Algorithm for calculating shortest distance within a time frame

Hi

I am trying to solve a real tough problem ANY HELP WILL BE REALLY APPRECIATED.

I am trying to simulate planes flying within a sector, i need to check whether they have a specified horizontal seperation (if at same altitude) or vertical seperation. I need a algorithm which will help me calculate shortest distance between two lines within a time interval., i have starting x1,y1 coordinate and ending x2,y2 coordinate, the user will enter the altitude, speed and time entered and exited from the sector.

Please help

thanks

nimesh

the distance between them will be

sqrt( (x1 - x2)^2 + (y1 - y2)^2 + (z1 - z2)^2)

Does that help at all?

Other wise you can use vectors and the dot product to find the shortest distance

Hi

I was thinking of incorporating vectors and dot product but how do i incoporate the fact that i have a two dimensional line as the third dimension which is alitude will remain the same, also since they are moving how do i implement that fact.

thanks

nimesh

if their altitude is the same, then you don't need to worry about z (or k)

so for the first plane, say it's moving north at 5m/s (lol, so slow),

its vector would be

a = x1i + (y1+5t)j

and plane b is heading east at 10m/s

so its vector would be
b = (x2+10t)i + y2j

then you'd find the time when the two vectors are perpendicular to each other

a.b = x1(x2+10t) + y2(y1+5t) = 0

solve for t, substitute the value of t into the 2 vectors, then find the distance between the two

or i guess you could find |a-b|

which would be like

sqrt((x1-(x2+10t))^2 + ((y1+5t)-y2)^2)

i think...

play around a little :p

Hi

Ya that could work out, i am right on it now. I really appreciate your help.

thanks

Nimesh