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    <p>Just a note on convention: you should start function names with upper case, and variables with lower case. In the function <code>sortByAngle</code>, you have a reference to the parameter <code>angle</code> and the function <code>angle</code> simultaneously.</p> <p>Assuming <code>Angle(...)</code> is simply meant to calculate the angle between two points:</p> <pre><code>private static double Angle(Vertex v1, Vertex v2) { return Math.Atan2(v2.Y - v1.Y, v2.X - v1.X); } </code></pre> <p>will give you the angle from <code>v1</code> to <code>v2</code>, in radians between -pi and +pi. Do not mix degrees and radians. My suggestion is to always use radians, and only convert to degrees if necessary for human-readable output.</p> <pre><code>private static Vertex[] SortByAngle(Vertex[] vs, Vertex v, double angle) { List&lt;Vertex&gt; vertList = new List&lt;Vertex&gt;(vs); vertList.Sort((v1, v2) =&gt; AngleDifference(angle, Angle(v, v1)).CompareTo(AngleDifference(angle, Angle(v, v2)))); return vertList.ToArray(); } </code></pre> <p>uses <code>List.Sort</code> to sort the vertices from greatest to least angle difference between the vertices <code>point</code> and itself, and <code>angle</code>. The order of <code>v1</code> and <code>v2</code> are swapped in the input tuple to sort descending, that is, greatest difference first. The difference between angles is calculated like so:</p> <pre><code>private static double AngleDifference(double a, double b) { while (a &lt; b - Math.PI) a += Math.PI * 2; while (b &lt; a - Math.PI) b += Math.PI * 2; return Math.Abs(a - b); } </code></pre> <p>The first two lines ensure that the angles are not more than 180 degrees apart.</p>
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    1. USJordan Trudgett
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    1. COThis answer is theoretical correct. What I don't understand is why to restrict the angle smaller than 180 degrees. Since the paper specified that the angle are sorted in right-hand turn, that is, an angle which is larger then 180 degrees is possible, unless the vertex is a candidate in previous calculation should be excluded.
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      1. USKen Kin
    2. CO@KenKin I might be wrong, but this calculates the acute difference between two angles which is never > 180 degrees. I believe by taking out the first two lines in `AngleDifference` it will compute the right-hand turn difference, perhaps also with `b - a` .
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