poj 1279 Art Gallery (Half Plane Intersection)

  1 #include <cstdio>
  2 #include <cstring>
  3 #include <iostream>
  4 #include <algorithm>
  5 #include <vector>
  6 #include <cmath>
  7 
  8 using namespace std;
  9 
 10 struct Point {
 11     double x, y;
 12     Point() {}
 13     Point(double x, double y) : x(x), y(y) {}
 14 } ;
 15 template<class T> T sqr(T x) { return x * x;}
 16 typedef Point Vec;
 17 Vec operator + (Vec a, Vec b) { return Vec(a.x + b.x, a.y + b.y);}
 18 Vec operator - (Vec a, Vec b) { return Vec(a.x - b.x, a.y - b.y);}
 19 Vec operator * (Vec a, double p) { return Vec(a.x * p, a.y * p);}
 20 Vec operator / (Vec a, double p) { return Vec(a.x / p, a.y / p);}
 21 
 22 const double EPS = 1e-8;
 23 const double PI = acos(-1.0);
 24 inline int sgn(double x) { return (x > EPS) - (x < -EPS);}
 25 
 26 inline double dotDet(Vec a, Vec b) { return a.x * b.x + a.y * b.y;}
 27 inline double crossDet(Vec a, Vec b) { return a.x * b.y - a.y * b.x;}
 28 inline double dotDet(Point o, Point a, Point b) { return dotDet(a - o, b - o);}
 29 inline double crossDet(Point o, Point a, Point b) { return crossDet(a - o, b - o);}
 30 inline double vecLen(Vec x) { return sqrt(dotDet(x, x));}
 31 inline double toRad(double deg) { return deg / 180.0 * PI;}
 32 inline double angle(Vec v) { return atan2(v.y, v.x);}
 33 inline Vec vecUnit(Vec x) { return x / vecLen(x);}
 34 inline Vec normal(Vec x) { return Vec(-x.y, x.x) / vecLen(x);}
 35 
 36 const int N = 2222;
 37 struct DLine {
 38     Point p;
 39     Vec v;
 40     double ang;
 41     DLine() {}
 42     DLine(Point p, Vec v) : p(p), v(v) { ang = atan2(v.y, v.x);}
 43     bool operator < (DLine L) const { return ang < L.ang;}
 44 } dl[N];
 45 Point pt[N];
 46 
 47 inline bool onLeft(DLine L, Point p) { return crossDet(L.v, p - L.p) > 0;}
 48 Point dLineIntersect(DLine a, DLine b) {
 49     Vec u = a.p - b.p;
 50     double t = crossDet(b.v, u) / crossDet(a.v, b.v);
 51     return a.p + a.v * t;
 52 }
 53 
 54 struct Poly {
 55     vector<Point> pt;
 56     Poly() { pt.clear();}
 57     ~Poly() {}
 58     Poly(vector<Point> &pt) : pt(pt) {}
 59     Point operator [] (int x) { return pt[x];}
 60     int size() { return pt.size();}
 61     double area() {
 62         double ret = 0.0;
 63         int sz = pt.size();
 64         pt.push_back(pt[0]);
 65         for (int i = 1; i <= sz; i++) ret += crossDet(pt[i], pt[i - 1]);
 66         pt.pop_back();
 67         return fabs(ret / 2.0);
 68     }
 69 } ;
 70 
 71 Poly halfPlane(DLine *L, int n) {
 72     Poly ret = Poly();
 73     sort(L, L + n);
 74     int fi, la;
 75     Point *p = new Point[n];
 76     DLine *q = new DLine[n];
 77     q[fi = la = 0] = L[0];
 78     for (int i = 1; i < n; i++) {
 79         while (fi < la && !onLeft(L[i], p[la - 1])) la--;
 80         while (fi < la && !onLeft(L[i], p[fi])) fi++;
 81         q[++la] = L[i];
 82         if (sgn(crossDet(q[la].v, q[la - 1].v)) == 0) {
 83             la--;
 84             if (onLeft(q[la], L[i].p)) q[la] = L[i];
 85         }
 86         if (fi < la) p[la - 1] = dLineIntersect(q[la - 1], q[la]);
 87     }
 88     while (fi < la && !onLeft(q[fi], p[la - 1])) la--;
 89     if (la < fi) return ret;
 90     p[la] = dLineIntersect(q[la], q[fi]);
 91     for (int i = fi; i <= la; i++) ret.pt.push_back(p[i]);
 92     return ret;
 93 }
 94 
 95 bool isClockwise(Point *pt, int n) {
 96     double sum = 0.0;
 97     pt[n] = pt[0];
 98     Point O = Point(0.0, 0.0);
 99     for (int i = 0; i < n; i++) {
100         sum += crossDet(O, pt[i], pt[i + 1]);
101     }
102     return sum < 0;
103 }
104 
105 int main() {
106     int T, n;
107     cin >> T;
108     while (T-- && cin >> n) {
109         for (int i = 0; i < n; i++) cin >> pt[i].x >> pt[i].y;
110         pt[n] = pt[0];
111         if (isClockwise(pt, n)) for (int i = 0; i < n; i++) dl[i] = DLine(pt[i + 1], pt[i] - pt[i + 1]);
112         else for (int i = 0; i < n; i++) dl[i] = DLine(pt[i], pt[i + 1] - pt[i]);
113         Poly tmp = halfPlane(dl, n);
114         if (tmp.size() >= 3) printf("%.2f
", tmp.area());
115         else puts("0.00");
116     }
117     return 0;
118 }