float UMathUtils::CalculateTrajectory(float distance, float gravity, float projectileVelocity)
{
    return 0.5f * FMath::Asin((-gravity * distance) / (projectileVelocity*projectileVelocity));
}

float UMathUtils::FirstOrderInterceptTime(float speed, FVector targetRelativePosition, FVector targetRelativeVelocity)
{
    float velocitySquared = targetRelativeVelocity.SizeSquared();
    if (velocitySquared < 0.001f)
        velocitySquared = 0.0f;

    float a = velocitySquared - speed * speed;

    if (FMath::Abs(a) < 0.001f)
    {
        float t = -targetRelativePosition.SizeSquared() / (2.0f * FVector::DotProduct(targetRelativeVelocity, targetRelativePosition));
        return FMath::Max(t, 0.0f);
    }
    float b = 2.0f * FVector::DotProduct(targetRelativeVelocity, targetRelativePosition);
    float c = targetRelativeVelocity.SizeSquared();
    float determinant = b * b - 4.0f * a * c;
    if (determinant > 0.0f)
    {
        float t1 = (-b + FMath::Sqrt(determinant)) / (2.0f * a);
        float t2 = (-b - FMath::Sqrt(determinant)) / (2.0f * a);
        if (t1 > 0)
        {
            if (t2 > 0) return FMath::Min(t1, t2);
            return t1;
        }
        return FMath::Max(t2, 0.0f);
    }
    if (determinant < 0) return 0;
    return FMath::Max(-b / (2.0f * a), 0.0f);
}

FVector UMathUtils::FirstOrderIntercept(FVector location, FVector velocity, float speed, FVector targetLocation, FVector targetVelocity)
{
    FVector targetRelativePosition = targetLocation - location;
    FVector targetRelativeVelocity = targetVelocity - velocity;
    float t = FirstOrderInterceptTime(speed, targetRelativePosition, targetRelativeVelocity);
    return targetLocation + t * targetRelativeVelocity;
}