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POGiven centers, find minimum radius for set of circles such that they fully cover another
 

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  1. POGiven centers, find minimum radius for set of circles such that they fully cover another
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    <p>I have the following geometry problem: You are given a circle with the center in origin - C(0, 0), and radius 1. Inside the circle are given N points which represent the centers of N different circles. You are asked to find the minimum radius of the small circles (the radius of all the circles are equal) in order to cover all the boundary of the large circle.</p> <p>The number of circles is: 3 ≤ N ≤ 10000 and the problem has to be solved with a precision of P decimals where 1 ≤ P ≤ 6.</p> <p>For example:<br> N = 3 and P = 4</p> <p>and the coordinates:<br> (0.193, 0.722)<br> (-0.158, -0.438)<br> (-0.068, 0.00)</p> <p>The radius of the small circles is: 1.0686.</p> <p>I have the following idea but my problem is implementing it. The idea consists of a binary search to find the radius and for each value given by the binary search to try and find all the intersection point between the small circles and the large one. Each intersection will have as result an arc. The next step is to 'project' the coordinates of the arcs on to the X axis and Y axis, the result being a number of intervals. If the reunions of the intervals from the X and the Y axis have as result the interval [-1, 1] on each axis, it means that all the circle is covered. </p> <p>In order to avoid precision problems I thought of searching between 0 and 2&times;10<sup>P</sup>, and also taking the radius as 10<sup>P</sup>, thus eliminating the figures after the comma, but my problem is figuring out how to simulate the intersection of the circles and afterwards how to see if the reunion of the resulting intervals form the interval [-1, 1].</p> <p>Any suggestions are welcomed! </p>
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    1. COAre you saying which circle of the 3-10000 will require the smallest radius to cover the original circle? Or are you using all 3-10000 circles at one time to cover the original circle?
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    2. COYour algorithm only looks at the circle's circumference, but it's possible that the whole circumference is covered while there is uncovered area in the middle.
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    3. CO@puddingfox. You have to use all the smaller circles in order to cover the original one.
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