Accounting for life time

d is distance to SURFACE of obj.
T is life time
r is object radius
ObsSpeed is max speed of observer
MinDist is minimum distance between observer and object
returns {reachable distance >= MinDist, maximum θ reachable}
  Note that reachable distance and maximum θ are BOTH WORST CASE
  The route to be walked is of course different for them
Note that  function is not upper bounded. We could set an upper bound of 180Ú on θ,
but this is not necessary as distortion will be too high much earlier for imposters.

[Graphics:Images/lifetime_gr_1.gif]
[Graphics:Images/lifetime_gr_2.gif]
[Graphics:Images/lifetime_gr_3.gif]
[Graphics:Images/lifetime_gr_4.gif]
[Graphics:Images/lifetime_gr_5.gif]
[Graphics:Images/lifetime_gr_6.gif]
[Graphics:Images/lifetime_gr_7.gif]

[Graphics:Images/lifetime_gr_8.gif]

[Graphics:Images/lifetime_gr_9.gif]
[Graphics:Images/lifetime_gr_10.gif]

[Graphics:Images/lifetime_gr_11.gif]

[Graphics:Images/lifetime_gr_12.gif]

We could cut off at 90Ú or 180Ú, but that is not necessary for other modules.

Old approximation

[Graphics:Images/lifetime_gr_13.gif]
[Graphics:Images/lifetime_gr_14.gif]

[Graphics:Images/lifetime_gr_15.gif]

[Graphics:Images/lifetime_gr_16.gif]


Converted by Mathematica      February 7, 2002