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)

Ive read through the entire thing but I cant figure out how to implement sortByAngle and angle, im not to sure what method I should do inside of them. This is what I have so far:

//Main method
public static Vertex[] ConcaveHull(Vertex[] points, int k = 3)
{
    if (k < 3)
        throw new ArgumentException("K is required to be 3 or more", "k");
    List<Vertex> hull = new List<Vertex>();
    //Clean first, may have lots of duplicates
    Vertex[] clean = RemoveDuplicates(points);
    if (clean.Length < 3)
        throw new ArgumentException("At least 3 dissimilar points reqired", "points");
    if (clean.Length == 3)//This is the hull, its already as small as it can be.
        return clean;
    if (clean.Length < k)
        throw new ArgumentException("K must be equal to or smaller then the amount of dissimilar points", "points");
    Vertex firstPoint = clean[0]; //TODO find mid point
    hull.Add(firstPoint);
    Vertex currentPoint = firstPoint;
    Vertex[] dataset = RemoveIndex(clean, 0);
    double previousAngle = 0;
    int step = 2;
    int i;
    while (((currentPoint != firstPoint) || (step == 2)) && (dataset.Length > 0))
    {
        if (step == 5)
            dataset = Add(dataset, firstPoint);
        Vertex[] kNearestPoints = nearestPoints(dataset, currentPoint, k);
        Vertex[] cPoints = sortByAngle(kNearestPoints, currentPoint, previousAngle);
        bool its = true;
        i = 0;
        while ((its) && (i < cPoints.Length))
        {
            i++;
            int lastPoint = 0;
            if (cPoints[0] == firstPoint)
                lastPoint = 1;
            int j = 2;
            its = false;
            while ((!its) && (j < hull.Count - lastPoint))
            {
                its = intersectsQ(hull[step - 1 - 1], cPoints[0], hull[step - i - j - 1], hull[step - j - 1]);
                j++;
            }
        }
        if (its)
        {
            return ConcaveHull(points, k + 1);
        }
        currentPoint = cPoints[0];
        hull.Add(currentPoint);
        previousAngle = angle(hull[step - 1], hull[step - 2]);
        dataset = RemoveIndex(dataset, 0);
        step++;
    }
    bool allInside = true;
    i = dataset.Length;
    while (allInside && i > 0)
    {
        allInside = new Polygon(dataset).Contains(currentPoint); //TODO havent finished ray casting yet.
        i--;
    }
    if (!allInside)
        return ConcaveHull(points, k + 1);
    return hull.ToArray();
}

private static Vertex[] Add(Vertex[] vs, Vertex v)
{
    List<Vertex> n = new List<Vertex>(vs);
    n.Add(v);
    return n.ToArray();
}

private static Vertex[] RemoveIndex(Vertex[] vs, int index)
{
    List<Vertex> removed = new List<Vertex>();
    for (int i = 0; i < vs.Length; i++)
        if (i != index)
            removed.Add(vs[i]);
    return removed.ToArray();
}

private static Vertex[] RemoveDuplicates(Vertex[] vs)
{
    List<Vertex> clean = new List<Vertex>();
    VertexComparer vc = new VertexComparer();
    foreach (Vertex v in vs)
    {
        if (!clean.Contains(v, vc))
            clean.Add(v);
    }
    return clean.ToArray();
}

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();
}

private static Vertex[] sortByAngle(Vertex[] vs, Vertex v, double angle)
{
    //TODO
    return new Vertex[]{};
}

private static bool intersectsQ(Vertex v1, Vertex v2, Vertex v3, Vertex v4)
{
    return intersectsQ(new Edge(v1, v2), new Edge(v3, v4));
}

private static bool intersectsQ(Edge e1, Edge e2)
{
    double x1 = e1.A.X;
    double x2 = e1.B.X;
    double x3 = e2.A.X;
    double x4 = e2.B.X;

    double y1 = e1.A.Y;
    double y2 = e1.B.Y;
    double y3 = e2.A.Y;
    double y4 = e2.B.Y;

    var x = ((x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4)) / ((x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4));
    var y = ((x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (x3 * y4 - y3 * x4)) / ((x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4));
    if (double.IsNaN(x) || double.IsNaN(y))
    {
        return false;
    }
    else
    {
        if (x1 >= x2)
        {
            if (!(x2 <= x && x <= x1)) { return false; }
        }
        else
        {
            if (!(x1 <= x && x <= x2)) { return false; }
        }
        if (y1 >= y2)
        {
            if (!(y2 <= y && y <= y1)) { return false; }
        }
        else
        {
            if (!(y1 <= y && y <= y2)) { return false; }
        }
        if (x3 >= x4)
        {
            if (!(x4 <= x && x <= x3)) { return false; }
        }
        else
        {
            if (!(x3 <= x && x <= x4)) { return false; }
        }
        if (y3 >= y4)
        {
            if (!(y4 <= y && y <= y3)) { return false; }
        }
        else
        {
            if (!(y3 <= y && y <= y4)) { return false; }
        }
    }
    return true;
}

private static double angle(Vertex v1, Vertex v2)
{
    // TODO fix
    Vertex v3 = new Vertex(v1.X, 0);
    if (Orientation(v3, v1, v2) == 0)
        return 180;

    double b = EuclideanDistance(v3, v1);
    double a = EuclideanDistance(v1, v2);
    double c = EuclideanDistance(v3, v2);
    double angle = Math.Acos((Math.Pow(a, 2) + Math.Pow(b, 2) - Math.Pow(c, 2)) / (2 * a * b));

    if (Orientation(v3, v1, v2) < 0)
        angle = 360 - angle;

    return angle;
}

private static double EuclideanDistance(Vertex v1, Vertex v2)
{
    return Math.Sqrt(Math.Pow((v1.X - v2.X), 2) + Math.Pow((v1.Y - v2.Y), 2));
}

public static double Orientation(Vertex p1, Vertex p2, Vertex p)
{
    double Orin = (p2.X - p1.X) * (p.Y - p1.Y) - (p.X - p1.X) * (p2.Y - p1.Y);
    if (Orin > 0)
        return -1;//Left
    if (Orin < 0)
        return 1;//Right
    return 0;//Colinier
}

I know that there is a load of code here. But im not sure if I can show the context and what I have without it.

Other classes:

public class Polygon
{

    private Vertex[] vs;

    public Polygon(Vertex[] Vertexes)
    {
        vs = Vertexes;
    }

    public Polygon(Bounds bounds)
    {
        vs = bounds.ToArray();
    }

    public Vertex[] ToArray()
    {
        return vs;
    }

    public IEnumerable<Edge> Edges()
    {
        if (vs.Length > 1)
        {
            Vertex P = vs[0];
            for (int i = 1; i < vs.Length; i++)
            {
                yield return new Edge(P, vs[i]);
                P = vs[i];
            }
            yield return new Edge(P, vs[0]);
        }
    }

    public bool Contains(Vertex v)
    {
        return RayCasting.RayCast(this, v);
    }
}

public class Edge
{
    public Vertex A = new Vertex(0, 0);
    public Vertex B = new Vertex(0, 0);
    public Edge() { }
    public Edge(Vertex a, Vertex b)
    {
        A = a;
        B = b;
    }
    public Edge(double ax, double ay, double bx, double by)
    {
        A = new Vertex(ax, ay);
        B = new Vertex(bx, by);
    }
}

public class Bounds
{
    public Vertex TopLeft;
    public Vertex TopRight;
    public Vertex BottomLeft;
    public Vertex BottomRight;
    public Bounds() { }

    public Bounds(Vertex TL, Vertex TR, Vertex BL, Vertex BR)
    {
        TopLeft = TL;
        TopRight = TR;
        BottomLeft = BL;
        BottomRight = BR;
    }

    public Vertex[] ToArray()
    {
        return new Vertex[] { TopLeft, TopRight, BottomRight, BottomLeft };
    }

}

public class Vertex
{
    public double X = 0;
    public double Y = 0;
    public Vertex() { }
    public Vertex(double x, double y)
    {
        X = x;
        Y = y;
    }

    public static Vertex[] Convert(string vs)
    {
        vs = vs.Replace("[", "");
        vs = vs.Replace("]", "");
        string[] spl = vs.Split(';');
        List<Vertex> nvs = new List<Vertex>();
        foreach (string s in spl)
        {
            try
            {
                nvs.Add(new Vertex(s));
            }
            catch
            {

            }
        }
        return nvs.ToArray();
    }

    public static string Stringify(Vertex[] vs)
    {
        string res = "[";
        foreach (Vertex v in vs)
        {
            res += v.ToString();
            res += ";";
        }
        res = res.RemoveLastCharacter();
        res += "]";
        return res;
    }

    public static string ToString(Vertex[] array)
    {
        string res = "[";
        foreach (Vertex v in array)
            res += v.ToString() + ",";
        return res.RemoveLastCharacter() + "]";
    }

    /*
    //When x < y return -1
    //When x == y return 0
    //When x > y return 1
    public static int Compare(Vertex x, Vertex y)
    {
        //To find lowest
        if (x.X < y.X)
        {
            return -1;
        }
        else if (x.X == y.X)
        {
            if (x.Y < y.Y)
            {
                return -1;
            }
            else if (x.Y == y.Y)
            {
                return 0;
            }
            else
            {
                return 1;
            }
        }
        else
        {
            return 1;
        }
    }
    */
    public static int CompareY(Vertex a, Vertex b)
    {
        if (a.Y < b.Y)
            return -1;
        if (a.Y == b.Y)
            return 0;
        return 1;
    }

    public static int CompareX(Vertex a, Vertex b)
    {
        if (a.X < b.X)
            return -1;
        if (a.X == b.X)
            return 0;
        return 1;
    }

    public double distance (Vertex b){
        double dX = b.X - this.X;
        double dY = b.Y - this.Y;
        return Math.Sqrt((dX*dX) + (dY*dY));
    }

    public double slope (Vertex b){
        double dX = b.X - this.X;
        double dY = b.Y - this.Y;
        return dY / dX;
    }

    public static int Compare(Vertex u, Vertex a, Vertex b)
    {
        if (a.X == b.X && a.Y == b.Y) return 0;

        Vertex upper = new Vertex();
        Vertex p1 = new Vertex();
        Vertex p2 = new Vertex();
        upper.X = (u.X + 180) * 360;
        upper.Y = (u.Y + 90) * 180;
        p1.X = (a.X + 180) * 360;
        p1.Y = (a.Y + 90) * 180;
        p2.X = (b.X + 180) * 360;
        p2.Y = (b.Y + 90) * 180;
        if(p1 == upper) return -1;
        if(p2 == upper) return 1;

        double m1 = upper.slope(p1);
        double m2 = upper.slope(p2);

        if (m1 == m2)
        {
            return p1.distance(upper) < p2.distance(upper) ? -1 : 1;
        }

        if (m1 <= 0 && m2 > 0) return -1;

        if (m1 > 0 && m2 <= 0) return -1;

        return m1 > m2 ? -1 : 1;
    }

    public static Vertex UpperLeft(Vertex[] vs)
    {
        Vertex top = vs[0];
        for (int i = 1; i < vs.Length; i++)
        {
            Vertex temp = vs[i];
            if (temp.Y > top.Y || (temp.Y == top.Y && temp.X < top.X))
            {
                top = temp;
            }
        }
        return top;
    }

}

Malvina

With the code below and replacing new Polygon(...).Contains(..) with a ray casing algorithm works. I will os the code soon. – Malvina

I tested the code with the marked answer and ray casting algorithm a few days ago, but it actually doesn't work. What changes have you made to let it work? – Hammad

Well I assumed it worked. I will look into my data further to check whats up. Maybe the ray casting is off? – Malvina

No. The problem is the condition of leaving recursion. – Hammad

I shall have a look into it. I haven't had much time lately to get back to this. – Malvina

Hello. Could you share a complete code with Vertex/Edge/Polygon classes? – Topper

Done, added the classes. – Malvina

Thank you for the classes. I have a question. Does it work for you? Because for 1,4k points I get and input about 1k (seems to be okay, but...) - when I want to check the returned points, all are the same:S Maybe there are some differences between your complete algorithm and above code. I used methods written by guys beneath this post. – Topper

can you please post some lost class? VertexComparer and RayCasting – Areopagite

Can you please post the complete code as nuget or in stack?? – Salomie

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.

Leverrier

This 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. – Hammad

@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 . – Leverrier

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?

Pubescent

I don't think anyone did. By the time it was answered I had moved onto other bits of work. – Malvina

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.

Joettajoette

In this case the OP really means a concave hull. – Island

That's cool, I just meant that my knowledge of convex hulls may (or may not) be applicable to this case. – Joettajoette

Okay, from the paper "SortByAngle[kNearestPoints,currentPoint,prevAngle] ► sort the candidates (neighbours) in descending order of right-hand turn", so I believe my answer is essentially correct. – Joettajoette

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;
    }

Toodleoo