#include #define VARNAME(x) #x #define show(x) cerr << #x << " = " << x << endl //#define QUADRA 1 using namespace std; using ll = long long; #ifdef QUADRA using ld = __float128; #else using ld = long double; #endif 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(3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303); 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; #ifdef QUADRA ans.dx = cosq(theta) * dx - sinq(theta) * dy; ans.dy = sinq(theta) * dx + cosq(theta) * dy; #else ans.dx = cos(theta) * dx - sin(theta) * dy; ans.dy = sin(theta) * dx + cos(theta) * dy; #endif return ans; } Vec operator*(const ld x) const { Vec ans = *this; ans.dx *= x; ans.dy *= x; return ans; } ld norm() const { #ifdef QUADRA return hypotq(dx, dy); #else return hypot(dx, dy); #endif } void normalize() { const ld n = norm(); dx /= n; dy /= n; } }; ostream& operator<<(ostream& os, const Vec& v) { os << "(" << v.dx << "," << v.dy << ")"; return os; } ld power(const ld p, const int n) { assert(n >= 0); if (n == 0) { return 1; } if (n % 2 == 1) { return power(p, n - 1) * p; } else { const ld pp = power(p, n / 2); return pp * pp; } } //#define LOCAL_DEBUG 1 int main() { int N; cin >> N; for (int q = 0; q < N; q++) { int T; cin >> T; long double p_, omega_, v_, gx_, gy_; cin >> p_ >> omega_ >> v_ >> gx_ >> gy_; const ld p = p_; const ld omega = omega_; const ld v = v_; const ld gx = gx_; const ld gy = gy_; #ifdef QUADRA const ld l = hypotq(omega, (ld)(1 + v)); const ld theta = (1 + v > 0 ? atanq(omega / (1 + v)) : PI + atanq(omega / (1 + v))); Vec g{gx - power(l, T) * cosq(theta * T), gy - power(l, T) * sinq(theta * T)}; #else 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 - power(l, T) * cos((ld)T * theta), gy - power(l, T) * sin((ld)T * theta)}; #endif ld F = 0; for (int i = 0; i < T; i++) { if (l < 1) { F += power(l, 2 * T - 2 - 2 * i); } else { F += power(l, 2 * i); } } ld sum = 0; vector u(T); for (int i = 0; i < T; i++) { const Vec v = g.rotate(theta * (ld)(i + 1 - T)) * (power(l, T - 1 - i) / F); u[i] = v; sum += v.norm() * v.norm(); cout << fixed << setprecision(50) << (long double)v.dx << " " << (long double)v.dy << endl; } #ifdef LOCAL_DEBUG cerr << "# HP #" << endl; cerr << fixed << setprecision(30) << (long double)p << endl; cerr << "# used #" << endl; cerr << fixed << setprecision(30) << (long double)sum << endl; ld xpos = 1; ld ypos = 0; 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; xpos = x; ypos = y; } cerr << "# actual goal#" << endl; cerr << fixed << setprecision(30) << (long double)gx << " " << (long double)gy << endl; cerr << "# result #" << endl; cerr << fixed << setprecision(30) << (long double)xpos << " " << (long double)ypos << endl; #endif } return 0; }