#include #define VARNAME(x) #x #define show(x) cerr << #x << " = " << x << endl using namespace std; using ll = long long; using ld = long double; template ostream& operator<<(ostream& os, const vector& v) { os << "sz:" << v.size() << "\n["; for (const auto& p : v) { os << p << ","; } os << "]\n"; return os; } template ostream& operator<<(ostream& os, const pair& p) { os << "(" << p.first << "," << p.second << ")"; return os; } constexpr ll MOD = (ll)1e9 + 7LL; constexpr ld PI = static_cast(3.1415926535898); template constexpr T INF = numeric_limits::max() / 10; struct Vec { Vec() : dx{0}, dy{0} {} Vec(const ld dx, const ld dy) : dx{dx}, dy{dy} {} ld dx; ld dy; Vec rotate(const ld theta) const { Vec ans; ans.dx = cos(theta) * dx - sin(theta) * dy; ans.dy = sin(theta) * dx + cos(theta) * dy; return ans; } Vec operator*(const ld x) const { Vec ans = *this; ans.dx *= x; ans.dy *= x; return ans; } ld norm() const { return hypot(dx, dy); } void normalize() { const ld n = norm(); dx /= n; dy /= n; } }; ostream& operator<<(ostream& os, const Vec& v) { os << "(" << v.dx << "," << v.dy << ")"; return os; } //#define LOCAL_DEBUG 1 int main() { int N; cin >> N; for (int q = 0; q < N; q++) { int T; cin >> T; ld p, omega, v, gx, gy; cin >> p >> omega >> v >> gx >> gy; const ld l = hypot(omega, (ld)(1 + v)); const ld theta = (1 + v > 0 ? atan(omega / (1 + v)) : PI + atan(omega / (1 + v))); Vec g{gx - pow(l, T) * cos(T * theta), gy - pow(l, T) * sin(T * theta)}; ld F = 0; for (int i = 0; i < T; i++) { if (l < 1) { F += pow(l, 2 * T - 2 - 2 * i); } else { F += pow(l, 2 * i); } } ld sum = 0; vector u(T); for (int i = 0; i < T; i++) { const Vec v = g.rotate((i + 1 - T) * theta) * (pow(l, T - 1 - i) / F); u[i] = v; sum += v.norm() * v.norm(); cout << v.dx << " " << v.dy << endl; } assert(sum < p); #ifdef LOCAL_DEBUG ld xpos = 1; ld ypos = 0; const string name = "data_" + to_string(T) + "_" + to_string(p) + "_" + to_string(omega) + "_" + to_string(v) + "_" + to_string(gx) + "_" + to_string(gy); ofstream fout(name); fout << fixed << setprecision(15) << xpos << " " << ypos << endl; for (int i = 0; i < T; i++) { ld x = xpos * (1 + v) - ypos * omega + u[i].dx; ld y = ypos * (1 + v) + xpos * omega + u[i].dy; fout << x << " " << y << endl; xpos = x; ypos = y; } cerr << "# result #" << endl; cerr << gx << " " << gy << endl; cerr << xpos << " " << ypos << endl; fout.close(); FILE* fp = popen("gnuplot -persist", "w"); if (not fp) { cerr << "udwiqhduqdhwiodhqoidw" << endl; } else { fprintf(fp, "set terminal png\n"); fprintf(fp, "set output \"%s.png\"\n", name.c_str()); fprintf(fp, "plot \"%s\" w lp\n", name.c_str()); fflush(fp); fclose(fp); } #endif } return 0; }