rects, j, false, score1, score2);
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if (score1 > bestScore1 || (score1 == bestScore1 && score2 > bestScore2))
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{
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bestRect = j;
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bestScore1 = score1;
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bestScore2 = score2;
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bestFlipped = false;
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bestSplitHorizontal = false;
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}
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CountNumFitting(freeRect, rects[j].width, rects[j].height, rects, j, true, score1, score2);
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if (score1 > bestScore1 || (score1 == bestScore1 && score2 > bestScore2))
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{
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bestRect = j;
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bestScore1 = score1;
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bestScore2 = score2;
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bestFlipped = false;
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bestSplitHorizontal = true;
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}
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}
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if (rects[j].height == freeRect.width && rects[j].width == freeRect.height)
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{
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bestRect = j;
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bestFlipped = true;
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bestScore1 = bestScore2 = std::numeric_limits<int>::max();
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break;
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}
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else if (rects[j].height <= freeRect.width && rects[j].width <= freeRect.height)
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{
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CountNumFitting(freeRect, rects[j].height, rects[j].width, rects, j, false, score1, score2);
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if (score1 > bestScore1 || (score1 == bestScore1 && score2 > bestScore2))
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{
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bestRect = j;
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bestScore1 = score1;
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bestScore2 = score2;
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bestFlipped = true;
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bestSplitHorizontal = false;
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}
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CountNumFitting(freeRect, rects[j].height, rects[j].width, rects, j, true, score1, score2);
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if (score1 > bestScore1 || (score1 == bestScore1 && score2 > bestScore2))
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{
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bestRect = j;
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bestScore1 = score1;
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bestScore2 = score2;
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bestFlipped = true;
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bestSplitHorizontal = true;
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}
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}
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}
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if (bestScore1 >= 0)
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{
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Rect newNode;
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newNode.x = freeRect.x;
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newNode.y = freeRect.y;
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newNode.width = rects[bestRect].width;
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newNode.height = rects[bestRect].height;
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if (bestFlipped)
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std::swap(newNode.width, newNode.height);
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assert(disjointRects.Disjoint(newNode));
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SplitFreeRectAlongAxis(freeRect, newNode, bestSplitHorizontal);
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rects.erase(rects.begin() + bestRect);
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if (merge)
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MergeFreeList();
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usedRectangles.push_back(newNode);
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#ifdef _DEBUG
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disjointRects.Add(newNode);
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#endif
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}
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freeRectangles.erase(freeRectangles.begin());
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}
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}
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*/
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Rect GuillotineBinPack::Insert(int width, int height, bool merge, FreeRectChoiceHeuristic rectChoice,
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GuillotineSplitHeuristic splitMethod)
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{
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// Find where to put the new rectangle.
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int freeNodeIndex = 0;
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Rect newRect = FindPositionForNewNode(width, height, rectChoice, &freeNodeIndex);
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// Abort if we didn't have enough space in the bin.
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if (newRect.height == 0)
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return newRect;
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// Remove the space that was just consumed by the new rectangle.
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SplitFreeRectByHeuristic(freeRectangles[freeNodeIndex], newRect, splitMethod);
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freeRectangles.Delete(freeNodeIndex);
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// Perform a Rectangle Merge step if desired.
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if (merge)
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MergeFreeList();
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// Remember the new used rectangle.
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usedRectangles.Push(newRect);
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// Check that we're really producing correct packings here.
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#ifdef _DEBUG
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assert(disjointRects.Add(newRect) == true);
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#endif
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return newRect;
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}
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/// Computes the ratio of used surface area to the total bin area.
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float GuillotineBinPack::Occupancy() const
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{
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///\todo The occupancy rate could be cached/tracked incrementally instead
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/// of looping through the list of packed rectangles here.
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unsigned long usedSurfaceArea = 0;
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for(unsigned i = 0; i < usedRectangles.Size(); ++i)
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usedSurfaceArea += usedRectangles[i].width * usedRectangles[i].height;
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return (float)usedSurfaceArea / (binWidth * binHeight);
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}
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/// Returns the heuristic score value for placing a rectangle of size width*height into freeRect. Does not try to rotate.
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int GuillotineBinPack::ScoreByHeuristic(int width, int height, const Rect &freeRect, FreeRectChoiceHeuristic rectChoice)
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{
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switch(rectChoice)
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{
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case RectBestAreaFit: return ScoreBestAreaFit(width, height, freeRect);
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case RectBestShortSideFit: return ScoreBestShortSideFit(width, height, freeRect);
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case RectBestLongSideFit: return ScoreBestLongSideFit(width, height, freeRect);
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case RectWorstAreaFit: return ScoreWorstAreaFit(width, height, freeRect);
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case RectWorstShortSideFit: return ScoreWorstShortSideFit(width, height, freeRect);
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case RectWorstLongSideFit: return ScoreWorstLongSideFit(width, height, freeRect);
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default: assert(false); return INT_MAX;
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}
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}
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int GuillotineBinPack::ScoreBestAreaFit(int width, int height, const Rect &freeRect)
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{
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return freeRect.width * freeRect.height - width * height;
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}
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int GuillotineBinPack::ScoreBestShortSideFit(int width, int height, const Rect &freeRect)
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{
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int leftoverHoriz = abs(freeRect.width - width);
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int leftoverVert = abs(freeRect.height - height);
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int leftover = MIN(leftoverHoriz, leftoverVert);
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return leftover;
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}
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int GuillotineBinPack::ScoreBestLongSideFit(int width, int height, const Rect &freeRect)
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{
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int leftoverHoriz = abs(freeRect.width - width);
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int leftoverVert = abs(freeRect.height - height);
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int leftover = MAX(leftoverHoriz, leftoverVert);
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return leftover;
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}
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int GuillotineBinPack::ScoreWorstAreaFit(int width, int height, const Rect &freeRect)
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{
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return -ScoreBestAreaFit(width, height, freeRect);
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}
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int GuillotineBinPack::ScoreWorstShortSideFit(int width, int height, const Rect &freeRect)
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{
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return -ScoreBestShortSideFit(width, height, freeRect);
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}
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int GuillotineBinPack::ScoreWorstLongSideFit(int width, int height, const Rect &freeRect)
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{
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return -ScoreBestLongSideFit(width, height, freeRect);
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}
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Rect GuillotineBinPack::FindPositionForNewNode(int width, int height, FreeRectChoiceHeuristic rectChoice, int *nodeIndex)
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{
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Rect bestNode;
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memset(&bestNode, 0, sizeof(Rect));
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int bestScore = INT_MAX;
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/// Try each free rectangle to find the best one for placement.
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for(unsigned i = 0; i < freeRectangles.Size(); ++i)
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{
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// If this is a perfect fit upright, choose it immediately.
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if (width == freeRectangles[i].width && height == freeRectangles[i].height)
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{
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bestNode.x = freeRectangles[i].x;
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bestNode.y = freeRectangles[i].y;
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bestNode.width = width;
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bestNode.height = height;
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bestScore = INT_MIN;
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*nodeIndex = i;
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#ifdef _DEBUG
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assert(disjointRects.Disjoint(bestNode));
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#endif
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break;
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}
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// If this is a perfect fit sideways, choose it.
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/* else if (height == freeRectangles[i].width && width == freeRectangles[i].height)
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{
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bestNode.x = freeRectangles[i].x;
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bestNode.y = freeRectangles[i].y;
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bestNode.width = height;
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bestNode.height = width;
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bestScore = INT_MIN;
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*nodeIndex = i;
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assert(disjointRects.Disjoint(bestNode));
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break;
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}
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*/ // Does the rectangle fit upright?
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else if (width <= freeRectangles[i].width && height <= freeRectangles[i].height)
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{
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int score = ScoreByHeuristic(width, height, freeRectangles[i], rectChoice);
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if (score < bestScore)
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{
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bestNode.x = freeRectangles[i].x;
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bestNode.y = freeRectangles[i].y;
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bestNode.width = width;
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bestNode.height = height;
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bestScore = score;
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*nodeIndex = i;
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#ifdef _DEBUG
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assert(disjointRects.Disjoint(bestNode));
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#endif
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}
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}
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// Does the rectangle fit sideways?
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/* else if (height <= freeRectangles[i].width && width <= freeRectangles[i].height)
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{
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int score = ScoreByHeuristic(height, width, freeRectangles[i], rectChoice);
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if (score < bestScore)
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{
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bestNode.x = freeRectangles[i].x;
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bestNode.y = freeRectangles[i].y;
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bestNode.width = height;
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bestNode.height = width;
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bestScore = score;
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*nodeIndex = i;
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assert(disjointRects.Disjoint(bestNode));
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}
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}
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*/ }
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return bestNode;
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}
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void GuillotineBinPack::SplitFreeRectByHeuristic(const Rect &freeRect, const Rect &placedRect, GuillotineSplitHeuristic method)
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{
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// Compute the lengths of the leftover area.
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const int w = freeRect.width - placedRect.width;
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const int h = freeRect.height - placedRect.height;
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// Placing placedRect into freeRect results in an L-shaped free area, which must be split into
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// two disjoint rectangles. This can be achieved with by splitting the L-shape using a single line.
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// We have two choices: horizontal or vertical.
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// Use the given heuristic to decide which choice to make.
|
|
|
|
bool splitHorizontal;
|
|
switch(method)
|
|
{
|
|
case SplitShorterLeftoverAxis:
|
|
// Split along the shorter leftover axis.
|
|
splitHorizontal = (w <= h);
|
|
break;
|
|
case SplitLongerLeftoverAxis:
|
|
// Split along the longer leftover axis.
|
|
splitHorizontal = (w > h);
|
|
break;
|
|
case SplitMinimizeArea:
|
|
// Maximize the larger area == minimize the smaller area.
|
|
// Tries to make the single bigger rectangle.
|
|
splitHorizontal = (placedRect.width * h > w * placedRect.height);
|
|
break;
|
|
case SplitMaximizeArea:
|
|
// Maximize the smaller area == minimize the larger area.
|
|
// Tries to make the rectangles more even-sized.
|
|
splitHorizontal = (placedRect.width * h <= w * placedRect.height);
|
|
break;
|
|
case SplitShorterAxis:
|
|
// Split along the shorter total axis.
|
|
splitHorizontal = (freeRect.width <= freeRect.height);
|
|
break;
|
|
case SplitLongerAxis:
|
|
// Split along the longer total axis.
|
|
splitHorizontal = (freeRect.width > freeRect.height);
|
|
break;
|
|
default:
|
|
splitHorizontal = true;
|
|
assert(false);
|
|
}
|
|
|
|
// Perform the actual split.
|
|
SplitFreeRectAlongAxis(freeRect, placedRect, splitHorizontal);
|
|
}
|
|
|
|
/// This function will add the two generated rectangles into the freeRectangles array. The caller is expected to
|
|
/// remove the original rectangle from the freeRectangles array after that.
|
|
void GuillotineBinPack::SplitFreeRectAlongAxis(const Rect &freeRect, const Rect &placedRect, bool splitHorizontal)
|
|
{
|
|
// Form the two new rectangles.
|
|
Rect bottom;
|
|
bottom.x = freeRect.x;
|
|
bottom.y = freeRect.y + placedRect.height;
|
|
bottom.height = freeRect.height - placedRect.height;
|
|
|
|
Rect right;
|
|
right.x = freeRect.x + placedRect.width;
|
|
right.y = freeRect.y;
|
|
right.width = freeRect.width - placedRect.width;
|
|
|
|
if (splitHorizontal)
|
|
{
|
|
bottom.width = freeRect.width;
|
|
right.height = placedRect.height;
|
|
}
|
|
else // Split vertically
|
|
{
|
|
bottom.width = placedRect.width;
|
|
right.height = freeRect.height;
|
|
}
|
|
|
|
// Add the new rectangles into the free rectangle pool if they weren't degenerate.
|
|
if (bottom.width > 0 && bottom.height > 0)
|
|
freeRectangles.Push(bottom);
|
|
if (right.width > 0 && right.height > 0)
|
|
freeRectangles.Push(right);
|
|
|
|
#ifdef _DEBUG
|
|
assert(disjointRects.Disjoint(bottom));
|
|
assert(disjointRects.Disjoint(right));
|
|
#endif
|
|
}
|
|
|
|
void GuillotineBinPack::MergeFreeList()
|
|
{
|
|
#ifdef _DEBUG
|
|
DisjointRectCollection test;
|
|
for(unsigned i = 0; i < freeRectangles.Size(); ++i)
|
|
assert(test.Add(freeRectangles[i]) == true);
|
|
#endif
|
|
|
|
// Do a Theta(n^2) loop to see if any pair of free rectangles could me merged into one.
|
|
// Note that we miss any opportunities to merge three rectangles into one. (should call this function again to detect that)
|
|
for(unsigned i = 0; i < freeRectangles.Size(); ++i)
|
|
for(unsigned j = i+1; j < freeRectangles.Size(); ++j)
|
|
{
|
|
if (freeRectangles[i].width == freeRectangles[j].width && freeRectangles[i].x == freeRectangles[j].x)
|
|
{
|
|
if (freeRectangles[i].y == freeRectangles[j].y + freeRectangles[j].height)
|
|
{
|
|
freeRectangles[i].y -= freeRectangles[j].height;
|
|
freeRectangles[i].height += freeRectangles[j].height;
|
|
freeRectangles.Delete(j);
|
|
--j;
|
|
}
|
|
else if (freeRectangles[i].y + freeRectangles[i].height == freeRectangles[j].y)
|
|
{
|
|
freeRectangles[i].height += freeRectangles[j].height;
|
|
freeRectangles.Delete(j);
|
|
--j;
|
|
}
|
|
}
|
|
else if (freeRectangles[i].height == freeRectangles[j].height && freeRectangles[i].y == freeRectangles[j].y)
|
|
{
|
|
if (freeRectangles[i].x == freeRectangles[j].x + freeRectangles[j].width)
|
|
{
|
|
freeRectangles[i].x -= freeRectangles[j].width;
|
|
freeRectangles[i].width += freeRectangles[j].width;
|
|
freeRectangles.Delete(j);
|
|
--j;
|
|
}
|
|
else if (freeRectangles[i].x + freeRectangles[i].width == freeRectangles[j].x)
|
|
{
|
|
freeRectangles[i].width += freeRectangles[j].width;
|
|
freeRectangles.Delete(j);
|
|
--j;
|
|
}
|
|
}
|
|
}
|
|
|
|
#ifdef _DEBUG
|
|
test.Clear();
|
|
for(unsigned i = 0; i < freeRectangles.Size(); ++i)
|
|
assert(test.Add(freeRectangles[i]) == true);
|
|
#endif
|
|
}
|