This documentation is automatically generated by online-judge-tools/verification-helper
#include "geo/outcircle.hpp"
#pragma once
#include "geo/base.hpp"
#include "geo/triangle_area.hpp"
template <typename REAL, typename T>
Circle<REAL> outcircle(Point<T> A, Point<T> B, Point<T> C) {
REAL b1 = B.x - A.x, b2 = B.y - A.y;
REAL c1 = C.x - A.x, c2 = C.y - A.y;
REAL bb = (b1 * b1 + b2 * b2) / 2;
REAL cc = (c1 * c1 + c2 * c2) / 2;
REAL det = b1 * c2 - b2 * c1;
REAL x = (bb * c2 - b2 * cc) / det;
REAL y = (b1 * cc - bb * c1) / det;
REAL r = sqrt(x * x + y * y);
x += A.x, y += A.y;
return Circle<REAL>(x, y, r);
}
// ABC の外接円に対して内外どちらにあるか
// 中:1, 境界:0, 外:-1
// 座標の 4 乗がオーバーフローしないようにする
template <typename T>
int outcircle_side(Point<T> A, Point<T> B, Point<T> C, Point<T> p) {
T d = (B - A).det(C - A);
assert(d != 0);
if (d < 0) swap(B, C);
array<Point<T>, 3> pts = {A, B, C};
array<array<T, 3>, 3> mat;
FOR(i, 3) {
T dx = pts[i].x - p.x, dy = pts[i].y - p.y;
mat[i][0] = dx, mat[i][1] = dy, mat[i][2] = dx * dx + dy * dy;
}
T det = 0;
det += mat[0][0] * (mat[1][1] * mat[2][2] - mat[1][2] * mat[2][1]);
det += mat[0][1] * (mat[1][2] * mat[2][0] - mat[1][0] * mat[2][2]);
det += mat[0][2] * (mat[1][0] * mat[2][1] - mat[1][1] * mat[2][0]);
if (det == 0) return 0;
return (det > 0 ? 1 : -1);
}
#line 2 "geo/base.hpp"
template <typename T>
struct Point {
T x, y;
Point() : x(0), y(0) {}
template <typename A, typename B>
Point(A x, B y) : x(x), y(y) {}
template <typename A, typename B>
Point(pair<A, B> p) : x(p.fi), y(p.se) {}
Point operator+=(const Point p) {
x += p.x, y += p.y;
return *this;
}
Point operator-=(const Point p) {
x -= p.x, y -= p.y;
return *this;
}
Point operator+(Point p) const { return {x + p.x, y + p.y}; }
Point operator-(Point p) const { return {x - p.x, y - p.y}; }
bool operator==(Point p) const { return x == p.x && y == p.y; }
bool operator!=(Point p) const { return x != p.x || y != p.y; }
Point operator-() const { return {-x, -y}; }
Point operator*(T t) const { return {x * t, y * t}; }
Point operator/(T t) const { return {x / t, y / t}; }
bool operator<(Point p) const {
if (x != p.x) return x < p.x;
return y < p.y;
}
T dot(const Point& other) const { return x * other.x + y * other.y; }
T det(const Point& other) const { return x * other.y - y * other.x; }
double norm() { return sqrtl(x * x + y * y); }
double angle() { return atan2(y, x); }
Point rotate(double theta) {
static_assert(!is_integral<T>::value);
double c = cos(theta), s = sin(theta);
return Point{c * x - s * y, s * x + c * y};
}
Point rot90(bool ccw) { return (ccw ? Point{-y, x} : Point{y, -x}); }
};
#ifdef FASTIO
template <typename T>
void rd(Point<T>& p) {
fastio::rd(p.x), fastio::rd(p.y);
}
template <typename T>
void wt(Point<T>& p) {
fastio::wt(p.x);
fastio::wt(' ');
fastio::wt(p.y);
}
#endif
// A -> B -> C と進むときに、左に曲がるならば +1、右に曲がるならば -1
template <typename T>
int ccw(Point<T> A, Point<T> B, Point<T> C) {
T x = (B - A).det(C - A);
if (x > 0) return 1;
if (x < 0) return -1;
return 0;
}
template <typename REAL, typename T, typename U>
REAL dist(Point<T> A, Point<U> B) {
REAL dx = REAL(A.x) - REAL(B.x);
REAL dy = REAL(A.y) - REAL(B.y);
return sqrt(dx * dx + dy * dy);
}
// ax+by+c
template <typename T>
struct Line {
T a, b, c;
Line(T a, T b, T c) : a(a), b(b), c(c) {}
Line(Point<T> A, Point<T> B) { a = A.y - B.y, b = B.x - A.x, c = A.x * B.y - A.y * B.x; }
Line(T x1, T y1, T x2, T y2) : Line(Point<T>(x1, y1), Point<T>(x2, y2)) {}
template <typename U>
U eval(Point<U> P) {
return a * P.x + b * P.y + c;
}
template <typename U>
T eval(U x, U y) {
return a * x + b * y + c;
}
// 同じ直線が同じ a,b,c で表現されるようにする
void normalize() {
static_assert(is_same_v<T, int> || is_same_v<T, long long>);
T g = gcd(gcd(abs(a), abs(b)), abs(c));
a /= g, b /= g, c /= g;
if (b < 0) { a = -a, b = -b, c = -c; }
if (b == 0 && a < 0) { a = -a, b = -b, c = -c; }
}
bool is_parallel(Line other) { return a * other.b - b * other.a == 0; }
bool is_orthogonal(Line other) { return a * other.a + b * other.b == 0; }
};
template <typename T>
struct Segment {
Point<T> A, B;
Segment(Point<T> A, Point<T> B) : A(A), B(B) {}
Segment(T x1, T y1, T x2, T y2) : Segment(Point<T>(x1, y1), Point<T>(x2, y2)) {}
bool contain(Point<T> C) {
T det = (C - A).det(B - A);
if (det != 0) return 0;
return (C - A).dot(B - A) >= 0 && (C - B).dot(A - B) >= 0;
}
Line<T> to_Line() { return Line(A, B); }
};
template <typename REAL>
struct Circle {
Point<REAL> O;
REAL r;
Circle(Point<REAL> O, REAL r) : O(O), r(r) {}
Circle(REAL x, REAL y, REAL r) : O(x, y), r(r) {}
template <typename T>
bool contain(Point<T> p) {
REAL dx = p.x - O.x, dy = p.y - O.y;
return dx * dx + dy * dy <= r * r;
}
};
#line 1 "geo/triangle_area.hpp"
template <typename REAL, typename T>
REAL triangle_area(Point<T> A, Point<T> B, Point<T> C) {
return abs((B - A).det(C - A)) * 0.5;
}
#line 4 "geo/outcircle.hpp"
template <typename REAL, typename T>
Circle<REAL> outcircle(Point<T> A, Point<T> B, Point<T> C) {
REAL b1 = B.x - A.x, b2 = B.y - A.y;
REAL c1 = C.x - A.x, c2 = C.y - A.y;
REAL bb = (b1 * b1 + b2 * b2) / 2;
REAL cc = (c1 * c1 + c2 * c2) / 2;
REAL det = b1 * c2 - b2 * c1;
REAL x = (bb * c2 - b2 * cc) / det;
REAL y = (b1 * cc - bb * c1) / det;
REAL r = sqrt(x * x + y * y);
x += A.x, y += A.y;
return Circle<REAL>(x, y, r);
}
// ABC の外接円に対して内外どちらにあるか
// 中:1, 境界:0, 外:-1
// 座標の 4 乗がオーバーフローしないようにする
template <typename T>
int outcircle_side(Point<T> A, Point<T> B, Point<T> C, Point<T> p) {
T d = (B - A).det(C - A);
assert(d != 0);
if (d < 0) swap(B, C);
array<Point<T>, 3> pts = {A, B, C};
array<array<T, 3>, 3> mat;
FOR(i, 3) {
T dx = pts[i].x - p.x, dy = pts[i].y - p.y;
mat[i][0] = dx, mat[i][1] = dy, mat[i][2] = dx * dx + dy * dy;
}
T det = 0;
det += mat[0][0] * (mat[1][1] * mat[2][2] - mat[1][2] * mat[2][1]);
det += mat[0][1] * (mat[1][2] * mat[2][0] - mat[1][0] * mat[2][2]);
det += mat[0][2] * (mat[1][0] * mat[2][1] - mat[1][1] * mat[2][0]);
if (det == 0) return 0;
return (det > 0 ? 1 : -1);
}