#include <cstdio>#include <cstdlib>#include <climits>#include <iostream>#include <algorithm>#include <cstring>#include <string>#include <queue>#include <map>#include <vector>#include <bitset>#include <cmath>#include <set>#include <utility>#include <ctime>#define sqr(x) ((x)*(x))using namespace std;const int N = 110;const int M = 20;const double eps = 1e-8;int n, n2, vis[N][M];int dcmp(double x) { if (x < -eps) return -1; else return x > eps;}struct cpoint { double x, y; cpoint() {} cpoint(double x, double y) : x(x), y(y) {} bool operator == (const cpoint &u) const { return dcmp(x - u.x) == 0 && dcmp(y - u.y) == 0; } void get() { scanf("%lf%lf", &x, &y); }}tp[N * M], bp;struct poly { int n; cpoint cp[M]; cpoint& operator [] (int k) { return cp[k]; }}ply[N], ply2[N];double cross(cpoint p0, cpoint p1, cpoint p2) { return (p1.x - p0.x) * (p2.y - p0.y) - (p1.y - p0.y) * (p2.x - p0.x);}double dot(cpoint p0, cpoint p1, cpoint p2) { return (p1.x - p0.x) * (p2.x - p0.x) + (p1.y - p0.y) * (p2.y - p0.y);}int PointonSegment(cpoint p0, cpoint p1, cpoint p2) { return dcmp(cross(p0, p1, p2)) == 0 && dcmp(dot(p0, p1, p2)) <= 0;}int LineInter(cpoint p1, cpoint p2, cpoint p3, cpoint p4, cpoint &cp) { double u = cross(p1, p2, p3), v = cross(p2, p1, p4); if ( dcmp(u + v) ) { cp.x = (p3.x * v + p4.x * u) / (u + v); cp.y = (p3.y * v + p4.y * u) / (u + v); return 1; } if ( dcmp(u) ) return 0; if ( dcmp(cross(p3, p4, p1)) ) return 0; return -1;}int SegmentInter(cpoint p1, cpoint p2, cpoint p3, cpoint p4, cpoint &cp) { int ret = LineInter(p1, p2, p3, p4, cp); if (ret == 1) return PointonSegment(cp, p1, p2) && PointonSegment(cp, p3, p4); if (ret == -1 && (PointonSegment(p1, p3, p4) || PointonSegment(p2, p3, p4) || PointonSegment(p3, p1, p2) || PointonSegment(p4, p1, p2) )) return -1; return 0;}bool cmp(const cpoint &u, const cpoint &v) { return dcmp( fabs(u.x - bp.x) + fabs(u.y - bp.y) - fabs(v.x - bp.x) - fabs(v.y - bp.y)) < 0;}bool check(cpoint u, cpoint v, poly ply[], int id) { int i, k, d1, d2, wn = 0; cpoint cp, *p1, *p2 = ply[id].cp; cp.x = (u.x + v.x) / 2; cp.y = (u.y + v.y) / 2; for (i = 0; i < ply[id].n; ++i) { p1 = p2++; if (PointonSegment(cp, *p1, *p2)) { int chk = dcmp(u.x - v.x) * dcmp(p1->x - p2->x); if (chk == 0) chk = dcmp(u.y - v.y) * dcmp(p1->y - p2->y); if (chk == -1) return 0; return vis[id][i]; } k = dcmp( cross(*p1, *p2, cp) ); d1 = dcmp( p1->y - cp.y ); d2 = dcmp( p2->y - cp.y ); if (k > 0 && d1 <= 0 && d2 > 0) wn++; if (k < 0 && d2 <= 0 && d1 > 0) wn--; } return wn != 0;}double PolyUnion(poly ply[], int &n) { double ans = 0; int i, j, k, vi, vj, tn = n; n = 0; cpoint cp, p1, p2; memset(vis, 0, sizeof(vis)); for (i = 0; i < tn; ++i) { if (dcmp(cross(ply[i][0], ply[i][1], ply[i][2])) <= 0) continue; ply[i][ply[i].n] = ply[i][0]; ply[n++] = ply[i]; } for (i = 0; i < n; ++i) { for (vi = 0; vi < ply[i].n; ++vi) { tp[0] = p1 = bp = ply[i][vi]; tp[1] = p2 = ply[i][vi + 1]; tn = 2; for (j = 0; j < n; ++j) if (i != j) for (vj = 0; vj < ply[j].n; ++vj) if (SegmentInter(p1, p2, ply[j][vj], ply[j][vj + 1], cp) == 1) tp[tn++] = cp; sort(tp, tp + tn, cmp); tn = unique(tp, tp + tn) - tp; for (k = 1; k < tn; ++k) { for (j = 0; j < n; ++j) if (i != j) if (check(tp[k - 1], tp[k], ply, j)) break; if (j == n) ans += tp[k - 1].x * tp[k].y - tp[k - 1].y * tp[k].x; } vis[i][vi] = 1; } } return ans / 2;}double dissqr(cpoint u, cpoint v) { return sqr(u.x - v.x) + sqr(u.y - v.y);}int PolarCmp(const cpoint &p1, const cpoint &p2) { int u = dcmp(cross(bp, p1, p2)); return u > 0 || (u == 0 && dcmp(dissqr(bp, p1)-dissqr(bp, p2)) < 0);}void graham(cpoint pin[], int n, cpoint ch[], int &m) { int i, j, k, u, v; memcpy(ch, pin, n * sizeof(cpoint)); for (i = k = 0; i < n; ++i) { u = dcmp(ch[i].x - ch[k].x); v = dcmp(ch[i].y - ch[k].y); if (v < 0 || (v == 0 && u < 0)) k = i; } bp = ch[k]; sort(ch, ch + n, PolarCmp); n = unique(ch, ch + n) - ch; if (n <= 1) { m = n; return ;} if (dcmp(cross(ch[0], ch[1], ch[n - 1])) == 0) { m = 2; ch[1] = ch[n - 1]; return; } ch[n++] = ch[0]; for (i = 1, j = 2; j < n; ++j) { while (i > 0 && dcmp(cross(ch[i - 1], ch[i], ch[j])) <= 0) i--; ch[++i] = ch[j]; } m = i;}void solve(int cas) { double h, x, y, bh; scanf("%lf%lf%lf", &h, &x, &y); int m; n = n2 = 0; scanf("%d", &m); cpoint a[5], tmp[20]; double ans = 0; for (int i = 0; i < m; ++i) { for (int j = 0; j < 3; ++j) a[j].get(); scanf("%lf", &bh); bool flag = false; for (int j = 0; j < 3; ++j) { if (dcmp(dot(a[j], a[(j + 1) % 3], a[(j + 2) % 3])) == 0) { swap(a[j], a[1]); a[3].x = a[0].x + a[2].x - a[1].x; a[3].y = a[0].y + a[2].y - a[1].y; flag = true; break; } } if (dcmp(cross(a[0], a[1], a[2])) < 0) reverse(a, a + 4); a[4] = a[0]; int tn = 0; for (int j = 0; j < 4; ++j) { tmp[tn++] = a[j]; tmp[tn++] = cpoint(a[j].x + x * bh / h, a[j].y + y * bh / h); } graham(tmp, tn, ply[n].cp, ply[n].n); n++; ans -= fabs(cross(a[0], a[1], a[2])); } ans += PolyUnion(ply, n); printf("Case %d: %.3lfn", cas, ans);}int main() { int cas; scanf("%d", &cas); for (int i = 1; i <= cas; ++i) { solve(i); } return 0;}
