Thank you Bus Driver Man! Now it makes more sense.
The thing that I have been having difficulty with is contradictory information regarding TCAS logic on the Net. On the one hand I have read that TCAS logic doesn't use the bearing (because of errors due to antennas) and it only uses range and closure rate to compute the time-to-go to CPA, and in doing so it compares this value to TAU threshold (Is that right??). But it simulates the case in which the two A/C would be on crossing trajectory and their CPA would be confonded with that crossing point! But obviously it doesn't always happen and even more so in 3D. For me CPA means that there can be horizontal and vertical miss distances at the CPA, so to find the Time-to-go to the CPA I would have expected to find an expression to derive... I must have missed something..
The other thing I have read, which is also on the document you gave me (thanks for that btw) is that TCAS logic uses bearing, range, closing rate, altitude and its own position to simulate both aircraft trajectories and find out where the CPA is, check the horizontal and vertical miss distance and then derive the Time-to-go to the CPA to compare it to TAU threshold... and Eureka! I personnaly would prefere this method which seems far more logical to me.
What do you think about this? Because I don't know which method TCAS logic uses. I am thinking of using the second one for my program.
Thank you for your answer,
Célia