1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
#include <bits/stdc++.h>
using namespace std;
typedef vector<int> VI;
typedef pair <int,int> ii;
typedef pair <double,double> dd;
typedef pair <ii,int> iii;
typedef long long LL;
#define pb push_back
const int INF = 2147483647;
const int N = 105;
const double eps = 1e-9;

struct pI {
	int x, y;
};

struct pD {
	double x, y;
};


struct line {
	pI a1;
	pI a2;
};

int detI(pI& a, pI& b, pI& c) {
	return a.x * b.y + b.x * c.y + c.x * a.y - a.x * c.y - b.x * a.y - c.x * b.y;
}

double detD(pD& a, pD& b, pD& c) {
	return a.x * b.y + b.x * c.y + c.x * a.y - a.x * c.y - b.x * a.y - c.x * b.y;
}

// funkcja sprawdza czy przechodzac z a do b i c skrecamy w lewo(1), w prawo(-1) czy punkty są wspollniowe(0)
int ccwI(pI& a, pI& b, pI& c) {
	int d = detI(a, b, c);
	return (d > 0) ? 1 : ((d < 0) ? -1 : 0);
}

// funkcja sprawdza czy przechodząc z a do b i c skręcamy w lewo(1), w prawo(-1) czy punkty są współlniowe(0)
int ccwD(pD& a, pD& b, pD& c) {
	double d = detD(a, b, c);
	return (d > eps) ? 1 : ((d < -eps) ? -1 : 0);
}

// funkcja sprawdza położenie punktu c wspolliniowego z odcinkiem a-b
// zwraca 1 - c lezy na odcinku, 0 - nie
bool inside(pI& a, pI& b, pI& c) {
 	return (c.x <= max(a.x,b.x) && c.x >= min(a.x,b.x) && c.y <= max(a.y,b.y) && c.y >= min(a.y,b.y));
}

char get_line_intersection(int p0_x, int p0_y, int p1_x, int p1_y, 
    int p2_x, int p2_y, int p3_x, int p3_y, double& i_x, double& i_y)
{
    int s1_x, s1_y, s2_x, s2_y;
    s1_x = p1_x - p0_x;     s1_y = p1_y - p0_y;
    s2_x = p3_x - p2_x;     s2_y = p3_y - p2_y;
    double s, t;
    s = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) * 1.0 / (-s2_x * s1_y + s1_x * s2_y);
    t = ( s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) * 1.0 / (-s2_x * s1_y + s1_x * s2_y);
    if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
        // Collision detected
        i_x = p0_x + (t * s1_x);
        i_y = p0_y + (t * s1_y);
        return 1;
    }

    return 0; // No collision
}

pI p1[N], p2[N];
int i, j, n;
double xx, yy;
vector<line> vec;
vector<int> vecI;
vector<pD> crosses;
VI res;

void check2(pI& p_1, pI& p_2, pI& p_3, pI& p_4, int a, int b) {
	int w1 = ccwI(p_1, p_2, p_3);
	int w2 = ccwI(p_1, p_2, p_4);
	if (w1 * w2 == -1) return;
	if (w1 == 0 && inside(p_1, p_2, p_3)) return;
	if (w2 == 0 && inside(p_1, p_2, p_4)) return;
	for (int i=0;i<n;i++) if (i != a && i != b) {
		int w3 = ccwI(p_1, p_2, p1[i]);
		int w4 = ccwI(p_1, p_2, p2[i]);
		if (w3 * w4 == 1) {
			if (w1 == w3 || w2 == w3) return;
		}
	}
	line l;
	l.a1 = p_1;
	l.a2 = p_2;
	vec.pb(l);
	vecI.pb(w1 != 0 ? w1 : w2);
}

void check(int a, int b) {
	check2(p1[a], p1[b], p2[a], p2[b], a, b);
	check2(p1[a], p2[b], p2[a], p1[b], a, b);
	check2(p2[a], p1[b], p1[a], p2[b], a, b);
	check2(p2[a], p2[b], p1[a], p1[b], a, b);
}

void convexHull(VI& res) {
	int n = crosses.size();
	int ind = 0, i, kol[n];
	double dx, dy;
	for (i = 1; i < n; i++) if (dd(crosses[i].y, crosses[i].x) < dd(crosses[ind].y, crosses[ind].x)) ind = i;
	dx = crosses[ind].x;
	dy = crosses[ind].y;
	for (i = 0; i < n; i++) {
		crosses[i].x -= dx;
		crosses[i].y -= dy;
		kol[i] = i;
	}
	sort(kol, kol + n, [] (const int& lhs, const int& rhs) {
		double diff = crosses[lhs].x * crosses[rhs].y - crosses[rhs].x * crosses[lhs].y;
		if (diff != 0) return (diff > 0);
		if (abs(crosses[lhs].x - crosses[rhs].x) < eps) return abs(crosses[lhs].y) < abs(crosses[rhs].y);
		return abs(crosses[lhs].x) < abs(crosses[rhs].x);
	});
	res.resize(0);
	res.pb(kol[0]);
	for (i = 1; i < n; i++) {
		while (res.size() > 1 && ccwD(crosses[res[res.size() - 2]], crosses[res[res.size() - 1]], crosses[kol[i]]) <= 0) res.pop_back();
		res.pb(kol[i]);
	}
	for (i = 0; i < n; i++) {
		crosses[i].x += dx;
		crosses[i].y += dy;
	}
}

double getArea() {
   	int i, j;
   	double result = 0.0;
   	for (i=0;i < res.size();i++) {
		j = (i + 1) % res.size();
		result += crosses[res[i]].x * crosses[res[j]].y - crosses[res[j]].x * crosses[res[i]].y;
	}
   	return result / 2;
}

bool onEdge(double xx, double yy, line& l1, line& l2) {
	pD p1, p2, p3;
	p3.x = xx;
	p3.y = yy;
	for (int i=0;i<vecI.size();i++) if (vecI[i] != 0) {
		p1.x = vec[i].a1.x;
		p1.y = vec[i].a1.y;
		p2.x = vec[i].a2.x;
		p2.y = vec[i].a2.y;
		int w = ccwD(p1, p2, p3);
		if (w == vecI[i]) return false;
	}
	return true;
}

int main() {
srand(time(0));
scanf("%d", &n);
vec.clear();
vecI.clear();
crosses.clear();
for (i=0;i<n;i++) scanf("%d %d %d %d", &p1[i].x, &p1[i].y, &p2[i].x, &p2[i].y);
for (i=0;i<n;i++) for (j=i+1;j<n;j++) check(i, j);
for (i=0;i<vec.size();i++) for (j=i+1;j<vec.size();j++) {
	if (get_line_intersection(vec[i].a1.x, vec[i].a1.y, vec[i].a2.x, vec[i].a2.y, vec[j].a1.x, vec[j].a1.y, vec[j].a2.x, vec[j].a2.y, xx, yy)) {
		bool already = false;
		for (pD& pd : crosses) if (abs(pd.x - xx) < eps && abs(pd.y - yy) < eps) {
			already = true;
			break;
		}
		if (!already && onEdge(xx, yy, vec[i], vec[j])) {
			pD p;
			p.x = xx;
			p.y = yy;
			crosses.pb(p);
		}
	}
}
if (crosses.size() < 3) {
	printf("0.000000000\n");
	return 0;
}
res.clear();
convexHull(res);
if (res.size() < 3) {
	printf("0.000000000\n");
	return 0;
}
printf("%.16lf\n", getArea());
return 0;
}