Thread: intersecting circles (trilateration)

  1. #1
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    intersecting circles (trilateration)

    i was reading up on some info about GPS and how it works.. and i came across something called trilateration, from what i understand its when you are given 3 or more points and distances from each of those points, you construct the circles using the distances as radius' and they all intersect at 1 point..

    anyway, i tried that out on paper but i couldnt figure out a way to 'prove' that the method works.. ie.. i know you can SEE the intersection but how can you prove its there? (using math).. so i made a little program that basically just let me define 3 points and the distances and it would draw the circles and they would all intersect at 1 point..

    im trying to figure out how i can calculate the x,y position of the intersection given only the 3 x,y points and the 3 radius'... im pretty sure this must be easy but for some reason i cannot figure it out :\

    i tried looking for function that check for intersecting circles but no luck so far.. i tried intersecting rectangles instead but that didnt work out..

    anyone know a formula or a function or something i can use to calculate the position?

    thanks in advance

  2. #2
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    You need to find the points on the circles circumference (then find the one that appears in all three).

    You know the radius and center so you can calculate a starting point (ie center_x + radius, center_y).
    Increase the angle and use trig functions (sin, cos to get the new offset x,y from center) to calculate the next point on the circumfrence.

    Watch for rounding errors.

    I would search two circles. Find the two points they intersect and check the third for these points.
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  3. #3
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    Quote Originally Posted by X PaYnE X
    so i made a little program that basically just let me define 3 points and the distances and it would draw the circles and they would all intersect at 1 point..
    I don't really understand... When you take 3 random coords and 3 random radius' it would be pure luck if all three have one common point in their circumference right?

  4. #4
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    i thought the formula for a circle was

    y^2 = r^2 - x^2

    why would i need to use sin/cos/tan? anyway, i did what you said with the formula above but my circle is.. missing alot of points, anyway, what i did is, i gave each circle a color like.. red for 1.. green for the other.. etc.. and whenever they would overlap each other, the colors would mix, then when it was done intersecting.. there wud be 1 point that is white.. but when i compare that with the original value i get an error of 2 - 3 pixels..

    anyway, anyone know a better method to use to draw a circle?

    btw snip, the 3 circles all have 1 point on the circumference in common so it always intersects..

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