基础计算机和-----半交面

半交面主要分下面几个步骤

1.建边(需要逆时针输入)

2.极角排序

3.判断重边

4.双端队列储存线的几何，因为新加入的线对头尾都会有影响

5.判断新加入的线的影响//也就是最重要的一步了。

6.把被新加入的线无效化的线去掉，也就是说新生命进来了，得把没有价值的线给去掉

POJ 3335

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
using namespace std;
const int maxn = 1e3;
const double EPS = 1e-5;
int T, n;
typedef struct Grid {
  double x, y;
  Grid(double a = 0, double b = 0) {x = a, y = b;}
} Point, Vector;
Vector operator - (Point a, Point b) {return Vector(b.x - a.x, b.y - a.y);}
double operator ^ (Vector a, Vector b) {return a.x * b.y - a.y * b.x;}//叉乘
struct Line {
  Point s, e;
  Line() {}
  Line(Point a, Point b) {s = a, e = b;}
};
Point p[maxn];
Line L[maxn], que[maxn];

//得到极角角度
double getAngle(Vector a) {
  return atan2(a.y, a.x);
}

//得到极角角度
double getAngle(Line a) {
  return atan2(a.e.y - a.s.y, a.e.x - a.s.x);
}

//排序：极角小的排前面，极角相同时，最左边的排在最后面，以便去重
bool cmp(Line a, Line b) {
  Vector va = a.e - a.s, vb = b.e - b.s;
  double A =  getAngle(va), B = getAngle(vb);
  if (fabs(A - B) < EPS) return ((va) ^ (b.e - a.s)) >= 0;
  return A < B;
}

//得到两直线相交的交点
Point getIntersectPoint(Line a, Line b) {
  double a1 = a.s.y - a.e.y, b1 = a.e.x - a.s.x, c1 = a.s.x * a.e.y - a.e.x * a.s.y;
  double a2 = b.s.y - b.e.y, b2 = b.e.x - b.s.x, c2 = b.s.x * b.e.y - b.e.x * b.s.y;
  return Point((c1*b2-c2*b1)/(a2*b1-a1*b2), (a2*c1-a1*c2)/(a1*b2-a2*b1));
}

//判断 b,c 的交点是否在 a 的右边
bool onRight(Line a, Line b, Line c) {
  Point o = getIntersectPoint(b, c);
  if (((a.e - a.s) ^ (o - a.s)) < 0) return true;
  return false;
}

bool HalfPlaneIntersection() {
  sort(L, L + n, cmp);//排序
  int head = 0, tail = 0, cnt = 0;//模拟双端队列
  //去重，极角相同时取最后一个。
  for (int i = 0; i < n - 1; i++) {
    if (fabs(getAngle(L[i]) - getAngle(L[i + 1])) < EPS) {
      continue;
    }
    L[cnt++] = L[i];
  }
  L[cnt++] = L[n - 1];


  for (int i = 0; i < cnt; i++) {
    //判断新加入直线产生的影响
    while(tail - head > 1 && onRight(L[i], que[tail - 1], que[tail - 2])) tail--;
    while(tail - head > 1 && onRight(L[i], que[head], que[head + 1])) head++;
    que[tail++] = L[i];
  }
  //最后判断最先加入的直线和最后的直线的影响
  while(tail - head > 1 && onRight(que[head], que[tail - 1], que[tail - 2])) tail--;
  while(tail - head > 1 && onRight(que[tail - 1], que[head], que[head + 1])) head++;
  if (tail - head < 3) return false;
  return true;
}

//判断输入点的顺序，如果面积 <0，说明输入的点为逆时针，否则为顺时针
bool judge() {
  double ans = 0;
  for (int i = 1; i < n - 1; i++) {
    ans += ((p[i] - p[0]) ^ (p[i + 1] - p[0]));
  }
  return ans < 0;
}

int main()
{
  scanf("%d", &T);
  while (T--) {
    scanf("%d", &n);
    for (int i = n - 1; i >= 0; i--) {
      scanf("%lf %lf", &p[i].x, &p[i].y);
    }

    if (judge()) {//判断输入顺序，保证逆时针连边。
      for (int i = 0; i < n; i++) {
        L[i] = Line(p[(i + 1)%n], p[i]);
      }
    } else {
      for (int i = 0; i < n; i++) {
        L[i] = Line(p[i], p[(i + 1)%n]);
      }
    }

    if (HalfPlaneIntersection()) printf("YES\n");
    else printf("NO\n");
  }

  return 0;
}