创建3D球体和3D盒子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 (SX < C1.X) dist_squared -= squared(SX - C1.X); else if (SX > C2.X) dist_squared -= squared(SX - C2.X); if (SY < C1.Y) dist_squared -= squared(SY - C1.Y); else if (SY > C2.Y) dist_squared -= squared(SY - C2.Y); if (SZ < C1.Z) dist_squared -= squared(SZ - C1.Z); else if (SZ > C2.Z) dist_squared -= squared(SZ - 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, eg:

|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 = { Sx-d, Sy-d, Sz-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;
}