Box2D-like collision of lots of circles - c++

Question

I am trying to write a very stripped down, simple collider similar to Box2D-- absent all physics, rotation, etc. I'm doing this both to keep the code footprint tiny and understandable, and also to simply learn the inner workings of these things personally.
All I'm trying to do is collide circles and lines, and keep them from getting embedded in eachother.
Box2D does this almost perfectly-- very tiny amounts of overlap! However, when I write my own simple simulator, I get a lot of overlap: .
When I run the same simulation using Box2D (this is just all circles chasing a point in the center of the screen), I get no visible overlap at ALL.
In pseudocode, this is what I do:
For each Circle In List:
Determine who will collide with the circle in next step
Sort collisions by closest first
For each possible collision:
Add the unembed vector to the Circle's movement vector
...and then:
For each Circle In List:
At the movement to the circle
So, if the circles don't get pushed into anything else, this also works perfectly. When things pile up, though, it does NOT work, and I know why-- the unembeds simply accumulate and everyone pushes and jostles because later circles get unembedded into earlier circles, and at the end of the simulation, some are just stuck inside others. Makes enormous sense.
Here's where I'm confused:
Near as I can tell, Box2D operates EXACTLY the same way-- get possible collisions, unembed from eachother, done. But Box2D never, ever, gets overlapping like mine (or it gets them so small as to not matter).
Can someone tell me what step I have missed here? I can do tweaking to improve things (like iterating anyone who collided again and again... but Box2D does not appear to do this, and I want to understand while keeping the code light and fast).
Thanks!
Pertinent real code below:
aO->mPos = x,y of object
aO->mMove = x,y of movement this step
aO->mRadius = radius of object
aO->MovingBound() = bound of object including the move
void Step()
{
EnumList(MCObject,aO,mMovingObjectList)
{
mTree.GetAllNearbyObjects(aO->MovingBound().Expand(aO->mRadius/4),&aHitList);
aHitList-=aO; // Remove self from list
if (aHitList.GetCount()>0)
{
// Sort the collisions by closest first
if (mSortCollisions)
{
// Snip, took this out for clarity...
// It just sorts aHitList by who is closest
// to the current object
}
// Apply the unembedding
EnumList(MCObject,aO2,aHitList) CollideObjectObject(aO,aO2);
}
}
// Do the actual moves
EnumList(MCObject,aO,mMovingObjectList)
{
mTree.Move(aO->mProxy,aO->Bound(),aO->mMove);
aO->mPos+=aO->mMove;
aO->mMove=0;
}
}
void CollideObjectObject(MCObject* theO1, MCObject* theO2)
{
float aOverlap=gMath.DistanceSquared(theO1->mPos+theO1->mMove,theO2->mPos+theO2->mMove);
float aMixRadius=theO1->mRadius+theO2->mRadius;
if (aOverlap<=aMixRadius*aMixRadius)
{
Point aUnembed=(theO1->mPos-theO2->mPos);
float aUnembedLength=aMixRadius-sqrt(aOverlap);
aUnembed.SetLength(aUnembedLength);
float aMod=.5f;
if (theO2->mCollideFlags&COLLIDEFLAG_STATIONARY) aMod=1.0f;
theO1->mMove+=aUnembed*aMod;
}
}

Answer 1

Resolving collisions between many objects is quite a difficult problem because, in addition to the basic maths of collisions, you have to work much more diligently at fixing the accumulation of mathematical errors that come from approximative solvers (physics in the real world work based on integration which dictates infinitesimally small time-steps; while in our simulations, we usually only solve some 60 times a second).
Let's have a look at Box2D's constraint solver loop, located in b2island.cpp: In every world step, the collision resolver does not only run once. It will repeat velocityIterations times, which in the official test cases is usually set to 6 or 8. And that is what you will have to do as well.