Contents

Introduction A Sphere-Sphere Sweep Test An Axis-Aligned Bounding Box (AABB) Sweep Test A Box-Sphere Intersection Test An Oriented Bounding Box (OBB) Intersection Test An OBB-Line Segment Test A Box-Plane Intersection Test, References

A Box-Sphere Intersection Test

A very elegant box-sphere intersection test is described in [1]. Figure 7 shows two configurations of a sphere and a box in 2D. Sphere A is closest to an edge, whereas sphere B is closest to a corner. The algorithm calculates the square of the distance from the box to the sphere by analyzing the orientation of the sphere relative to the box in a single loop.

If the box is not axis aligned, simply transform the center of the sphere to the box's local coordinate frame. Listing 5 gives an implementation of Arvo's algorithm.

Listing 5. Arvo's algorithm.

#include "aabb.h"

//Check to see if the sphere overlaps the AABB
const bool AABBOverlapsSphere ( const AABB& B, const SCALAR r, VECTOR& C )
{

//find the square of the distance
//from the sphere to the box
for( long i=0 ; i<3 ; i++ )
{

if( C[i] < B.min(i) )
{

s = C[i] - B.min(i);
d += s*s;

}

else if( C[i] > B.max(i) )
{

s = C[i] - B.max(i);
d += s*s;

}

}
return d <= r*r;

}