Calculate if a bullet hits the balloon-CodePudding

I have this problem I can't figure out and need help. The problem is about calculating how many balloons are hit by a pellet gun. Balloons positions are described by 3D coordinates (X,Y,Z) and radius R. The gunshot is defined by 3D location of the end of the barrel "p" (Px,Py,Pz) and vector "v" (Vx, Vy, Vz) describing the direction barrel is pointing to.

I've tried to implement the solution suggested here: https://math.stackexchange.com/questions/1939423/calculate-if-vector-intersects-sphere

// C = center of sphere
// r = radius of sphere
// P = point on line
// U = unit vector in direction of line

Q = P - C;
a = U*U;      // should be = 1
b = 2*U*Q
c = Q*Q - r*r;
d = b*b - 4*a*c;  // discriminant of quadratic

if d <  0 then solutions are complex, so no intersections
if d >= 0 then solutions are real, so there are intersections

But the problem with this is that I get intersection with balloons that are positioned behind the gun. How can I modify this algorithm in order to produce the correct result? Or is my approach maybe wrong?

CodePudding user response：

You need to actually solve the quadratic equation defined by your variables a, b and c.

(t1,t2) = QuadraticSolve(a, b, c);

If t1 and t2 are positive then the intersections are in front of your gun

CodePudding user response：

I can tell you the idea how you can do it. Refer this article. It tells you exact solution for your problem. solution