Create a 3D sphere and 3D box C++ - c++

Question

I need to implement a tool to detect intersction between a 3D box and 3D Sphere in c++. Write now I find a way how to detect the intersection using that code.
inline float squared(float v) { return v * v; }
bool doesCubeIntersectSphere(vec3 C1, vec3 C2, vec3 S, float R)
{
float dist_squared = R * R;
/* assume C1 and C2 are element-wise sorted, if not, do that now */
if (S.X < C1.X) dist_squared -= squared(S.X - C1.X);
else if (S.X > C2.X) dist_squared -= squared(S.X - C2.X);
if (S.Y < C1.Y) dist_squared -= squared(S.Y - C1.Y);
else if (S.Y > C2.Y) dist_squared -= squared(S.Y - C2.Y);
if (S.Z < C1.Z) dist_squared -= squared(S.Z - C1.Z);
else if (S.Z > C2.Z) dist_squared -= squared(S.Z - C2.Z);
return dist_squared > 0;
}
What I need is an example of C++ code to create a 3D sphere using origin vector and a radius and
I need to create a 3D sphere using origin vector and a radius and a 3D box through its maximum and minimum corner vector.

Answer 1

I may be mistaken, but (assuming Axis-Aligned boxes):
The length of a vector from origin to corner C1 or C2 should be the radius r, right?
Explanation for my deriviation below: An Axis-Aligned-box with equal distance from center to all corners is a perfect cube. Translating such a cube to the origin puts two of the corners exactly at the line from the origin through the point {x=1,y=1,z=1}. Thus those two corners will have coordinates {d,d,d} and {-d, -d, -d}, where d is "distance" of the corner along the axises X,Y,Z. The distance to say the first corner is squaring and adding all components of the vector, and taking the square root, e.g:
|C1| = |{d,d,d}| = sqrt(d * d + d * d + d * d) = sqrt(3 * d * d)
Therefore solve:
r = sqrt(3 *d * d)
<=>
r * r = 3 * d * d
<=>
d = sqrt(r*r/3)
<=>
d = r/sqrt(3)
This needs to be translated back to the center of the Sphere, thus:
C1 = { S.x+d, S.y+d, S.z+d}
C2 = { S.x-d, S.y-d, S.z-d}
Your explanation is a little vague, so I made some assumptions. Perhaps I'm dead wrong. Anyway here is some non-tested code showing what I mean:
void makeCube(vec3 S, float R, vec3* C1, vec3* C2)
{
static const float sqrt_one_third = sqrtf(1.0f/3.0f);
float d = R * sqrt_one_third;
C1->X = S.X + d;
C1->Y = S.Y + d;
C1->Z = S.Z + d;
C2->X = S.X - d;
C2->Y = S.Y - d;
C2->Z = S.Z - d;
}