#include #include #include #include using namespace std; #define V P const double eps = 1e-6; inline int dcmp (double x) { return x < -eps ? -1 : x > eps; } struct P { double x, y; void scan() { scanf("%lf%lf", &x, &y); } P(double _x = 0, double _y = 0) : x(_x), y(_y) { } V operator + (V a) const { return V(x + a.x, y + a.y); } V operator - (V a) const { return V(x - a.x, y - a.y); } V operator * (double p) const { return V(p * x, p * y); } V operator / (double p) const { return V(x / p, y / p); } bool operator < (P a) const { return x < a.x || (dcmp(x - a.x) == 0 && y < a.y); } bool operator == (P a) const { return dcmp(x - a.x) == 0 && dcmp(y - a.y) == 0; } }; inline double dot(V a, V b) { return a.x * b.x + a.y * b.y; } inline double len(V a) { return sqrt(dot(a, a)); } inline double dis(P a, P b) { return len(b - a); } inline double ang(V a, V b) { return acos(dot(a, b) / len(a) / len(b)); } inline double cross(V a, V b) { return a.x * b.y - a.y * b.x; } inline double area(P a, P b, P c) { return cross(b - a, c - a); } V rot(V a, double p) { return V(a.x * cos(p) - a.y * sin(p), a.x * sin(p) + a.y * cos(p)); } V normal(V a) { double L = len(a); return V(-a.y / L, a.x / L); } P inter(P p, V v, P q, V w) { V u = p - q; double t = cross(w, u) / cross(v, w); return p + v * t; } double dis(P p, P a, P b) { V v1 = b - a, v2 = p - a; return fabs(cross(v1, v2)) / len(v1); } double dis2(P p, P a, P b) { if (a == b) return len(p - a); V v1 = b - a, v2 = p - a, v3 = p - b; if (dcmp(dot(v1, v2)) < 0) return len(v2); else if (dcmp(dot(v1, v3)) > 0) return len(v3); else return fabs(cross(v1, v2)) / len(v1); } P proj(P p, P a, P b) { V v = b - a; return a + v * (dot(v, p - a) / dot(v, v)); } bool isInter(P a1, P a2, P b1, P b2) { double c1 = cross(a2 - a1, b1 - a1), c2 = cross(a2 - a1, b2 - a1), c3 = cross(b2 - b1, a1 - b1), c4 = cross(b2 - b1, a2 - b1); return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0; } bool onSeg(P p, P a1, P a2) { return dcmp(cross(a1 - p, a2 - p)) == 0 && dcmp(dot(a1 - p, a2 - p)) < 0; } double area(P* p, int n) { double s = 0; p[n] = p[0]; for (int i = 1; i < n; i ++) s += cross(p[i] - p[0], p[i + 1] - p[0]); return s / 2; } int graham(P* p, int n, P* ch) { sort(p, p + n); int m = 0; for (int i = 0; i < n; i ++) { while (m > 1 && cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]) <= 0) m --; ch[m ++] = p[i]; } int k = m; for (int i = n - 2; i >= 0; i --) { while (m > k && cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]) <= 0) m --; ch[m ++] = p[i]; } if (n > 1) m --; return m; } struct L { P p; V v; double ang; L() {} L(P _p, V _v) : p(_p), v(_v) { ang = atan2(v.y, v.y); } bool operator < (const L& L) const { return ang < L.ang; } }; inline int get(P a) { if( a.x > 0 && a.y >= 0) return 1; if( a.x <= 0 && a.y > 0) return 2; if( a.x < 0 && a.y <= 0) return 3; if( a.x >= 0 && a.y < 0) return 4; return 0; } inline bool cmp2 (L a, L b) { return get(a.v) < get(b.v) || (get(a.v) == get(b.v) && dcmp( cross(a.v, b.v) ) >0); } bool onLeft(L l, P p) { return cross(l.v, p - l.p) > 0; } P inter(L a, L b) { return inter(a.p, a.v, b.p, b.v); } int half(L* l, int n, P* po) { sort(l, l + n, cmp2); int h, t; P *p = new P[n]; L *q = new L[n]; q[h = t = 0] = l[0]; for (int i = 1; i < n; i ++) { while (h < t && !onLeft(l[i], p[t - 1])) t --; while (h < t && !onLeft(l[i], p[h])) h ++; q[++ t] = l[i]; if (dcmp(cross(q[t].v, q[t - 1].v)) == 0) { t --; if (onLeft(q[t], l[i].p)) q[t] = l[i]; } if (h < t) p[t - 1] = inter(q[t - 1], q[t]); } while (h < t && !onLeft(q[h], p[t - 1])) t --; if (t - h <= 1) return 0; p[t] = inter(q[t], q[h]); int m = 0; for (int i = h; i <= t; i ++) po[m ++] = p[i]; return m; } inline bool cmp (V a, V b) { return get(a) < get(b) || (get(a) == get(b) && dcmp( cross(a, b) ) >0); } const int N = 101000; int n; P a[N], b[N], res[N]; L l[N]; int main() { int T; scanf("%d", &T); for (int cas = 1; cas <= T; cas ++) { scanf("%d", &n); for (int i = 0; i < n; i ++) a[i].scan(); int bound = n / 3 - 1, l_c = 0; for (int i = 0; i < n; i ++) { int cnt = 0; for (int j = 0; j < n; j ++) if (j != i) b[cnt ++] = a[j] - a[i]; sort(b, b + cnt, cmp); int t = 0, sum = 0; for (int j = 0; j < cnt; j ++) { while ((dcmp(cross(b[j], b[(t + 1) % cnt])) == 1) || (dcmp(cross(b[j], b[(t + 1) % cnt])) == 0 && dcmp(dot(b[j], b[(t + 1) % cnt])) == -1)) t = (t + 1) % cnt, sum ++; if (cnt - (sum + 1) == bound) l[l_c ++] = L(a[i], b[j]); if (t == j) t ++; else { while (dcmp(cross(b[j], b[(j + 1) % cnt])) == 0) j ++, sum --; sum --; } } } int ans = half(l, l_c, res); printf("Case #%d: %.6lf\n", cas, area(res, ans)); } return 0; }