凹壳实现

Question

我正在尝试实现下面http://repositorium.sdum.uminho.pt/bitstream/1822/6429/1/ConcaveHull_ACM_MYS.pdf中描述的算法

我正在使用以下类库。 Loyc 库来自http://core.loyc.net/

using System;
using System.Collections.Generic;
using System.Linq;
using System.Device.Location;
using Loyc.Collections;
using Loyc.Geometry;
using Loyc;

这是基础类

public class Hulls
{
    private static List<Point<double>> KNearestNeighbors(List<Point<double>> points, Point<double> currentPoint, int k, out int kk)
    {
        kk = Math.Min(k, points.Count - 1);
        var ret = points
            .OrderBy(x => PointMath.Length(new Vector<double>(currentPoint.X - x.X, currentPoint.Y - x.Y)))
            .Take(k)
            .ToList();
        return ret;
    }
    private static double Angle(Point<double> a, Point<double> b)
    {
        var ret = -Math.Atan2(b.Y - a.Y, b.X - a.X);
        return NormaliseAngle(ret);
    }
    private static double NormaliseAngle(double a)
    {
        //while (a < b - Math.PI) a += Math.PI * 2;
        //while (b < a - Math.PI) b += Math.PI * 2;
        if (a < 0.0) { return a + Math.PI + Math.PI; }
        return a;
    }
    private static List<Point<double>> SortByAngle(List<Point<double>> kNearest, Point<double> currentPoint, double angle)
    {
        //kNearest
        //    .Sort((v1, v2) => AngleDifference(angle, Angle(currentPoint, v1)).CompareTo(AngleDifference(angle, Angle(currentPoint, v2))));
        //return kNearest.ToList();
        kNearest = kNearest.OrderByDescending(x => NormaliseAngle(Angle(currentPoint, x) - angle)).ToList();
        return kNearest;
    }

    private static bool CCW(Point<double> p1, Point<double> p2, Point<double> p3)
    {
        var cw = ((p3.Y - p1.Y) * (p2.X - p1.X)) - ((p2.Y - p1.Y) * (p3.X - p1.X));
        return cw > 0 ? true : cw < 0 ? false : true; // colinear 
    }

    private static bool _Intersect(LineSegment<double> seg1, LineSegment<double> seg2)
    {
        return CCW(seg1.A, seg2.A, seg2.B) != CCW(seg1.B, seg2.A, seg2.B) && CCW(seg1.A, seg1.B, seg2.A) != CCW(seg1.A, seg1.B, seg2.B);
    }

    private static bool Intersect(LineSegment<double> seg1, LineSegment<double> seg2)
    {
        if ((seg1.A.X == seg2.A.X && seg1.A.Y == seg2.A.Y) 
            || (seg1.B.X == seg2.B.X && seg1.B.Y == seg2.B.Y))
        {
            return false;
        }
        if (_Intersect(seg1, seg2))
        {
            return true;
        }
        return false;
    }

    public IListSource<Point<double>> KNearestConcaveHull(List<Point<double>> points, int k)
    {
        points.Sort((a, b) => a.Y == b.Y ? (a.X > b.X ? 1 : -1) : (a.Y >= b.Y ? 1 : -1));
        Console.WriteLine("Starting with size {0}", k.ToString());

        DList<Point<double>> hull = new DList<Point<double>>();
        var len = points.Count;

        if (len < 3) { return null; }
        if (len == 3) { return hull; }

        var kk = Math.Min(Math.Max(k, 3), len);

        var dataset = new List<Point<double>>();
        dataset.AddRange(points.Distinct());

        var firstPoint = dataset[0];
        hull.PushFirst(firstPoint);

        var currentPoint = firstPoint;
        dataset.RemoveAt(0);

        double previousAngle = 0;
        int step = 2;
        int i;
        while ((currentPoint != firstPoint || step == 2) && dataset.Count > 0)
        {
            if (step == 5) { dataset.Add(firstPoint); }
            var kNearest = KNearestNeighbors(dataset, currentPoint, k, out kk);
            var cPoints = SortByAngle(kNearest, currentPoint, previousAngle);
            var its = true;
            i = 0;
            while (its == true && i < cPoints.Count)
            {
                i++;
                int lastPoint = 0;
                if (cPoints[i - 1] == firstPoint)
                {
                    lastPoint = 1;
                }
                int j = 2;
                its = false;
                while (its == false && j < hull.Count - lastPoint)
                {
                    LineSegment<double> line1 = new LineSegment<double>(hull[step - 2], cPoints[i - 1]);
                    LineSegment<double> line2 = new LineSegment<double>(hull[step - 2 - j], hull[step - 1 - j]);

                    //its = LineMath.ComputeIntersection(line1, line2, out pfrac, LineType.Segment);
                    its = Intersect(line1, line2);
                    j++;
                }
            }
            if (its == true)
            {
                return KNearestConcaveHull(points, kk + 1);
            }
            currentPoint = cPoints[i - 1];
            hull.PushLast(currentPoint);
            previousAngle = Angle(hull[step - 1], hull[step - 2]);
            dataset.Remove(currentPoint); 
            step++;
        }
        bool allInside = true;
        i = dataset.Count;
        while (allInside == true && i > 0)
        {
            allInside = PolygonMath.IsPointInPolygon(hull, dataset[i - 1]);
            i--;
        }
        if (allInside == false) { return KNearestConcaveHull(points, kk + 1); }
        return hull;
    }
}

上面的内容应该基于从前一个边缘绕逆时针设置的点向右转最远的位置为边界选择一个新边缘。该代码似乎从具有最低 y 值的初始顶点中选择了正确的第一条边，但是当偏移角不为零时，它没有正确选择下一条边。我认为问题是 SortByAngle 或 Angle。 -atan2 会返回顺时针方向，对吗？可能我应该添加偏移角度？

编辑（解决方案）：在遵循 Eric 在对该问题的第一条评论中提供的有用建议后发现了该问题。是 SortByAngle 和 Angle：

private static double Angle(Point<double> a, Point<double> b)
    {
        var ret = Math.Atan2(b.Y - a.Y, b.X - a.X);
        return NormaliseAngle(ret);
    }

    private static double NormaliseAngle(double a)
    {
        if (a < 0.0) { return a + Math.PI + Math.PI; }
        return a;
    }

    private static List<Point<double>> SortByAngle(List<Point<double>> kNearest, Point<double> currentPoint, double angle)
    {
        //kNearest = kNearest.OrderByDescending(x => NormaliseAngle(Angle(currentPoint, x) - angle)).ToList();
        kNearest.Sort((a, b) => NormaliseAngle(Angle(currentPoint, a) - angle) > NormaliseAngle(Angle(currentPoint, b) - angle) ? 1 : -1);
        return kNearest;
    }

Answer 1

你有一些错误：

var kNearest = KNearestNeighbors(dataset, currentPoint, k, out kk);

将 kk 更改为只是一些 var。你覆盖了那个“kk”值的增量，然后你得到了 StackOverflow 异常。

将您的代码更改为以下内容：

int someVal;    
var kNearest = KNearestNeighbors(dataset, currentPoint, k, out someVal);