Game Development Reference
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spheres. The distance between any two points in 3D space is found by
calculating a vector from one point to the next, starting at either end, then
finding the square root of the sum of the squares of components of this
double CalcDistance(VECTOR a, VECTOR b){
ab.x = a.x - b.x;
ab.y = a.y - b.y;
ab.z = a.z - b.z;
return sqrt(ab.x*ab.x + ab.y*ab.y + ab.z*ab.z);
Unfortunately, square root operations are computationally expensive.
But, wait a minute, we don't actually need a distance, we are only
interested in a condition, namely is sphere A intersecting with sphere B.
For this we can use the squared distance and the combined radii squared,
avoiding any use of square roots.
//a and b give the sphere centres, R and r give the sphere radii
typedef struct stSPHERE{
double x,y, z; //Centre
double r; //radius
BOOL DoSpheresIntersect(SPHERE a, SPHERE b){
double sqdist, sqrad;
//Vector from b to a
ab.x = a.x - b.x;
ab.y = a.y - b.y;
ab.z = a.z - b.z;
sqdist = ab.x*ab.x + ab.y*ab.y + ab.z*ab.z;
//Combined radii squared
sqrad = a.r*a.r + b.r*b.r;
return (sqdist<sqrad);
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