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Introduction

Collision detection is an important part of most 3D games. Shooting enemies, avoiding (or failing to avoid) obstacles, even simply staying on the ground usually requires some form of collision-detection.  It's a vast subject and there are many excellent articles written about it. However, most of them concern the more sophisticated algorithms, such as BSP and the simple bounding-sphere check receives no more than a passing mention. It is a quite simple procedure but it still could be very useful and there are a couple of subtle points involved. So I thought perhaps I should write something about it.

Straightforward version

The simplest possible way to do bounding-sphere test is to measure the (squared) distance between the two objects in question and to compare the result with the (squared again) sum of their radii.  The reason we use the squared distances is to avoid the costly square-root calculation. The code will look something like this:

BOOL bSphereTest(CObject3D* obj1, CObject3D* obj2 )
{
  D3DVECTOR relPos = obj1->prPosition - obj2->prPosition;
  float dist = relPos.x * relPos.x + relPos.y * relPos.y + relPos.z * relPos.z;
  float minDist = obj1->fRadius + obj2->fRadius;
  return dist <= minDist * minDist;
}

Code Snippet 1.

Note: This and the following code snippets use the D3DVECTOR type from Microsoft's Direct3D, if you are using some other 3D library, change the code accordingly.

This procedure is easy indeed and some cases may be even adequate but what if your objects are moving at a considerable speed? Then it could happen that at the beginning of a frame the bounding spheres do not intersect yet by the end of the frame they have passed through each other. If the distance your objects travel in one frame is greater than the size of the object this scenario is quite likely. Clearly we need something more advanced to handle this case.

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