compro_library
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test/mytest/geometry/geometry.test.cpp
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- Last update: 2026-08-30 15:33:14+09:00
- Problem: https://judge.yosupo.jp/problem/aplusb
Depends on
- geometry/base.hpp
- geometry/ccw.hpp
- geometry/circle.hpp
- geometry/convex-cut.hpp
- geometry/convex-hull.hpp
- geometry/cross-point.hpp
- geometry/cross.hpp
- geometry/degree-to-radian.hpp
- geometry/distance-between-line-and-point.hpp
- geometry/distance-between-segment-and-point.hpp
- geometry/distance-between-segments.hpp
- geometry/dot.hpp
- geometry/is-contained.hpp
- geometry/is-convex.hpp
- geometry/is-in-circle.hpp
- geometry/is-intersect.hpp
- geometry/is-orthogonal.hpp
- geometry/is-parallel.hpp
- geometry/is-point-on-line.hpp
- geometry/is-point-on-segment.hpp
- geometry/line.hpp
- geometry/normal-vector.hpp
- geometry/polygon-area.hpp
- geometry/projection.hpp
- geometry/radian-to-degree.hpp
- geometry/reflection.hpp
- geometry/rotate.hpp
- geometry/segment.hpp
- geometry/tangent-to-circle.hpp
- geometry/tangent.hpp
- geometry/unit-vector.hpp
- template/template.cpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "../../../template/template.cpp"
#include "../../../geometry/ccw.hpp"
#include "../../../geometry/convex-cut.hpp"
#include "../../../geometry/convex-hull.hpp"
#include "../../../geometry/degree-to-radian.hpp"
#include "../../../geometry/distance-between-segments.hpp"
#include "../../../geometry/is-contained.hpp"
#include "../../../geometry/is-convex.hpp"
#include "../../../geometry/is-in-circle.hpp"
#include "../../../geometry/is-orthogonal.hpp"
#include "../../../geometry/is-point-on-line.hpp"
#include "../../../geometry/is-point-on-segment.hpp"
#include "../../../geometry/normal-vector.hpp"
#include "../../../geometry/polygon-area.hpp"
#include "../../../geometry/radian-to-degree.hpp"
#include "../../../geometry/reflection.hpp"
#include "../../../geometry/tangent-to-circle.hpp"
#include "../../../geometry/tangent.hpp"
using namespace geometry;
void geometry_test() {
Point origin(0, 0), x(1, 0), y(0, 1);
assert(equal(dot(x, y), 0));
assert(equal(cross(x, y), 1));
assert(equal(std::abs(unitVector(Point(3, 4))), 1));
assert(normalVector(x) == y);
assert(std::abs(rotate(x, PI / 2) - y) < EPS);
assert(equal(radianToDegree(degreeToRadian(90)), 90));
assert(ccw(origin, x, y) == 1);
Line horizontal(origin, x), vertical(origin, y);
Segment horizontal_segment(origin, Point(2, 0));
Circle unit_circle(origin, 1);
assert(isOrthogonal(horizontal, vertical));
assert(isParallel(horizontal, Line(Point(0, 1), Point(1, 1))));
assert(isPointOnLine(origin, x, Point(2, 0)));
assert(isPointOnSegment(origin, Point(2, 0), x));
assert(equal(distanceBetweenLineAndPoint(horizontal, y), 1));
assert(equal(distanceBetweenSegmentAndPoint(horizontal_segment, Point(3, 0)), 1));
assert(crossPoint(horizontal, vertical) == origin);
assert(isIntersect(horizontal_segment, Segment(Point(1, -1), Point(1, 1)), true));
assert(equal(distanceBetweenSegments(horizontal_segment,
Segment(Point(3, 0), Point(4, 0))),
1));
assert(projection(horizontal, y) == origin);
assert(reflection(horizontal, y) == Point(0, -1));
assert(isIntersect(unit_circle, Circle(Point(2, 0), 1)) == 3);
assert(crossPoint(unit_circle, Circle(Point(2, 0), 1)).size() == 1);
assert(crossPoint(unit_circle, horizontal).size() == 2);
assert(isInCircle(unit_circle, origin));
assert(tangentToCircle(Point(2, 0), unit_circle).size() == 2);
assert(tangent(unit_circle, Circle(Point(4, 0), 1)).size() == 4);
std::vector<Point> triangle = {origin, x, y};
assert(equal(PolygonArea(triangle), 0.5));
assert(isConvex(triangle));
assert(ConvexHull(triangle).size() == 3);
assert(isContained(triangle, Point(0.1, 0.1)) == 2);
assert(!ConvexCut(triangle, Line(Point(0.5, -1), Point(0.5, 1))).empty());
}
int main() {
geometry_test();
INT(a, b);
print(a + b);
}#line 1 "test/mytest/geometry/geometry.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "template/template.cpp"
#pragma region Macros
#include <bits/stdc++.h>
using namespace std;
// input output utils
namespace siro53_io {
// https://maspypy.github.io/library/other/io_old.hpp
struct has_val_impl {
template <class T>
static auto check(T &&x) -> decltype(x.val(), std::true_type{});
template <class T> static auto check(...) -> std::false_type;
};
template <class T>
class has_val : public decltype(has_val_impl::check<T>(std::declval<T>())) {
};
// debug
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void dump(const T t) {
cerr << t;
}
template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
void dump(const T t) {
cerr << t;
}
template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
void dump(const T &t) {
cerr << t.val();
}
void dump(__int128_t n) {
if(n == 0) {
cerr << '0';
return;
} else if(n < 0) {
cerr << '-';
n = -n;
}
string s;
while(n > 0) {
s += (char)('0' + n % 10);
n /= 10;
}
reverse(s.begin(), s.end());
cerr << s;
}
void dump(const string &s) { cerr << s; }
void dump(const char *s) {
int n = (int)strlen(s);
for(int i = 0; i < n; i++) cerr << s[i];
}
template <class T1, class T2> void dump(const pair<T1, T2> &p) {
cerr << '(';
dump(p.first);
cerr << ',';
dump(p.second);
cerr << ')';
}
template <class T> void dump(const vector<T> &v) {
cerr << '{';
for(int i = 0; i < (int)v.size(); i++) {
dump(v[i]);
if(i < (int)v.size() - 1) cerr << ',';
}
cerr << '}';
}
template <class T> void dump(const set<T> &s) {
cerr << '{';
for(auto it = s.begin(); it != s.end(); it++) {
dump(*it);
if(next(it) != s.end()) cerr << ',';
}
cerr << '}';
}
template <class Key, class Value> void dump(const map<Key, Value> &mp) {
cerr << '{';
for(auto it = mp.begin(); it != mp.end(); it++) {
dump(*it);
if(next(it) != mp.end()) cerr << ',';
}
cerr << '}';
}
template <class Key, class Value>
void dump(const unordered_map<Key, Value> &mp) {
cerr << '{';
for(auto it = mp.begin(); it != mp.end(); it++) {
dump(*it);
if(next(it) != mp.end()) cerr << ',';
}
cerr << '}';
}
template <class T> void dump(const deque<T> &v) {
cerr << '{';
for(int i = 0; i < (int)v.size(); i++) {
dump(v[i]);
if(i < (int)v.size() - 1) cerr << ',';
}
cerr << '}';
}
template <class T> void dump(queue<T> q) {
cerr << '{';
while(!q.empty()) {
dump(q.front());
if((int)q.size() > 1) cerr << ',';
q.pop();
}
cerr << '}';
}
void debug_print() { cerr << endl; }
template <class Head, class... Tail>
void debug_print(const Head &h, const Tail &...t) {
dump(h);
if(sizeof...(Tail)) dump(' ');
debug_print(t...);
}
// print
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void print_single(const T t) {
cout << t;
}
template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
void print_single(const T t) {
cout << t;
}
template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
void print_single(const T t) {
cout << t.val();
}
void print_single(__int128_t n) {
if(n == 0) {
cout << '0';
return;
} else if(n < 0) {
cout << '-';
n = -n;
}
string s;
while(n > 0) {
s += (char)('0' + n % 10);
n /= 10;
}
reverse(s.begin(), s.end());
cout << s;
}
void print_single(const string &s) { cout << s; }
void print_single(const char *s) {
int n = (int)strlen(s);
for(int i = 0; i < n; i++) cout << s[i];
}
template <class T1, class T2> void print_single(const pair<T1, T2> &p) {
print_single(p.first);
cout << ' ';
print_single(p.second);
}
template <class T> void print_single(const vector<T> &v) {
for(int i = 0; i < (int)v.size(); i++) {
print_single(v[i]);
if(i < (int)v.size() - 1) cout << ' ';
}
}
template <class T> void print_single(const set<T> &s) {
for(auto it = s.begin(); it != s.end(); it++) {
print_single(*it);
if(next(it) != s.end()) cout << ' ';
}
}
template <class T> void print_single(const deque<T> &v) {
for(int i = 0; i < (int)v.size(); i++) {
print_single(v[i]);
if(i < (int)v.size() - 1) cout << ' ';
}
}
template <class T> void print_single(queue<T> q) {
while(!q.empty()) {
print_single(q.front());
if((int)q.size() > 1) cout << ' ';
q.pop();
}
}
void print() { cout << '\n'; }
template <class Head, class... Tail>
void print(const Head &h, const Tail &...t) {
print_single(h);
if(sizeof...(Tail)) print_single(' ');
print(t...);
}
// input
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void input_single(T &t) {
cin >> t;
}
template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
void input_single(T &t) {
cin >> t;
}
template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
void input_single(T &t) {
cin >> t;
}
void input_single(__int128_t &n) {
string s;
cin >> s;
if(s == "0") {
n = 0;
return;
}
bool is_minus = false;
if(s[0] == '-') {
s = s.substr(1);
is_minus = true;
}
n = 0;
for(int i = 0; i < (int)s.size(); i++) n = n * 10 + (int)(s[i] - '0');
if(is_minus) n = -n;
}
void input_single(string &s) { cin >> s; }
template <class T1, class T2> void input_single(pair<T1, T2> &p) {
input_single(p.first);
input_single(p.second);
}
template <class T> void input_single(vector<T> &v) {
for(auto &e : v) input_single(e);
}
void input() {}
template <class Head, class... Tail> void input(Head &h, Tail &...t) {
input_single(h);
input(t...);
}
}; // namespace siro53_io
#ifdef DEBUG
#define debug(...) \
cerr << __LINE__ << " [" << #__VA_ARGS__ << "]: ", debug_print(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif
// io setup
struct Setup {
Setup() {
cin.tie(0);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
}
} __Setup;
using namespace siro53_io;
// types
using ll = long long;
using i128 = __int128_t;
// input macros
#define INT(...) \
int __VA_ARGS__; \
input(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
input(__VA_ARGS__)
#define STRING(...) \
string __VA_ARGS__; \
input(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
input(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
input(__VA_ARGS__)
#define LD(...) \
long double __VA_ARGS__; \
input(__VA_ARGS__)
#define UINT(...) \
unsigned int __VA_ARGS__; \
input(__VA_ARGS__)
#define ULL(...) \
unsigned long long __VA_ARGS__; \
input(__VA_ARGS__)
#define VEC(name, type, len) \
vector<type> name(len); \
input(name);
#define VEC2(name, type, len1, len2) \
vector name(len1, vector<type>(len2)); \
input(name);
// other macros
// https://trap.jp/post/1224/
#define OVERLOAD3(_1, _2, _3, name, ...) name
#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()
#define REP1(i, n) for(int i = 0; i < int(n); i++)
#define REP2(i, a, b) for(int i = (a); i < int(b); i++)
#define REP(...) OVERLOAD3(__VA_ARGS__, REP2, REP1)(__VA_ARGS__)
#define SORT(v) sort(ALL(v))
#define RSORT(v) sort(RALL(v))
#define UNIQUE(v) \
sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()), v.shrink_to_fit()
#define REV(v) reverse(ALL(v))
#define SZ(v) ((int)(v).size())
#define MIN(v) (*min_element(ALL(v)))
#define MAX(v) (*max_element(ALL(v)))
// util const
const int INF = 1 << 30;
const ll LLINF = 1LL << 60;
constexpr int MOD = 1000000007;
constexpr int MOD2 = 998244353;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
// util functions
void Case(int i) { cout << "Case #" << i << ": "; }
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
template <class T> inline bool chmax(T &a, T b) {
return (a < b ? a = b, true : false);
}
template <class T> inline bool chmin(T &a, T b) {
return (a > b ? a = b, true : false);
}
template <class T, int dim>
auto make_vector_impl(vector<int>& sizes, const T &e) {
if constexpr(dim == 1) {
return vector(sizes[0], e);
} else {
int n = sizes[dim - 1];
sizes.pop_back();
return vector(n, make_vector_impl<T, dim - 1>(sizes, e));
}
}
template <class T, int dim>
auto make_vector(const int (&sizes)[dim], const T &e = T()) {
vector<int> s(dim);
for(int i = 0; i < dim; i++) s[i] = sizes[dim - i - 1];
return make_vector_impl<T, dim>(s, e);
}
vector<int> iota_gen(int n, int start = 0) {
vector<int> ord(n);
iota(ord.begin(), ord.end(), start);
return ord;
}
template<typename T>
vector<int> ord_sort(const vector<T>& v, bool greater = false) {
auto ord = iota_gen((int)v.size());
sort(ALL(ord), [&](int i, int j) {
if(greater) return v[i] > v[j];
return v[i] < v[j];
});
return ord;
}
#pragma endregion Macros
#line 3 "test/mytest/geometry/geometry.test.cpp"
#line 2 "geometry/ccw.hpp"
#line 2 "geometry/cross.hpp"
#line 2 "geometry/base.hpp"
#line 5 "geometry/base.hpp"
namespace geometry {
// Point : 複素数型を位置ベクトルとして扱う
// 実軸(real)をx軸、挙軸(imag)をy軸として見る
using D = long double;
using Point = std::complex<D>;
const D EPS = 1e-7;
const D PI = std::acos(D(-1));
inline bool equal(const D &a, const D &b) { return std::fabs(a - b) < EPS; }
} // namespace geometry
#line 4 "geometry/cross.hpp"
namespace geometry {
// 外積(cross product) : a×b = |a||b|sinΘ
inline D cross(const Point &a, const Point &b) {
return (a.real() * b.imag() - a.imag() * b.real());
}
} // namespace geometry
#line 2 "geometry/dot.hpp"
#line 4 "geometry/dot.hpp"
namespace geometry {
// 内積(dot product) : a・b = |a||b|cosΘ
inline D dot(const Point &a, const Point &b) {
return (a.real() * b.real() + a.imag() * b.imag());
}
} // namespace geometry
#line 5 "geometry/ccw.hpp"
namespace geometry {
// 点の回転方向
// 点a, b, cの位置関係について(aが基準点)
inline int ccw(const Point &a, Point b, Point c) {
b -= a, c -= a;
// 点a, b, c が
// 反時計回りの時、
if(cross(b, c) > EPS) return 1;
// 時計回りの時、
if(cross(b, c) < -EPS) return -1;
// c, a, bがこの順番で同一直線上にある時、
if(dot(b, c) < 0) return 2;
// a, b, cがこの順番で同一直線上にある場合、
if(std::norm(b) < std::norm(c)) return -2;
// cが線分ab上にある場合、
return 0;
}
} // namespace geometry
#line 2 "geometry/convex-cut.hpp"
#line 4 "geometry/convex-cut.hpp"
#line 2 "geometry/cross-point.hpp"
#line 5 "geometry/cross-point.hpp"
#line 2 "geometry/circle.hpp"
#line 4 "geometry/circle.hpp"
namespace geometry {
// Circle : 円を表す構造体
// pが中心の位置ベクトル、rは半径
struct Circle {
Point p;
D r;
Circle() = default;
Circle(Point p, D r) : p(p), r(r) {}
};
} // namespace geometry
#line 2 "geometry/distance-between-line-and-point.hpp"
#line 2 "geometry/line.hpp"
#line 4 "geometry/line.hpp"
namespace geometry {
// Line : 直線を表す構造体
// b - a で直線・線分を表せる
struct Line {
Point a, b;
Line() = default;
Line(Point a, Point b) : a(a), b(b) {}
// Ax+By=C
Line(D A, D B, D C) {
if(equal(A, 0)) {
a = Point(0, C / B), b = Point(1, C / B);
} else if(equal(B, 0)) {
a = Point(C / A, 0), b = Point(C / A, 1);
} else if(equal(C, 0)) {
a = Point(0, C / B), b = Point(1, (C - A) / B);
} else {
a = Point(0, C / B), b = Point(C / A, 0);
}
}
};
} // namespace geometry
#line 5 "geometry/distance-between-line-and-point.hpp"
namespace geometry {
// 直線lと点pの距離を求める
inline D distanceBetweenLineAndPoint(const Line &l, const Point &p) {
return std::abs(cross(l.b - l.a, p - l.a)) / std::abs(l.b - l.a);
}
} // namespace geometry
#line 2 "geometry/is-intersect.hpp"
#line 2 "geometry/segment.hpp"
#line 4 "geometry/segment.hpp"
namespace geometry {
// Segment : 線分を表す構造体
// Lineと同じ
struct Segment : Line {
Segment() = default;
Segment(Point a, Point b) : Line(a, b) {}
D get_dist() { return std::abs(a - b); }
};
} // namespace geometry
#line 6 "geometry/is-intersect.hpp"
namespace geometry {
// 線分sと線分tが交差しているかどうか
// bound:線分の端点を含むか
inline bool isIntersect(const Segment &s, const Segment &t, bool bound) {
return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) < bound &&
ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) < bound;
}
// 2つの円の交差判定
// 返り値は共通接線の数
inline int isIntersect(const Circle &c1, const Circle &c2) {
D d = std::abs(c1.p - c2.p);
// 2つの円が離れている場合
if(d > c1.r + c2.r + EPS) return 4;
// 外接している場合
if(equal(d, c1.r + c2.r)) return 3;
// 内接している場合
if(equal(d, std::abs(c1.r - c2.r))) return 1;
// 内包している場合
if(d < std::abs(c1.r - c2.r) - EPS) return 0;
return 2;
}
} // namespace geometry
#line 2 "geometry/projection.hpp"
#line 6 "geometry/projection.hpp"
namespace geometry {
// 射影(projection)
// 直線(線分)lに点pから引いた垂線の足を求める
inline Point projection(const Line &l, const Point &p) {
D t = dot(p - l.a, l.a - l.b) / std::norm(l.a - l.b);
return l.a + (l.a - l.b) * t;
}
inline Point projection(const Segment &l, const Point &p) {
D t = dot(p - l.a, l.a - l.b) / std::norm(l.a - l.b);
return l.a + (l.a - l.b) * t;
}
} // namespace geometry
#line 2 "geometry/unit-vector.hpp"
#line 4 "geometry/unit-vector.hpp"
namespace geometry {
// 単位ベクトル(unit vector)を求める
inline Point unitVector(const Point &a) { return a / std::abs(a); }
} // namespace geometry
#line 12 "geometry/cross-point.hpp"
namespace geometry {
// 直線s, tの交点の計算
inline Point crossPoint(const Line &s, const Line &t) {
D d1 = cross(s.b - s.a, t.b - t.a);
D d2 = cross(s.b - s.a, s.b - t.a);
if(equal(std::abs(d1), 0) && equal(std::abs(d2), 0)) return t.a;
return t.a + (t.b - t.a) * (d2 / d1);
}
// 線分s, tの交点の計算
inline Point crossPoint(const Segment &s, const Segment &t) {
return crossPoint(Line(s), Line(t));
}
// 2つの円の交点
inline std::vector<Point> crossPoint(const Circle &c1, const Circle &c2) {
std::vector<Point> res;
int mode = isIntersect(c1, c2);
// 2つの中心の距離
D d = std::abs(c1.p - c2.p);
// 2円が離れている場合
if(mode == 4) return res;
// 1つの円がもう1つの円に内包されている場合
if(mode == 0) return res;
// 2円が外接する場合
if(mode == 3) {
D t = c1.r / (c1.r + c2.r);
res.emplace_back(c1.p + (c2.p - c1.p) * t);
return res;
}
// 内接している場合
if(mode == 1) {
if(c2.r < c1.r - EPS) {
res.emplace_back(c1.p + (c2.p - c1.p) * (c1.r / d));
} else {
res.emplace_back(c2.p + (c1.p - c2.p) * (c2.r / d));
}
return res;
}
// 2円が重なる場合
D rc1 = (c1.r * c1.r + d * d - c2.r * c2.r) / (2 * d);
D rs1 = std::sqrt(c1.r * c1.r - rc1 * rc1);
if(c1.r - std::abs(rc1) < EPS) rs1 = 0;
Point e12 = (c2.p - c1.p) / std::abs(c2.p - c1.p);
res.emplace_back(c1.p + rc1 * e12 + rs1 * e12 * Point(0, 1));
res.emplace_back(c1.p + rc1 * e12 + rs1 * e12 * Point(0, -1));
return res;
}
// 円cと直線lの交点
inline std::vector<Point> crossPoint(const Circle &c, const Line &l) {
std::vector<Point> res;
D d = distanceBetweenLineAndPoint(l, c.p);
// 交点を持たない
if(d > c.r + EPS) return res;
// 接する
Point h = projection(l, c.p);
if(equal(d, c.r)) {
res.emplace_back(h);
return res;
}
Point e = unitVector(l.b - l.a);
D ph = std::sqrt(c.r * c.r - d * d);
res.emplace_back(h - e * ph);
res.emplace_back(h + e * ph);
return res;
}
} // namespace geometry
#line 7 "geometry/convex-cut.hpp"
namespace geometry {
// 凸多角形pを直線lで切断し、その左側を返す
inline std::vector<Point> ConvexCut(std::vector<Point> p, Line l) {
std::vector<Point> ret;
int sz = (int)p.size();
for(int i = 0; i < sz; i++) {
Point now = p[i];
Point nxt = p[i == sz - 1 ? 0 : i + 1];
if(ccw(l.a, l.b, now) != -1) ret.emplace_back(now);
if(ccw(l.a, l.b, now) * ccw(l.a, l.b, nxt) < 0) {
ret.emplace_back(crossPoint(Line(now, nxt), l));
}
}
return ret;
}
} // namespace geometry
#line 2 "geometry/convex-hull.hpp"
#line 5 "geometry/convex-hull.hpp"
#line 7 "geometry/convex-hull.hpp"
namespace geometry {
// 凸包 O(NlogN)
inline std::vector<Point> ConvexHull(std::vector<Point> p) {
int n = (int)p.size(), k = 0;
std::sort(p.begin(), p.end(), [](const Point &a, const Point &b) {
return (a.real() != b.real() ? a.real() < b.real()
: a.imag() < b.imag());
});
std::vector<Point> ch(2 * n);
// 一直線上の3点を含める -> (< -EPS)
// 含め無い -> (< EPS)
for(int i = 0; i < n; ch[k++] = p[i++]) { // lower
while(k >= 2 &&
cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < EPS)
--k;
}
for(int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) { // upper
while(k >= t &&
cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < EPS)
--k;
}
ch.resize(k - 1);
return ch;
}
} // namespace geometry
#line 2 "geometry/degree-to-radian.hpp"
#line 4 "geometry/degree-to-radian.hpp"
namespace geometry {
// 度->ラジアン
inline D degreeToRadian(const D °ree) { return degree * PI / 180.0; }
} // namespace geometry
#line 2 "geometry/distance-between-segments.hpp"
#line 4 "geometry/distance-between-segments.hpp"
#line 2 "geometry/distance-between-segment-and-point.hpp"
#line 6 "geometry/distance-between-segment-and-point.hpp"
namespace geometry {
// 線分lと点pの距離を求める
// 定義：点pから「線分lのどこか」への最短距離
inline D distanceBetweenSegmentAndPoint(const Segment &l, const Point &p) {
if(dot(l.b - l.a, p - l.a) < EPS) return std::abs(p - l.a);
if(dot(l.a - l.b, p - l.b) < EPS) return std::abs(p - l.b);
return std::abs(cross(l.b - l.a, p - l.a)) / std::abs(l.b - l.a);
}
} // namespace geometry
#line 7 "geometry/distance-between-segments.hpp"
namespace geometry {
// 線分sとtの距離
inline D distanceBetweenSegments(const Segment &s, const Segment &t) {
if(isIntersect(s, t, 1)) return (D)(0);
D ans = distanceBetweenSegmentAndPoint(s, t.a);
ans = std::min(ans, distanceBetweenSegmentAndPoint(s, t.b));
ans = std::min(ans, distanceBetweenSegmentAndPoint(t, s.a));
ans = std::min(ans, distanceBetweenSegmentAndPoint(t, s.b));
return ans;
}
} // namespace geometry
#line 2 "geometry/is-contained.hpp"
#line 4 "geometry/is-contained.hpp"
#line 7 "geometry/is-contained.hpp"
namespace geometry {
// 多角形gに点pが含まれているか?
// 含まれる:2, 辺上にある:1, 含まれない:0
inline int isContained(const std::vector<Point> &g, const Point &p) {
bool in = false;
int n = (int)g.size();
for(int i = 0; i < n; i++) {
Point a = g[i] - p, b = g[(i + 1) % n] - p;
if(imag(a) > imag(b)) swap(a, b);
if(imag(a) <= EPS && EPS < imag(b) && cross(a, b) < -EPS) in = !in;
if(cross(a, b) == 0 && dot(a, b) <= 0) return 1;
}
return (in ? 2 : 0);
}
} // namespace geometry
#line 2 "geometry/is-convex.hpp"
#line 4 "geometry/is-convex.hpp"
#line 6 "geometry/is-convex.hpp"
namespace geometry {
// 凸多角形かどうか
inline bool isConvex(const std::vector<Point> &p) {
int n = p.size();
int now, pre, nxt;
for(int i = 0; i < n; i++) {
pre = (i - 1 + n) % n;
nxt = (i + 1) % n;
now = i;
if(ccw(p[pre], p[now], p[nxt]) == -1) return false;
}
return true;
}
} // namespace geometry
#line 2 "geometry/is-in-circle.hpp"
#line 4 "geometry/is-in-circle.hpp"
namespace geometry {
// 点pが円cの内部(円周上も含む)に入っているかどうか
inline bool isInCircle(const Circle &c, const Point &p) {
D d = std::abs(c.p - p);
return (equal(d, c.r) || d < c.r - EPS);
}
} // namespace geometry
#line 2 "geometry/is-orthogonal.hpp"
#line 5 "geometry/is-orthogonal.hpp"
namespace geometry {
// 2直線の直交判定 : a⊥b <=> dot(a, b) = 0
inline bool isOrthogonal(const Line &a, const Line &b) {
return equal(dot(a.b - a.a, b.b - b.a), 0);
}
} // namespace geometry
#line 2 "geometry/is-point-on-line.hpp"
#line 2 "geometry/is-parallel.hpp"
#line 5 "geometry/is-parallel.hpp"
namespace geometry {
// 2直線の平行判定 : a//b <=> cross(a, b) = 0
inline bool isParallel(const Line &a, const Line &b) {
return equal(cross(a.b - a.a, b.b - b.a), 0);
}
} // namespace geometry
#line 4 "geometry/is-point-on-line.hpp"
namespace geometry {
// 点cが直線ab上にあるか
inline bool isPointOnLine(const Point &a, const Point &b, const Point &c) {
return isParallel(Line(a, b), Line(a, c));
}
} // namespace geometry
#line 2 "geometry/is-point-on-segment.hpp"
#line 4 "geometry/is-point-on-segment.hpp"
namespace geometry {
// 点cが"線分"ab上にあるか
inline bool isPointOnSegment(const Point &a, const Point &b, const Point &c) {
// |a-c| + |c-b| <= |a-b| なら線分上
return (std::abs(a - c) + std::abs(c - b) < std::abs(a - b) + EPS);
}
} // namespace geometry
#line 2 "geometry/normal-vector.hpp"
#line 4 "geometry/normal-vector.hpp"
namespace geometry {
// 法線ベクトル(normal vector)を求める
// 90度回転した単位ベクトルをかける
// -90度がよければPoint(0, -1)をかける
inline Point normalVector(const Point &a) { return a * Point(0, 1); }
} // namespace geometry
#line 2 "geometry/polygon-area.hpp"
#line 4 "geometry/polygon-area.hpp"
#line 6 "geometry/polygon-area.hpp"
namespace geometry {
// 多角形の面積を求める
inline D PolygonArea(const std::vector<Point> &p) {
D res = 0;
int n = p.size();
for(int i = 0; i < n - 1; i++) res += cross(p[i], p[i + 1]);
res += cross(p[n - 1], p[0]);
return res * 0.5;
}
} // namespace geometry
#line 2 "geometry/radian-to-degree.hpp"
#line 4 "geometry/radian-to-degree.hpp"
namespace geometry {
// ラジアン->度
inline D radianToDegree(const D &radian) { return radian * 180.0 / PI; }
} // namespace geometry
#line 2 "geometry/reflection.hpp"
#line 4 "geometry/reflection.hpp"
namespace geometry {
// 反射(reflection)
// 直線lを対称軸として点pと線対称の位置にある点を求める
inline Point reflection(const Line &l, const Point &p) {
return p + (projection(l, p) - p) * (D)2.0;
}
} // namespace geometry
#line 2 "geometry/tangent-to-circle.hpp"
#line 5 "geometry/tangent-to-circle.hpp"
#line 7 "geometry/tangent-to-circle.hpp"
namespace geometry {
// 点pを通る円cの接線
// 2本あるので、接点のみを返す
inline std::vector<Point> tangentToCircle(const Point &p, const Circle &c) {
return crossPoint(c,
Circle(p, std::sqrt(std::norm(c.p - p) - c.r * c.r)));
}
} // namespace geometry
#line 2 "geometry/tangent.hpp"
#line 5 "geometry/tangent.hpp"
#line 2 "geometry/rotate.hpp"
#line 4 "geometry/rotate.hpp"
namespace geometry {
// 点pを反時計回りにtheta度回転
// thetaはラジアン！！！
inline Point rotate(const Point &p, const D &theta) {
return Point(std::cos(theta) * p.real() - std::sin(theta) * p.imag(),
std::sin(theta) * p.real() + std::cos(theta) * p.imag());
}
} // namespace geometry
#line 10 "geometry/tangent.hpp"
namespace geometry {
// 円の共通接線
inline std::vector<Line> tangent(const Circle &a, const Circle &b) {
std::vector<Line> ret;
// 2円の中心間の距離
D g = std::abs(a.p - b.p);
// 円が内包されている場合
if(equal(g, 0)) return ret;
Point u = unitVector(b.p - a.p);
Point v = rotate(u, PI / 2);
for(int s : {-1, 1}) {
D h = (a.r + b.r * s) / g;
if(equal(h * h, 1)) {
ret.emplace_back(a.p + (h > 0 ? u : -u) * a.r,
a.p + (h > 0 ? u : -u) * a.r + v);
} else if(1 - h * h > 0) {
Point U = u * h, V = v * std::sqrt(1 - h * h);
ret.emplace_back(a.p + (U + V) * a.r,
b.p - (U + V) * (b.r * s));
ret.emplace_back(a.p + (U - V) * a.r,
b.p - (U - V) * (b.r * s));
}
}
return ret;
}
} // namespace geometry
#line 21 "test/mytest/geometry/geometry.test.cpp"
using namespace geometry;
void geometry_test() {
Point origin(0, 0), x(1, 0), y(0, 1);
assert(equal(dot(x, y), 0));
assert(equal(cross(x, y), 1));
assert(equal(std::abs(unitVector(Point(3, 4))), 1));
assert(normalVector(x) == y);
assert(std::abs(rotate(x, PI / 2) - y) < EPS);
assert(equal(radianToDegree(degreeToRadian(90)), 90));
assert(ccw(origin, x, y) == 1);
Line horizontal(origin, x), vertical(origin, y);
Segment horizontal_segment(origin, Point(2, 0));
Circle unit_circle(origin, 1);
assert(isOrthogonal(horizontal, vertical));
assert(isParallel(horizontal, Line(Point(0, 1), Point(1, 1))));
assert(isPointOnLine(origin, x, Point(2, 0)));
assert(isPointOnSegment(origin, Point(2, 0), x));
assert(equal(distanceBetweenLineAndPoint(horizontal, y), 1));
assert(equal(distanceBetweenSegmentAndPoint(horizontal_segment, Point(3, 0)), 1));
assert(crossPoint(horizontal, vertical) == origin);
assert(isIntersect(horizontal_segment, Segment(Point(1, -1), Point(1, 1)), true));
assert(equal(distanceBetweenSegments(horizontal_segment,
Segment(Point(3, 0), Point(4, 0))),
1));
assert(projection(horizontal, y) == origin);
assert(reflection(horizontal, y) == Point(0, -1));
assert(isIntersect(unit_circle, Circle(Point(2, 0), 1)) == 3);
assert(crossPoint(unit_circle, Circle(Point(2, 0), 1)).size() == 1);
assert(crossPoint(unit_circle, horizontal).size() == 2);
assert(isInCircle(unit_circle, origin));
assert(tangentToCircle(Point(2, 0), unit_circle).size() == 2);
assert(tangent(unit_circle, Circle(Point(4, 0), 1)).size() == 4);
std::vector<Point> triangle = {origin, x, y};
assert(equal(PolygonArea(triangle), 0.5));
assert(isConvex(triangle));
assert(ConvexHull(triangle).size() == 3);
assert(isContained(triangle, Point(0.1, 0.1)) == 2);
assert(!ConvexCut(triangle, Line(Point(0.5, -1), Point(0.5, 1))).empty());
}
int main() {
geometry_test();
INT(a, b);
print(a + b);
}