/// <summary>
/// Determines if a ray interescts a circle
/// </summary>
/// <param name="rayOrig">The origin of the ray</param>
/// <param name="rayDir">The direction of the ray</param>
/// <param name="center">The center of the circle</param>
/// <param name="r">The radius of the circle</param>
/// <returns></returns>
public static bool Intersects(Vector2D rayOrig, Vector2D rayDir, Vector2D center, double r)
{
// ray-circle intersection test
// P: hit point
// ray: P = O + tV
// circle: (P-C)dot(P-C)-r^2 = 0
// substitute to solve for t gives a quadratic equation:
// a = VdotV
// b = 2(O-C)dotV
// c = (O-C)dot(O-C)-r^2
// if the discriminant is negative, miss (no solution for P)
// otherwise, if both roots are positive, hit
double a = rayDir.Dot(rayDir);
double b = ((rayOrig - center) * 2.0).Dot(rayDir);
double c = (rayOrig - center).Dot(rayOrig - center) - r * r;
// discriminant
double disc = b * b - 4.0 * a * c;
if (disc < 0.0)
{
return(false);
}
// find the signs of the roots
// technically we should also divide by 2a
// but all we care about is the sign, not the magnitude
double root1 = -b + Math.Sqrt(disc);
double root2 = -b - Math.Sqrt(disc);
return(root1 > 0.0 && root2 > 0.0);
}
/// <summary>
/// Determines if a beam intersects a circle where:
/// the beam is a ray in the context of this method
/// the tank is a circle in the context of this method
/// </summary>
/// <returns></returns>
private bool IsBeamTankCollision(Beam beam, Tank tank)
{
// ray-circle intersection test
// P: hit point
// ray: P = O + tV
// circle: (P-C)dot(P-C)-r^2 = 0
// substitute to solve for t gives a quadratic equation:
// a = VdotV
// b = 2(O-C)dotV
// c = (O-C)dot(O-C)-r^2
// if the discriminant is negative, miss (no solution for P)
// otherwise, if both roots are positive, hit
Vector2D rayOrig = beam.Origin;
Vector2D rayDir = beam.Direction;
Vector2D center = tank.Location;
double r = gameSettings.TankSize / 2.0;
double a = rayDir.Dot(rayDir);
double b = ((rayOrig - center) * 2.0).Dot(rayDir);
double c = (rayOrig - center).Dot(rayOrig - center) - r * r;
// discriminant
double disc = b * b - 4.0 * a * c;
if (disc < 0.0)
{
return(false);
}
// find the signs of the roots
// technically we should also divide by 2a
// but all we care about is the sign, not the magnitude
double root1 = -b + Math.Sqrt(disc);
double root2 = -b - Math.Sqrt(disc);
return(root1 > 0.0 && root2 > 0.0);
}