Multi-dimensional bounding box collision detection

Question

There are answers for 2D/3D bounding box collision detection, however my problem is how to develop the situation to multi-dimension (4D or more) ?

Here is the code on 3D case.

template<typename T, typename _Prd>
bool BoundingBox3<T,_Prd>::Collision( const BoundingBox3<T,_Prd>& cube ) const
{

    Point3<T,_Prd> min_1 = center - Point3<T,_Prd>(length,depth,height)/2.0;
    Point3<T,_Prd> max_1 = center + Point3<T,_Prd>(length,depth,height)/2.0;

    Point3<T,_Prd> min_2 = cube.Center() - Point3<T,_Prd>(cube.Length(),cube.Depth(),cube.Height())/2.0;
    Point3<T,_Prd> max_2 = cube.Center() + Point3<T,_Prd>(cube.Length(),cube.Depth(),cube.Height())/2.0;

    if(Volume()<cube.Volume())
    {
        Vector3D::Swap(min_1,min_2);
        Vector3D::Swap(max_1,max_2);
    }

    if(min_1[0]<=min_2[0] && min_1[1]<=min_2[1] && min_1[2]<=min_2[2]
    && max_1[0]>=min_2[0] && max_1[1]>=min_2[1] && max_1[2]>=min_2[2])
        return true;

    if(min_1[0]<=max_2[0] && min_1[1]<=max_2[1] && min_1[2]<=max_2[2]
    && max_1[0]>=max_2[0] && max_1[1]>=max_2[1] && max_1[2]>=max_2[2])
        return true;

    return false;
};

@Aesthete, yes, I want to write a more general collision detection function. — tomriddle_1234
– tomriddle_1234, Commented Dec 5, 2012 at 6:04

Vaughn Cato · Accepted Answer · 2012-12-05 06:11:13Z

5

One box collides with another if there is an intersecting range in all dimensions.

The intersection of range [a,b] with range [c,d] is [max(a,c),min(b,d)].

In the case of the ranges not intersecting, the result will be an invalid range, with the start of the range greater than the end of the range.

So the collision can be done like this:

bool collides(const Box &box1,const Box &box2)
{
  assert(box1.numberOfDimensions()==box2.numberOfDimensions());
  for (size_t i=0; i!=box1.numberOfDimensions(); ++i) {
    float a = max(box1.minForDimension(i),box2.minForDimension(i));
    float b = min(box1.maxForDimension(i),box2.maxForDimension(i));
    if (a>b) return false;
  }
  return true;
}

edited Dec 5, 2012 at 6:11

answered Dec 5, 2012 at 6:04

Vaughn Cato

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1 Comment

tomriddle_1234 Over a year ago

Thank you, very smart answer. I didn't think it would be this easy.

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