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Posted 14 Jun 2011

Fast Optimizing Rectangle Packing Algorithm for Building CSS Sprites

, 14 Jun 2011
Describes a fast algorithm to pack a series of rectangles of varying widths and heights into an enclosing rectangle of minimum size
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;
using System.Drawing;

namespace Mapper
    public abstract class MapperOptimalEfficiency_Base<S> : IMapperReturningStats<S> where S : class, ISprite, new()
        private ICanvas _canvas = null;

        protected ICanvas Canvas { get { return _canvas; } }

        protected float CutoffEfficiency { get; private set; }
        protected int MaxNbrCandidateSprites { get; private set; }

        /// <summary>
        /// Constructor
        /// </summary>
        /// <param name="canvas">Canvas object to use to map the images</param>
        /// <param name="cutoffEfficiency">
        /// When the object's Mapping method produces a candidate sprite with this efficiency or higher, it stops
        /// trying to get a better one and returns the sprite.
        /// Set this to for example 0.9 if that efficiency is good enough for you. 
        /// Set to 1.0 or higher if you want the most efficient sprite.
        /// </param>
        /// <param name="maxNbrCandidateSprites">
        /// The maximum number of candidate sprites that will be generated by the Mapping method.
        /// Set this to 1 if you want it to return the very first sprite that it manages to generate.
        /// If you want it to try to generate no more than 2 sprites before returning the best one, set this to 2, etc.
        /// Set to Int32.MaxValue if you don't want any restrictions on the number of candidate sprites generated.
        /// If you set cutoff Efficiency to less than 1, and maxNbrCandidateSprites to less than Int32.MaxValue,
        /// the Mapper method will stop trying to get a better sprite the moment it hits one of these limitations.
        /// </param>
        public MapperOptimalEfficiency_Base(ICanvas canvas, float cutoffEfficiency, int maxNbrCandidateSprites)
            _canvas = canvas;
            CutoffEfficiency = cutoffEfficiency;
            MaxNbrCandidateSprites = maxNbrCandidateSprites;

        public MapperOptimalEfficiency_Base(ICanvas canvas) : this(canvas, 1.0f, Int32.MaxValue)

        /// <summary>
        /// See IMapping
        /// </summary>
        /// <param name="images"></param>
        /// <returns></returns>
        public S Mapping(IEnumerable<IImageInfo> images)
            return Mapping(images, null);

        /// <summary>
        /// See IMapping
        /// </summary>
        /// <param name="images"></param>
        /// <returns></returns>
        public abstract S Mapping(IEnumerable<IImageInfo> images, IMapperStats mapperStats);

        /// <summary>
        /// Produces a mapping to a sprite that has given maximum dimensions.
        /// If the mapping can not be done inside those dimensions, returns null.
        /// </summary>
        /// <param name="images">
        /// List of image infos. 
        /// This method will not sort this list. 
        /// All images in this collection will be used, regardless of size.
        /// </param>
        /// <param name="maxWidth">
        /// The sprite won't be wider than this.
        /// </param>
        /// <param name="maxHeight">
        /// The generated sprite won't be higher than this.
        /// </param>
        /// <param name="canvasStats">
        /// The statistics produced by the canvas. These numbers are since the last call to its SetCanvasDimensions method.
        /// </param>
        /// <param name="lowestFreeHeightDeficitTallestRightFlushedImage">
        /// The lowest free height deficit for the images up to and including the tallest rectangle whose right hand border sits furthest to the right
        /// of all images.
        /// This is the minimum amount by which the height of the canvas needs to be increased to accommodate that rectangle.
        /// if the width of the canvas is decreased to one less than the width now taken by images.
        /// Note that providing the additional height might get some other (not right flushed) image to be placed higher, thereby
        /// making room for the flushed right image.
        /// This will be set to Int32.MaxValue if there was never any free height deficit.
        /// </param>
        /// <returns>
        /// The generated sprite.
        /// null if not all the images could be placed within the size limitations.
        /// </returns>
        protected virtual S MappingRestrictedBox(
            IOrderedEnumerable<IImageInfo> images, 
            int maxWidth, int maxHeight, ICanvasStats canvasStats,
            out int lowestFreeHeightDeficitTallestRightFlushedImage)
            lowestFreeHeightDeficitTallestRightFlushedImage = 0;
            _canvas.SetCanvasDimensions(maxWidth, maxHeight);

            S spriteInfo = new S();
            int heightHighestRightFlushedImage = 0;
            int furthestRightEdge = 0;

            foreach (IImageInfo image in images)
                int xOffset;
                int yOffset;
                int lowestFreeHeightDeficit;
                if (!_canvas.AddRectangle(
                    image.Width, image.Height, 
                    out xOffset, out yOffset, 
                    out lowestFreeHeightDeficit))
                    // Not enough room on the canvas to place the rectangle
                    spriteInfo = null;

                MappedImageInfo imageLocation = new MappedImageInfo(xOffset, yOffset, image);

                // Update the lowestFreeHeightDeficitTallestRightFlushedImage
                int rightEdge = image.Width + xOffset;
                if ((rightEdge > furthestRightEdge) ||
                    ((rightEdge == furthestRightEdge) && (image.Height > heightHighestRightFlushedImage)))
                    // The image is flushed the furthest right of all images, or it is flushed equally far to the right
                    // as the furthest flushed image but it is taller. 

                    lowestFreeHeightDeficitTallestRightFlushedImage = lowestFreeHeightDeficit;
                    heightHighestRightFlushedImage = image.Height;
                    furthestRightEdge = rightEdge;


            return spriteInfo;


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About the Author

Matt Perdeck
Australia Australia
Twitter: @MattPerdeck
Current project: JSNLog JavaScript Logging Package

Matt has over 9 years .NET and SQL Server development experience. Before getting into .Net, he worked on a number of systems, ranging from the largest ATM network in The Netherlands to embedded software in advanced Wide Area Networks and the largest ticketing web site in Australia. He has lived and worked in Australia, The Netherlands, Slovakia and Thailand.

He is the author of the book ASP.NET Performance Secrets ( in which he shows in clear and practical terms how to quickly find the biggest bottlenecks holding back the performance of your web site, and how to then remove those bottlenecks. The book deals with all environments affecting a web site - the web server, the database server and the browser.

Matt currently lives in Sydney, Australia. He recently worked at Readify and the global professional services company PwC. He now works at SP Health, a global provider of weight loss web sites such at CSIRO's and

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