Help regarding overlapping areas

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this isn't a homework problem , but a real life one. I have got nowhere. Am stuck.
 
c0unse1 said:
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It would be helpful to know, for example, whether this is something you want to program in a computer, or to do humanly; and how much you know about trigonometry and vectors. This is part of the reason for asking to see what you have tried. (If I were going to do this to check a particular site, I'd probably draw it up in GeoGebra as you have done, and just look. And the locations could be entered as variables so you could easily check this for one plan after another by just typing in data.)

I think you need to do a (possibly long) series of tests, perhaps checking the easiest things first. You might, for example, first check whether any of the corners of one sector are inside the other. If not, they could still overlap, but only in certain ways, which you could check one at a time (for instance, the arcs might intersect, or an arc might intersect a line).

Rather than expect someone here to write the whole thing for you, I'd rather you did what you could, and then asked for a formula for a specific part, such as an arc intersecting a line.

It will also be helpful if you specify the actual input to be used, particularly for the direction. Will you be given the location of D (which gives both direction and range), or an angle from north, or a vector, or what?
 
Thank you for your patience.

yes, this is something I would like to program into a computer. I have reasonable maths knowledge , A level albeit 30 years ago.

i have a database containing many thousands of ‘paired’ cell sites. I wish to know in relation to any given pair, whether they might have the potential for overlap, or not.

in relation to each cell site I have it’s location (in eastings and northings - which equate to 1m each) and the azimuth the cell site is pointing from the vertical. Each cell site ‘broadcasts’ in an arc, +/-60 degrees from the direction its pointed.

each cell site has a range of approximately 2km, but this would best be expressed as a variable due to different ranges for urban and rural areas.

i can work out using Pythagorus whether the cell masts are too far away to provide overlap ie if >4km then cannot have overlap.
i had the thought that I need to work out firstly the point of intersection between the AB and EG in my example above, and then see if that is <2km from both A and E. I have no idea how to go about this.
 
c0unse1 said:
i can work out using Pythagorus whether the cell masts are too far away to provide overlap ie if >4km then cannot have overlap.
i had the thought that I need to work out firstly the point of intersection between the AB and EG in my example above, and then see if that is <2km from both A and E. I have no idea how to go about this.
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That's a good piece to ask about. Probably the most straightforward approach would be to write an equation for each line using point-slope, getting the slope from the direction (tangent of the azimuth plus or minus 60 degrees). Then just solve those two equations.
 
It looks like we will need another input besides the angles CAB, GEF and the coordinates of the points A and E. Note that we could rotate the circular sector on the right hand side keeping the angle GEF and the coordinates of E, and that would lead to a different overlap.
 
yes we do, but it is best expressed as a variable as it can change. Typically. it is 2km.
 
c0unse1 said:
yes we do, but it is best expressed as a variable as it can change. Typically. it is 2km.
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Of course, I didn't mean an specific number but if it is an input of your problem. Have you tried using analytic geometry, write the different objects (circular sectors and straight lines) in terms of Cartesian coordinates?
 
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