[ REQ 5390]: Hello

[rgeorge at hsv.tybrin.com]

We currently have a software tool which was developed in house  
which makes heavy use of planar and spherical geometry. I will not  
burden you will all of details at this point but I am looking for a  
fast algorithm to generate convex hulls on the surface of a sphere  
(the earth in this case) from a set of cospherical points. We have  
downloaded qhull, geomview, and a number of other files from your  
site. I might now have what I need to implement the spherical convex  
hull in our software.

Our particular application supports flight safety analysis. When a  
launch of an R&D missile system is conducted, a determination must  
be made of the risk to the population and the environment in the  
surrounding area. Should the flight test go awry, the thrust of the  
missile can be terminated, restricting the range to within safe  
limits. The process of terminating a missile's thrust often produces  
debris, big and small. Our application takes the geodetic  
coordinates of impact points for each piece of debris for sometimes  
hundreds of simulated flights to determine the discrete probability  
density of  debris impacts. From this probability density we can  
estimate the risk to virtually anything either on the ground or in  
the air.

So what does this have to do with computational geometry? Well, one  
of the pieces of information we keep track of is the hull of the  
debris impact points. One of these discrete distributions can be the  
result of tens of thousands of debris impact points. Currently one  
of the most costly operations in our software is building these  
hulls. Also, our current hull algorithm which treats latitude,  
longitude coordinate pair as pseudo-cartesian coordinates will fail  
for hulls which contain either one of the poles (north or south).  
This second issue has not been a problem so far, but it would be  
nice not to have such a limitation.

I you have any suggestions I would appreciate it. One warning  
though, this is the tip of a geometric iceberg which will eventually  
extend into three dimensions.

Wishing you and yours only the best,

Russell George
Range Safety Program Manager
TYBRIN Corporation