15
votes

I'm working on a simple demo for collision detection, which contains only a bunch of objects bouncing around in the window. (The goal is to see how many objects the game can handle at once without dropping frames.)

There is gravity, so the objects are either moving or else colliding with a wall.

The naive solution was O(n^2):

foreach Collidable c1:
      foreach Collidable c2:
             checkCollision(c1, c2);

This is pretty bad. So I set up CollisionCell objects, which maintain information about a portion of the screen. The idea is that each Collidable only needs to check for the other objects in its cell. With 60 px by 60 px cells, this yields almost a 10x improvement, but I'd like to push it further.

A profiler has revealed that the the code spends 50% of its time in the function each cell uses to get its contents. Here it is:

    // all the objects in this cell
    public ICollection<GameObject> Containing
    {
        get
        {
            ICollection<GameObject> containing = new HashSet<GameObject>();

            foreach (GameObject obj in engine.GameObjects) {
                // 20% of processor time spent in this conditional
                if (obj.Position.X >= bounds.X &&
                    obj.Position.X < bounds.X + bounds.Width &&
                    obj.Position.Y >= bounds.Y &&
                    obj.Position.Y < bounds.Y + bounds.Height) {

                    containing.Add(obj);
                }
            }

            return containing;
        }
    }

Of that 20% of the program's time is spent in that conditional.

Here is where the above function gets called:

    // Get a list of lists of cell contents
        List<List<GameObject>> cellContentsSet = cellManager.getCellContents();

        // foreach item, only check items in the same cell
        foreach (List<GameObject> cellMembers in cellContentsSet) {
            foreach (GameObject item in cellMembers) {
                 // process collisions
            }
        }


//...

    // Gets a list of list of cell contents (each sub list = 1 cell)
    internal List<List<GameObject>> getCellContents() {
        List<List<GameObject>> result = new List<List<GameObject>>();
        foreach (CollisionCell cell in cellSet) {
            result.Add(new List<GameObject>(cell.Containing.ToArray()));
        }
        return result;
    }

Right now, I have to iterate over every cell - even empty ones. Perhaps this could be improved on somehow, but I'm not sure how to verify that a cell is empty without looking at it somehow. (Maybe I could implement something like sleeping objects, in some physics engines, where if an object will be still for a while it goes to sleep and is not included in calculations for every frame.)

What can I do to optimize this? (Also, I'm new to C# - are there any other glaring stylistic errors?)

When the game starts lagging out, the objects tend to be packed fairly tightly, so there's not that much motion going on. Perhaps I can take advantage of this somehow, writing a function to see if, given an object's current velocity, it can possibly leave its current cell before the next call to Update()

UPDATE 1 I decided to maintain a list of the objects that were found to be in the cell at last update, and check those first to see if they were still in the cell. Also, I maintained an area of the CollisionCell variable, when when the cell was filled I could stop looking. Here is my implementation of that, and it made the whole demo much slower:

    // all the objects in this cell
    private ICollection<GameObject> prevContaining;
    private ICollection<GameObject> containing;
    internal ICollection<GameObject> Containing {
        get {
            return containing;
        }
    }

    /**
     * To ensure that `containing` and `prevContaining` are up to date, this MUST be called once per Update() loop in which it is used.
     * What is a good way to enforce this?
     */ 
    public void updateContaining()
    {
        ICollection<GameObject> result = new HashSet<GameObject>();
        uint area = checked((uint) bounds.Width * (uint) bounds.Height); // the area of this cell

        // first, try to fill up this cell with objects that were in it previously
        ICollection<GameObject>[] toSearch = new ICollection<GameObject>[] { prevContaining, engine.GameObjects };
        foreach (ICollection<GameObject> potentiallyContained in toSearch) {
            if (area > 0) { // redundant, but faster?
                foreach (GameObject obj in potentiallyContained) {
                    if (obj.Position.X >= bounds.X &&
                        obj.Position.X < bounds.X + bounds.Width &&
                        obj.Position.Y >= bounds.Y &&
                        obj.Position.Y < bounds.Y + bounds.Height) {

                        result.Add(obj);
                        area -= checked((uint) Math.Pow(obj.Radius, 2)); // assuming objects are square
                        if (area <= 0) {
                            break;
                        }
                    }
                }
            }
        }
        prevContaining = containing;
        containing = result;
   }

UPDATE 2 I abandoned that last approach. Now I'm trying to maintain a pool of collidables (orphans), and remove objects from them when I find a cell that contains them:

    internal List<List<GameObject>> getCellContents() {
        List<GameObject> orphans = new List<GameObject>(engine.GameObjects);
        List<List<GameObject>> result = new List<List<GameObject>>();
        foreach (CollisionCell cell in cellSet) {
            cell.updateContaining(ref orphans); // this call will alter orphans!
            result.Add(new List<GameObject>(cell.Containing)); 
            if (orphans.Count == 0) {
                break;
            }
        }
        return result;
    }

    // `orphans` is a list of GameObjects that do not yet have a cell
    public void updateContaining(ref List<GameObject> orphans) {
        ICollection<GameObject> result = new HashSet<GameObject>();

        for (int i = 0; i < orphans.Count; i++) {
            // 20% of processor time spent in this conditional
            if (orphans[i].Position.X >= bounds.X &&
                orphans[i].Position.X < bounds.X + bounds.Width &&
                orphans[i].Position.Y >= bounds.Y &&
                orphans[i].Position.Y < bounds.Y + bounds.Height) {

                result.Add(orphans[i]);
                orphans.RemoveAt(i);
            }
        }

        containing = result;
    }

This only yields a marginal improvement, not the 2x or 3x I'm looking for.

UPDATE 3 Again I abandoned the above approaches, and decided to let each object maintain its current cell:

    private CollisionCell currCell;
    internal CollisionCell CurrCell {
        get {
            return currCell;
        }
        set {
            currCell = value;
        }
    }

This value gets updated:

    // Run 1 cycle of this object
    public virtual void Run()
    {
        position += velocity;
        parent.CellManager.updateContainingCell(this);
    }

CellManager code:

private IDictionary<Vector2, CollisionCell> cellCoords = new Dictionary<Vector2, CollisionCell>();
    internal void updateContainingCell(GameObject gameObject) {
        CollisionCell currCell = findContainingCell(gameObject);
        gameObject.CurrCell = currCell;
        if (currCell != null) {
            currCell.Containing.Add(gameObject);
        }
    }

    // null if no such cell exists
    private CollisionCell findContainingCell(GameObject gameObject) {

        if (gameObject.Position.X > GameEngine.GameWidth
            || gameObject.Position.X < 0
            || gameObject.Position.Y > GameEngine.GameHeight
            || gameObject.Position.Y < 0) {
            return null;
        }

        // we'll need to be able to access these outside of the loops
        uint minWidth = 0;
        uint minHeight = 0;

        for (minWidth = 0; minWidth + cellWidth < gameObject.Position.X; minWidth += cellWidth) ;
        for (minHeight = 0; minHeight + cellHeight < gameObject.Position.Y; minHeight += cellHeight) ;

        CollisionCell currCell = cellCoords[new Vector2(minWidth, minHeight)];

        // Make sure `currCell` actually contains gameObject
        Debug.Assert(gameObject.Position.X >= currCell.Bounds.X && gameObject.Position.X <= currCell.Bounds.Width + currCell.Bounds.X,
            String.Format("{0} should be between lower bound {1} and upper bound {2}", gameObject.Position.X, currCell.Bounds.X, currCell.Bounds.X + currCell.Bounds.Width));
        Debug.Assert(gameObject.Position.Y >= currCell.Bounds.Y && gameObject.Position.Y <= currCell.Bounds.Height + currCell.Bounds.Y,
            String.Format("{0} should be between lower bound {1} and upper bound {2}", gameObject.Position.Y, currCell.Bounds.Y, currCell.Bounds.Y + currCell.Bounds.Height));

        return currCell;
    }

I thought this would make it better - now I only have to iterate over collidables, not all collidables * cells. Instead, the game is now hideously slow, delivering only 1/10th of its performance with my above approaches.

The profiler indicates that a different method is now the main hot spot, and the time to get neighbors for an object is trivially short. That method didn't change from before, so perhaps I'm calling it WAY more than I used to...

8
Have you tried using the farseer physcs engine for XNA? codeplex.com/FarseerPhysicsjjxtra
@Rosarch: great post. great updates. revised my response below, may be worth checking out, i tried to highlight adv\dis, explain more of what was happening and why, and mention some alternatives. also worth investigating thirdy party libraries, as Jeff Johnson suggests. if it works, may as well save yourself some grief ;)johnny g
I heard that the original Quake engine checked for collisions by shrinking the gameworld until the player was the size of a pixel, and using that to check collisions.NibblyPig

8 Answers

12
votes

It spends 50% of its time in that function because you call that function a lot. Optimizing that one function will only yield incremental improvements to performance.

Alternatively, just call the function less!

You've already started down that path by setting up a spatial partitioning scheme (lookup Quadtrees to see a more advanced form of your technique).

A second approach is to break your N*N loop into an incremental form and to use a CPU budget.

You can allocate a CPU budget for each of the modules that want action during frame times (during Updates). Collision is one of these modules, AI might be another.

Let's say you want to run your game at 60 fps. This means you have about 1/60 s = 0.0167 s of CPU time to burn between frames. No we can split those 0.0167 s between our modules. Let's give collision 30% of the budget: 0.005 s.

Now your collision algorithm knows that it can only spend 0.005 s working. So if it runs out of time, it will need to postpone some tasks for later - you will make the algorithm incremental. Code for achieving this can be as simple as:

const double CollisionBudget = 0.005;

Collision[] _allPossibleCollisions;
int _lastCheckedCollision;

void HandleCollisions() {

    var startTime = HighPerformanceCounter.Now;

    if (_allPossibleCollisions == null || 
        _lastCheckedCollision >= _allPossibleCollisions.Length) {

        // Start a new series
        _allPossibleCollisions = GenerateAllPossibleCollisions();
        _lastCheckedCollision = 0;
    }

    for (var i=_lastCheckedCollision; i<_allPossibleCollisions.Length; i++) {
        // Don't go over the budget
        if (HighPerformanceCount.Now - startTime > CollisionBudget) {
            break;
        }
        _lastCheckedCollision = i;

        if (CheckCollision(_allPossibleCollisions[i])) {
            HandleCollision(_allPossibleCollisions[i]);
        }
    }
}

There, now it doesn't matter how fast the collision code is, it will be done as quickly as is possible without affecting the user's perceived performance.

Benefits include:

  • The algorithm is designed to run out of time, it just resumes on the next frame, so you don't have to worry about this particular edge case.
  • CPU budgeting becomes more and more important as the number of advanced/time consuming algorithms increases. Think AI. So it's a good idea to implement such a system early on.
  • Human response time is less than 30 Hz, your frame loop is running at 60 Hz. That gives the algorithm 30 frames to complete its work, so it's OK that it doesn't finish its work.
  • Doing it this way gives stable, data-independent frame rates.
  • It still benefits from performance optimizations to the collision algorithm itself.
  • Collision algorithms are designed to track down the "sub frame" in which collisions happened. That is, you will never be so lucky as to catch a collision just as it happens - thinking you're doing so is lying to yourself.
8
votes

I can help here; i wrote my own collision detection as an experiment. I think i can tell you right now that you won't get the performance you need without changing algorithms. Sure, the naive way is nice, but only works for so many items before collapsing. What you need is Sweep and prune. The basic idea goes like this (from my collision detection library project):

using System.Collections.Generic;
using AtomPhysics.Interfaces;

namespace AtomPhysics.Collisions
{
    public class SweepAndPruneBroadPhase : IBroadPhaseCollider
    {
        private INarrowPhaseCollider _narrowPhase;
        private AtomPhysicsSim _sim;
        private List<Extent> _xAxisExtents = new List<Extent>();
        private List<Extent> _yAxisExtents = new List<Extent>();
        private Extent e1;

        public SweepAndPruneBroadPhase(INarrowPhaseCollider narrowPhase)
        {
            _narrowPhase = narrowPhase;
        }

        public AtomPhysicsSim Sim
        {
            get { return _sim; }
            set { _sim = null; }
        }
        public INarrowPhaseCollider NarrowPhase
        {
            get { return _narrowPhase; }
            set { _narrowPhase = value; }
        }
        public bool NeedsNotification { get { return true; } }


        public void Add(Nucleus nucleus)
        {
            Extent xStartExtent = new Extent(nucleus, ExtentType.Start);
            Extent xEndExtent = new Extent(nucleus, ExtentType.End);
            _xAxisExtents.Add(xStartExtent);
            _xAxisExtents.Add(xEndExtent);
            Extent yStartExtent = new Extent(nucleus, ExtentType.Start);
            Extent yEndExtent = new Extent(nucleus, ExtentType.End);
            _yAxisExtents.Add(yStartExtent);
            _yAxisExtents.Add(yEndExtent);
        }
        public void Remove(Nucleus nucleus)
        {
            foreach (Extent e in _xAxisExtents)
            {
                if (e.Nucleus == nucleus)
                {
                    _xAxisExtents.Remove(e);
                }
            }
            foreach (Extent e in _yAxisExtents)
            {
                if (e.Nucleus == nucleus)
                {
                    _yAxisExtents.Remove(e);
                }
            }
        }

        public void Update()
        {
            _xAxisExtents.InsertionSort(comparisonMethodX);
            _yAxisExtents.InsertionSort(comparisonMethodY);
            for (int i = 0; i < _xAxisExtents.Count; i++)
            {
                e1 = _xAxisExtents[i];
                if (e1.Type == ExtentType.Start)
                {
                    HashSet<Extent> potentialCollisionsX = new HashSet<Extent>();
                    for (int j = i + 1; j < _xAxisExtents.Count && _xAxisExtents[j].Nucleus.ID != e1.Nucleus.ID; j++)
                    {
                        potentialCollisionsX.Add(_xAxisExtents[j]);
                    }
                    HashSet<Extent> potentialCollisionsY = new HashSet<Extent>();
                    for (int j = i + 1; j < _yAxisExtents.Count && _yAxisExtents[j].Nucleus.ID != e1.Nucleus.ID; j++)
                    {
                        potentialCollisionsY.Add(_yAxisExtents[j]);
                    }

                    List<Extent> probableCollisions = new List<Extent>();
                    foreach (Extent e in potentialCollisionsX)
                    {
                        if (potentialCollisionsY.Contains(e) && !probableCollisions.Contains(e) && e.Nucleus.ID != e1.Nucleus.ID)
                        {
                            probableCollisions.Add(e);
                        }
                    }
                    foreach (Extent e2 in probableCollisions)
                    {
                        if (e1.Nucleus.DNCList.Contains(e2.Nucleus) || e2.Nucleus.DNCList.Contains(e1.Nucleus))
                            continue;
                        NarrowPhase.DoCollision(e1.Nucleus, e2.Nucleus);
                    }
                }
            }
        }

        private bool comparisonMethodX(Extent e1, Extent e2)
        {
            float e1PositionX = e1.Nucleus.NonLinearSpace != null ? e1.Nucleus.NonLinearPosition.X : e1.Nucleus.Position.X;
            float e2PositionX = e2.Nucleus.NonLinearSpace != null ? e2.Nucleus.NonLinearPosition.X : e2.Nucleus.Position.X;
            e1PositionX += (e1.Type == ExtentType.Start) ? -e1.Nucleus.Radius : e1.Nucleus.Radius;
            e2PositionX += (e2.Type == ExtentType.Start) ? -e2.Nucleus.Radius : e2.Nucleus.Radius;
            return e1PositionX < e2PositionX;
        }
        private bool comparisonMethodY(Extent e1, Extent e2)
        {
            float e1PositionY = e1.Nucleus.NonLinearSpace != null ? e1.Nucleus.NonLinearPosition.Y : e1.Nucleus.Position.Y;
            float e2PositionY = e2.Nucleus.NonLinearSpace != null ? e2.Nucleus.NonLinearPosition.Y : e2.Nucleus.Position.Y;
            e1PositionY += (e1.Type == ExtentType.Start) ? -e1.Nucleus.Radius : e1.Nucleus.Radius;
            e2PositionY += (e2.Type == ExtentType.Start) ? -e2.Nucleus.Radius : e2.Nucleus.Radius;
            return e1PositionY < e2PositionY;
        }
        private enum ExtentType { Start, End }
        private sealed class Extent
        {
            private ExtentType _type;
            public ExtentType Type
            {
                get
                {
                    return _type;
                }
                set
                {
                    _type = value;
                    _hashcode = 23;
                    _hashcode *= 17 + Nucleus.GetHashCode();
                }
            }
            private Nucleus _nucleus;
            public Nucleus Nucleus
            {
                get
                {
                    return _nucleus;
                }
                set
                {
                    _nucleus = value;
                    _hashcode = 23;
                    _hashcode *= 17 + Nucleus.GetHashCode();
                }
            }

            private int _hashcode;

            public Extent(Nucleus nucleus, ExtentType type)
            {
                Nucleus = nucleus;
                Type = type;
                _hashcode = 23;
                _hashcode *= 17 + Nucleus.GetHashCode();
            }

            public override bool Equals(object obj)
            {
                return Equals(obj as Extent);
            }
            public bool Equals(Extent extent)
            {
                if (this.Nucleus == extent.Nucleus)
                {
                    return true;
                }
                return false;
            }
            public override int GetHashCode()
            {
                return _hashcode;
            }
        }
    }
}

and here's the code that does the insertion sort (more-or-less a direct translation of the pseudocode here):

/// <summary>
/// Performs an insertion sort on the list.
/// </summary>
/// <typeparam name="T">The type of the list supplied.</typeparam>
/// <param name="list">the list to sort.</param>
/// <param name="comparison">the method for comparison of two elements.</param>
/// <returns></returns>
public static void InsertionSort<T>(this IList<T> list, Func<T, T, bool> comparison)
{
    for (int i = 2; i < list.Count; i++)
    {
        for (int j = i; j > 1 && comparison(list[j], list[j - 1]); j--)
        {
            T tempItem = list[j];
            list.RemoveAt(j);
            list.Insert(j - 1, tempItem);
        }
    }
}

IIRC, i was able to get an extremely large performance increase with that, especially when dealing with large numbers of colliding bodies. You'll need to adapt it for your code, but that's the basic premise behind sweep and prune.

The other thing i want to remind you is that you should use a profiler, like the one made by Red Gate. There's a free trial which should last you long enough.

5
votes

It looks like you are looping through all the game objects just to see what objects are contained in a cell. It seems like a better approach would be to store the list of game objects that are in a cell for each cell. If you do that and each object knows what cells it is in, then moving objects between cells should be easy. This seems like it will yield the biggest performance gain.

Here is another optimization tip for determing what cells an object is in: If you have already determined what cell(s) an object is in and know that based on the objects velocity it will not change cells for the current frame, there is no need to rerun the logic that determines what cells the object is in. You can do a quick check by creating a bounding box that contains all the cells that the object is in. You can then create a bounding box that is the size of the object + the velocity of the object for the current frame. If the cell bounding box contains the object + velocity bounding box, no further checks need to be done. If the object isn't moving, it's even easier and you can just use the object bounding box.

Let me know if that makes sense, or google / bing search for "Quad Tree", or if you don't mind using open source code, check out this awesome physics library: http://www.codeplex.com/FarseerPhysics

1
votes

I'm in the exact same boat as you. I'm trying to create an overhead shooter and need to push efficiency to the max so I can have tons of bullets and enemies on screen at once.

I'd get all of my collidable objects in an array with a numbered index. This affords the opportunity to take advantage of an observation: if you iterate over the list fully for each item you'll be duplicating efforts. That is (and note, I'm making up variables names just to make it easier to spit out some pseudo-code)

 if (objs[49].Intersects(objs[51]))

is equivalent to:

 if (objs[51].Intersects(objs[49]))

So if you use a numbered index you can save some time by not duplicating efforts. Do this instead:

for (int i1 = 0; i1 < collidables.Count; i1++)
{
    //By setting i2 = i1 + 1 you ensure an obj isn't checking collision with itself, and that objects already checked against i1 aren't checked again. For instance, collidables[4] doesn't need to check against collidables[0] again since this was checked earlier.
    for (int i2 = i1 + 1; i2 < collidables.Count; i2++)
    {
        //Check collisions here
    }
}

Also, I'd have each cell either have a count or a flag to determine if you even need to check for collisions. If a certain flag is set, or if the count is less than 2, than no need to check for collisions.

1
votes

Just a heads up: Some people suggest farseer; which is a great 2D physics library for use with XNA. If you're in the market for a 3D physics engine for XNA, I've used bulletx (a c# port of bullet) in XNA projects to great effect.

Note: I have no affiliation to the bullet or bulletx projects.

0
votes

An idea might be to use a bounding circle. Basically, when a Collidable is created, keep track of it's centre point and calculate a radius/diameter that contains the whole object. You can then do a first pass elimination using something like;

int r = C1.BoundingRadius + C2.BoundingRadius;

if( Math.Abs(C1.X - C2.X) > r && Math.Abs(C1.Y - C2.Y) > r )
/// Skip further checks...

This drops the comparisons to two for most objects, but how much this will gain you I'm not sure...profile!

0
votes

There are a couple of things that could be done to speed up the process... but as far as I can see your method of checking for simple rectangular collision is just fine.

But I'd replace the check

if (obj.Position.X ....)

With

if (obj.Bounds.IntersercsWith(this.Bounds))

And I'd also replace the line

result.Add(new List<GameObject>(cell.Containing.ToArray()));

For

result.Add(new List<GameObject>(cell.Containing));

As the Containing property returns an ICollection<T> and that inherits the IEnumerable<T> that is accepted by the List<T> constructor.

And the method ToArray() simply iterates to the list returning an array, and this process is done again when creating the new list.

0
votes

I know this Thread is old but i would say that the marked answar was completly wrong...

his code contain a fatal error and don´t give performance improvent´s it will take performence!

At first a little notic...

His code is created so that you have to call this code in your Draw methode but this is the wrong place for collision-detection. In your draw methode you should only draw nothing else!

But you can´t call HandleCollisions() in Update, because Update get a lots of more calls than Draw´s.

If you want call HandleCollisions() your code have to look like this... This code will prevent that your collision detection run more then once per frame.

private bool check = false;

protected override Update(GameTime gameTime)
{
    if(!check)
    {    
        check = true;
        HandleCollisions();
    }
}

protected override Draw(GameTime gameTime)
{
    check = false;
}

Now let us take a look what´s wrong with HandleCollisions().

Example: We have 500 objects and we would do a check for every possible Collision without optimizing our detection.

With 500 object we should have 249500 collision checks (499X500 because we don´t want to check if an object collide with it´s self)

But with Frank´s code below we will lose 99.998% of your collosions (only 500 collision-checks will done). << THIS WILL INCREASE THE PERFORMENCES!

Why? Because _lastCheckedCollision will never be the same or greater then allPossibleCollisions.Length... and because of that you would only check the last index 499

for (var i=_lastCheckedCollision; i<_allPossibleCollisions.Length; i++)
    _lastCheckedCollision = i;
//<< This could not be the same as _allPossibleCollisions.Length,
//because i have to be lower as _allPossibleCollisions.Length

you have to replace This

if (_allPossibleCollisions == null || 
    _lastCheckedCollision >= _allPossibleCollisions.Length)

with this

if (_allPossibleCollisions == null || 
    _lastCheckedCollision >= _allPossibleCollisions.Length - 1) {

so your whole code can be replaced by this.

private bool check = false;

protected override Update(GameTime gameTime)
{
    if(!check)
    {    
        check = true;
        _allPossibleCollisions = GenerateAllPossibleCollisions();
        for(int i=0; i < _allPossibleCollisions.Length; i++)
        {
            if (CheckCollision(_allPossibleCollisions[i]))
            {
                //Collision!
            }
        }
    }
}

protected override Draw(GameTime gameTime)
{
    check = false;
}

... this should be a lot of faster than your code ... and it works :D ...

RCIX answer should marked as correct because Frank´s answar is wrong.