Translating concave hull algorithm to c#

Question

So I am trying to translate the algorith found here for concave hulls: http://repositorium.sdum.uminho.pt/bitstream/1822/6429/1/ConcaveHull_ACM_MYS.pdf

(Page 65)

Answer 1

Just a note on convention: you should start function names with upper case, and variables with lower case. In the function sortByAngle, you have a reference to the parameter angle and the function angle simultaneously.

Assuming Angle(...) is simply meant to calculate the angle between two points:

private static double Angle(Vertex v1, Vertex v2)
{
    return Math.Atan2(v2.Y - v1.Y, v2.X - v1.X);
}

will give you the angle from v1 to v2, 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.

private static Vertex[] SortByAngle(Vertex[] vs, Vertex v, double angle)
{
    List<Vertex> vertList = new List<Vertex>(vs);
    vertList.Sort((v1, v2) => AngleDifference(angle, Angle(v, v1)).CompareTo(AngleDifference(angle, Angle(v, v2))));
    return vertList.ToArray();
}

uses List.Sort to sort the vertices from greatest to least angle difference between the vertices point and itself, and angle. The order of v1 and v2 are swapped in the input tuple to sort descending, that is, greatest difference first. The difference between angles is calculated like so:

private static double AngleDifference(double a, double b)
{
    while (a < b - Math.PI) a += Math.PI * 2;
    while (b < a - Math.PI) b += Math.PI * 2;

    return Math.Abs(a - b);
}

The first two lines ensure that the angles are not more than 180 degrees apart.

Answer 2

You have error in

private static Vertex[] nearestPoints(Vertex[] vs, Vertex v, int k)
{
    Dictionary<double, Vertex> lengths = new Dictionary<double, Vertex>();
    List<Vertex> n = new List<Vertex>();
    double[] sorted = lengths.Keys.OrderBy(d => d).ToArray();
    for (int i = 0; i < k; i++)
    {
        n.Add(lengths[sorted[i]]);
    }
    return n.ToArray();
}

according to code if you have several vertexes at the same distance, function returns only one. Since Dictionary uses unique keys.

BTW, did anyone finish this?

Answer 3

I don't have the time right now to read the paper, but I assume from my knowledge of conVEX hull algorithms that you're going around the points in a particular direction looking for the next point to link to.

If that's the case, "angle" would be the angle of the most recent line segment of the hull, and you want to sort the points by their angle from that line. Therefore you want to calculate the angles between a line (on the hull) and a set of lines (from the current point to each other point being considered). Whether the angles calculated are positive or negative depends upon whether you're going clockwise or anticlockwise. To calculate the angles, look at something like this:

Calculating the angle between two lines without having to calculate the slope? (Java)

Then just sort by the angles.

Answer 4

What about that?

private List<Vector> sortClockwiseFromCentroid(List<Vector> points, Vector center)
    {
        points = points.OrderBy(x => Math.Atan2(x.X - center.X, x.Y - center.Y)).ToList();
        return points;
    }