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    <p>Here is a little <a href="http://www.wolfram.com/mathematica/" rel="noreferrer">Mathematica</a> program. </p> <p>Although it is only two lines of code (<b>!</b>) you'll probably need more in a conventional language, as well as a math library able to find maximum of functions. </p> <p>I assume you are not fluent in Mathematica, so I'll explain and comment line by line. </p> <p>First we create a table with 10 random points in {0,1}x{0,1}, and name it <b>p</b>. </p> <pre><code>p = Table[{RandomReal[], RandomReal[]}, {10}]; </code></pre> <p>Now we create a function to maximize: </p> <pre><code>f[x_, y_] = Min[ x^2, y^2, (1 - x)^2, (1 - y)^2, ((x - #[[1]])^2 + (y - #[[2]])^2) &amp; /@ p]; </code></pre> <p>Ha! Syntax got tricky! Let's explain: </p> <p>The function gives you for any point in {0,1}x{0,1} the <b>minimum distance</b> from that point to our set p AND the edges. The first four terms are the distances to the edges and the last (difficult to read, I know) is a set containing the distance to all points. </p> <p>What we will do next is <b>maximizing</b> this function, so we will get THE point where the minimum distance to our targets in maximal. </p> <p>But first lets take a look at f[]. If you look at it critically, you'll see that it is not really the distance, but the distance squared. I defined it so, because that way the function is much easier to maximize and the results are the same. </p> <p>Also note that f[] is not a "pretty" function. If we plot it in {0,1}, we get something like: </p> <p><img src="https://i.stack.imgur.com/PerJJ.png" alt="alt text"> </p> <p>That's why you will need a nice math package to find the maximum. </p> <p>Mathematica is such a nice package, that we can maximize the thing straightforward: </p> <pre><code>max = Maximize[{f[x, y], {0 &lt;= x &lt;= 1, 0 &lt;= y &lt;= 1}}, {x, y}]; </code></pre> <p>And that is it. The Maximize function returns the point, and the squared distance to its nearest border/point. </p> <p><img src="https://i.stack.imgur.com/4YBvf.png" alt="alt text"> </p> <p>HTH! If you need help translating to another language, leave a comment. </p> <p><b>Edit</b></p> <p>Although I'm not a C# person, after looking for references in SO and googling, came to this:</p> <p>One candidate package is <a href="http://www.dotnumerics.com/Downloads.aspx" rel="noreferrer">DotNumerics</a></p> <p>You should follow the following example provided in the package:</p> <pre><code> file: \DotNumerics Samples\Samples\Optimization.cs Example header: [Category("Constrained Minimization")] [Title("Simplex method")] [Description("The Nelder-Mead Simplex method. ")] public void OptimizationSimplexConstrained() </code></pre> <p>HTH!</p>
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    1. POHow to find the point most distant from a given set and its bounding box
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    1. USDr. belisarius
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    1. POHow to find the point most distant from a given set and its bounding box
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    1. COThe "farthest away from the borders" bit means that if the algorithm is run with no points already in the box, it should find that a point in the center of the box is the ideal point, because it is the farthest possible point from the borders.
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    2. CO@Josh Do you have a test case to try the algorithm?
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    3. COHi belisarius -- thanks so much for your helpful answers here. The above images do look like they solve my problem, and I'd certainly love to learn the logic behind them.
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