学习凸包(一）:暴力算法求解

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。

Java代码

1. 算法代码:
2. import java.util.*;
3. class Line {//线
4. Point p1, p2;
5. Line(Point p1, Point p2) {
6. this.p1 = p1;
7. this.p2 = p2;
8. }
9. }
11. class Point{//点
12. int x;
13. int y;
14. }
16. public class BaoLiTuBao {
17. List<Point> pts = null;//点集
18. List<Line> lines = new ArrayList<Line>();//点集pts的凸包
20. public void setPointList(List<Point> pts) {
21. this.pts = pts;
22. }
24. public List<Line> eval() {
25. lines.clear();
26. if (pts == null) { return lines; }
27. int n = pts.size();
28. int a, b, c, cc, l, r;
29. for (int i = 0; i < n; i++) {
30. 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
31. a = pts.get(j).y - pts.get(i).y;//
32. b = pts.get(i).x - pts.get(j).x;
33. c = pts.get(i).x * pts.get(j).y -pts.get(i).y * pts.get(j).x;
34. l = r = 0;
35. int k;
36. for (k = 0; k < n; k++) {//穷举点集中的每一点
37. cc = a * pts.get(k).x + b * pts.get(k).y;
38. if (cc > c) l++;
39. else if (cc < c) r++;
40. if (l * r != 0) break;//直线两侧都有点,
41. }
42. if (k == n) {//凸包中添加一条边
43. lines.add(new Line(pts.get(i), pts.get(j)));
44. }
45. }
46. }
47. return lines;
48. }
49. }

算法代码:import java.util.*;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;  }}