Conflict Detection (Batcher’s Algorithm) Identifying two lines for a plane in (time axis)-(x axis) coordinate plane. –Suppose the current coordinate location of plane is (X,Y) on x-y plane. The height is missing here. –The point (0, X – 1.5) is a point on vertical X-axis on this planar graph and is an initial point on lower line. –The point (0, X + 1.5) is a point on the vertical X-axis on this planar graph and is an initial point on upper line. –We assume that the plane continues with same velocity, so that in k half-seconds, it will be in position (X+k*DX, Y+k*DY) on x-y plane. –At T = 20 minutes, the point (20, X – *120*DX) will be on lower line and (20, X *120*DX) will be on upper line.

Conflict Detection Algorithm (2) –The two points on each line determine the upper and lower line (see next slide). The two lines for the (T axis)-(Y axis) plane can be determined similarly. If the height of plane is changing by DH each 0.5 second, the two lines for (T axis)-(H axis) is determined similarly. –If the plane has a constant height H, then the two lines on (T axis)-(H axis) will be horizonal lines going through (0, H+1000 feet) and (0, H-1000 feet) respectively. On the next slide, we show the safety zone overlap for two planes A and B in x-dimension.

Conflict Detection (3)

Conflict Detection (4) These two planes only have a potential conflict if their safety spaces overlap in all three dimensions at a common time. To test for a potential conflict, first determine the biggest min-time on all three graphs and the smallest max-time for planes A and B on all three graphs. –If across the three dimensions, the biggest min-time is smaller than the smallest max- time, there is a potential conflict