ddd

  1 /*************************************************************************
  2     > File Name: board.cpp
  3     > Author: yijiull
  4     > Mail: 1147161372@qq.com 
  5     > Created Time: 2017年09月23日 星期六 10时50分19秒
  6  ************************************************************************/
  7 #include <iostream>
  8 #include <cstring>
  9 #include <cstdio>
 10 #include <bits/stdc++.h>
 11 using namespace std;
 12 #define FP freopen("in.txt", "r", stdin)
 13 const double eps = 1e-12;
 14 const double pi = acos(-1.0);
 15 const int inf = 0x3f3f3f3f;
 16 struct Point {
 17     double x,y;
 18     Point (double x = 0, double y = 0) : x(x), y(y) {}
 19 };
 20 typedef Point Vector;
 21 Vector operator + (Vector a, Vector b) {
 22     return Vector (a.x + b.x, a.y + b.y);
 23 }
 24 Vector operator * (Vector a, double s) {
 25     return Vector (a.x * s, a.y * s);
 26 }
 27 Vector operator / (Vector a, double p) {
 28     return Vector (a.x / p, a.y / p);
 29 }
 30 Vector operator - (Point a, Point b) {
 31     return Vector (a.x - b.x, a.y - b.y);
 32 }
 33 bool operator < (Point a, Point b) {
 34     return a.x < b.x || (a.x == b.x && a.y < b.y);
 35 }
 36 int dcmp (double x) {
 37     if(fabs(x) < eps) return 0;
 38     return x < 0 ? -1 : 1;
 39 }
 40 bool operator == (const Point &a, const Point &b) {
 41     return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0;
 42 }
 43 double Dot(Vector a, Vector b) {
 44     return a.x * b.x + a.y * b.y;
 45 }
 46 double Length (Vector a) {
 47     return sqrt(Dot(a, a));
 48 }
 49 double Angle (Vector a) {
 50     return atan2(a.y, a.x);
 51 }
 52 double Cross (Vector a, Vector b) {
 53     return a.x * b.y - a.y * b.x;
 54 }
 55 //判断两线段是否规范相交
 56 bool SegmentProperIntersection(Point a1, Point b1, Point a2, Point b2) { 
 57     double c1 = Cross(b1 - a1, a2 - a1), c2 = Cross(b1 - a1, b2 - a1),
 58            c3 = Cross(b2 - a2, a1 - a2), c4 = Cross(b2 - a2, b1 - a2);
 59     return dcmp(c1)*dcmp(c2) < 0 && dcmp(c3)*dcmp(4) < 0;
 60 }
 61 //判断点是否在线段上(即∠apb等于π)
 62 bool OnSegment(Point p, Point a, Point b) {
 63     return dcmp(Cross(a - p, b - p)) == 0 && dcmp(Dot(a - p, b - p)) < 0;
 64 }
 65 //两直线交点
 66 Point GetLineIntersection (Point p, Vector v, Point q, Vector w) {
 67     Vector u = p - q;
 68     double t1 = Cross(w, u) / Cross(v, w);
 69     double t2 = Cross(v, u) / Cross(v, w);
 70     return p + v * t1;  //  return q + w * t2;
 71 }
 72 const int maxn = 110;
 73 Point p[maxn], res[maxn], temp[maxn];
 74 double ang[maxn], s;
 75 int cnt;
 76 
 77 void add(Point a, Point b) {
 78     temp[cnt] = a;
 79     ang[cnt] = Angle(a - b) - s;
 80     while(dcmp(ang[cnt]) <= 0) ang[cnt] += 2*pi;
 81     cnt++;
 82 }
 83 
 84 int main(){
 85     int n;
 86     FP;
 87     while(scanf("%d", &n) != EOF) {
 88         int fg = 0;
 89         for(int i = 0; i < n; i++) {
 90             scanf("%lf %lf", &p[i].x, &p[i].y);
 91             if(p[i] < p[fg]) fg = i;
 92         }
 93         res[0] = p[fg];
 94         int num = 1;
 95         s = -pi;
 96         while (1) {
 97             cnt = 0;
 98             for (int i = 0; i < n; i++) {
 99                 if (res[num - 1] == p[i]) {
100                     add(p[(i + 1) % n], res[num - 1]);
101                     add(p[(i + n - 1) % n], res[num - 1]);
102                     break;
103                 }
104             }
105             for (int i = 0; i < n; i++) {
106                 if (OnSegment(res[num - 1], p[i], p[(i + 1) % n])) {
107                     add(p[(i + 1) % n], res[num - 1]);
108                     add(p[i], res[num - 1]);
109                 }
110             }
111             int id = 0;
112             for (int i = 0; i < cnt; i++)
113                 if (ang[i] < ang[id])
114                     id = i;
115             double minlen = 1e9;
116             Point RP = temp[id], its;
117             for (int i = 0; i < n; i++) {
118                 if (SegmentProperIntersection(temp[id], res[num - 1], p[i], p[(i + 1) % n])) {
119                     its = GetLineIntersection(temp[id], temp[id] - res[num - 1], p[i], p[i] - p[(i + 1) % n]);
120                     if (Length(its - res[num - 1]) < minlen) {
121                         minlen = Length(its - res[num - 1]);
122                         RP = its;
123                     }
124                 }
125             }
126             res[num] = RP;
127             s = atan2(res[num - 1].y - res[num].y, res[num - 1].x - res[num].x);
128             num++;
129             if (res[num - 1] == res[0])
130                 break;
131         }
132         printf("%d\n", num - 1);
133         for (int i = 0; i < num - 1; i++)
134             printf("%.4lf %.4lf\n", res[i].x, res[i].y);
135     }
136     return 0;
137 }