凸包求解之暴力算法

凸包求解之暴力算法
凸包:令S是平面上的一个点集，封闭S中所有顶点的最小凸多边形，称为S的凸包。

如下图中由红线段表示的多边形就是点集Q={p0,p1,...p12}的凸包。

 

class Line {//线
 Point p1, p2;
 Line(Point p1, Point p2) {
  this.p1 = p1;
  this.p2 = p2;
 }
}
class Point{//点
  int x;
  int y;
}
  
 public class BaoLiTuBao {
  List<Point> pts = null;//点集
  List<Line> lines = new ArrayList<Line>();//点集pts的凸包
   public void setPointList(List<Point> pts) {
     this.pts = pts;
   }
 
   public List<Line> eval() {
    lines.clear();
    if (pts == null) { return lines; }
    int n = pts.size();
    int a, b, c, cc, l, r;
    for (int i = 0; i < n; i++) {
     for (int j = i+1; j < n; j++) {//穷举点集中任意两点组成的直线ax+by=c
       a = pts.get(j).y - pts.get(i).y;//
       b = pts.get(i).x - pts.get(j).x;
       c = pts.get(i).x * pts.get(j).y -pts.get(i).y * pts.get(j).x;
       l = r = 0;
       int k;
       for (k = 0; k < n; k++) {//穷举点集中的每一点
         cc = a * pts.get(k).x + b * pts.get(k).y;
         if (cc > c) l++;
         else if (cc < c) r++;
         if (l * r != 0) break;//直线两侧都有点,
       }
      if (k == n) {//凸包中添加一条边
        lines.add(new Line(pts.get(i), pts.get(j)));
      }
     }
   }
   return lines;
  }
}

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