/* -*- coding: utf-8 -*- * * 132.cc: No.132 点と平面との距離 - yukicoder */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; /* constant */ const int MAX_N = 300; /* typedef */ template struct Pt3d { T x, y, z; Pt3d() {} Pt3d(T _x, T _y, T _z) : x(_x), y(_y), z(_z) {} Pt3d(const Pt3d& pt) : x(pt.x), y(pt.y), z(pt.z) {} bool operator==(const Pt3d pt) const { return x == pt.x && y == pt.y && z == pt.z; } Pt3d operator+(const Pt3d pt) const { return Pt3d(x + pt.x, y + pt.y, z + pt.z); } Pt3d operator-() const { return Pt3d(-x, -y, -z); } Pt3d operator-(const Pt3d pt) const { return Pt3d(x - pt.x, y - pt.y, z - pt.z); } Pt3d operator*(T t) const { return Pt3d(x * t, y * t, z * t); } Pt3d operator/(T t) const { return Pt3d(x / t, y / t, z / t); } T dot(Pt3d v) const { return x * v.x + y * v.y + z * v.z; } Pt3d cross(Pt3d v) const { return Pt3d(y * v.z - z * v.y, z * v.x - x * v.z, x * v.y - y * v.x); } Pt3d mid(const Pt3d pt) { return Pt3d((x + pt.x) / 2, (y + pt.y) / 2, (z + pt.z) / 2); } T d2() { return x * x + y * y + z * z; } double d() { return sqrt(d2()); } }; typedef Pt3d pt3d; /* global variables */ pt3d p, qs[MAX_N]; /* subroutines */ /* main */ int main() { int n; cin >> n; cin >> p.x >> p.y >> p.z; for (int i = 0; i < n; i++) cin >> qs[i].x >> qs[i].y >> qs[i].z; double sum = 0.0; for (int i = 0; i < n; i++) { pt3d &q0 = qs[i]; for (int j = i + 1; j < n; j++) { pt3d &q1 = qs[j]; pt3d v1 = q1 - q0; for (int k = j + 1; k < n; k++) { pt3d &q2 = qs[k]; pt3d v2 = q2 - q0; pt3d nv = v1.cross(v2); double d = abs((p - q0).dot(nv)) / nv.d(); sum += d; } } } printf("%.11lf\n", sum); return 0; }