Metric CalcInterceptTime (const CVector &vTarget, const CVector &vTargetVel, Metric rMissileSpeed, Metric *retrRange)
// CalcInterceptTime
//
// Returns the time that it would take to intercept a target
// at vTarget, moving with velocity vTargetVel, with
// a missile of speed rMissileSpeed. Returns < 0.0 if the missile cannot
// intercept the target.
//
// The formula for interception is:
//
// A +- B sqrt(C)
// t = --------------
// D
//
// Where A = B rVi
// B = 2 rRange
// C = rMissileSpeed^2 - rVj^2
// D = 2 (C - rVi^2)
{
Metric rRange = vTarget.Length();
CVector vPosNormal = vTarget / rRange;
if (retrRange)
*retrRange = rRange;
// Compute the orthogonals of the velocity along the position vector
Metric rVi, rVj;
vTargetVel.GenerateOrthogonals(vPosNormal, &rVi, &rVj);
// Figure out the inside of the square root. If this value is negative
// then we don't have an interception course.
Metric C = rMissileSpeed * rMissileSpeed - rVj * rVj;
if (C < 0.0)
return -1.0;
// Figure out the denominator. If this value is 0 then we don't
// have an interception course.
Metric D = 2 * (C - rVi * rVi);
if (D == 0.0)
return -1.0;
// Compute A and B
Metric B = 2 * rRange;
Metric A = B * rVi;
// Compute both roots
Metric Z = B * sqrt(C);
Metric R1 = (A + Z) / D;
Metric R2 = (A - Z) / D;
// If the first root is positive then return it
if (R1 > 0.0)
return R1;
// Otherwise we return the second root, which may or may not
// be positive
return R2;
}
