Algorithm for calculating shortest distance within a time frame

[nimesh_82]

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

[da_silvy]

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

[nimesh_82]

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

[da_silvy]

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

[nimesh_82]

Hi

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

thanks

Nimesh