Tifa's CP Library

:heavy_check_mark: tcenter_x (src/code/geo2d/tcenter_x.hpp)

Depends on

Verified with

Code

#ifndef TIFALIBS_GEO2D_TCENTER_X
#define TIFALIBS_GEO2D_TCENTER_X

#include "triangle.hpp"

namespace tifa_libs::geo {

// fermat center (X13)
template <class FP>
CEXP point<FP> center_X(triangle<FP> CR t) {
  auto [A, B, C] = t.angles();
  return t.trilinears(1 / std::sin(A + pi_v<FP> / 3), 1 / std::sin(B + pi_v<FP> / 3), 1 / std::sin(C + pi_v<FP> / 3));
}

}  // namespace tifa_libs::geo

#endif
#line 1 "src/code/geo2d/tcenter_x.hpp"



#line 1 "src/code/geo2d/triangle.hpp"



#line 1 "src/code/geo2d/ang_pp.hpp"



#line 1 "src/code/geo2d/point.hpp"



#line 1 "src/code/util/fp_comp.hpp"



#line 1 "src/code/util/traits.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/extc++.h>

#define CEXP constexpr
#define CEXPE constexpr explicit
#define TPN typename
#define CR const&

#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t), __VA_ARGS__, __VA_ARGS__ CR>
#define fle_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i <= i##e; ++i)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;
using f32 = float;
using f64 = double;
using f128 = long double;
using strn = std::string;
using strnv = std::string_view;

// clang-format off
template <class T, T v> using ic = std::integral_constant<T, v>;
template <class T> using ptt = std::pair<T, T>;
template <class T> struct edge_t {
  T w; u32 u, v;
  CEXP auto operator<=>(edge_t CR) const = default;
};
template <class T> struct pt3 {
  T _0, _1, _2;
  CEXP auto operator<=>(pt3 CR) const = default;
};
template <class T> struct pt4 {
  T _0, _1, _2, _3;
  CEXP auto operator<=>(pt4 CR) const = default;
};
template <class E> using itl = std::initializer_list<E>;
template <class T> using vec = std::vector<T>;
template <class T> using vvec = vec<vec<T>>;
template <class T> using v3ec = vec<vvec<T>>;
template <class T> using vecpt = vec<ptt<T>>;
template <class T> using vvecpt = vvec<ptt<T>>;
template <class T> using ptvec = ptt<vec<T>>;
template <class T> using ptvvec = ptt<vvec<T>>;

template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>;
template <class U, class T> using vecp = vec<std::pair<U, T>>;
template <class U, class T> using vvecp = vvec<std::pair<U, T>>;

template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
template <class T> using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;
// clang-format on

#define mk_(V, A, T) using V##A = V<T>;
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk_(spn, A, T) mk_(itl, A, T)
mk(b, bool) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64);
#undef mk
#undef mk_

using namespace std::literals;
CEXP i8 operator""_i8(unsigned long long x) { return (i8)x; }
CEXP i16 operator""_i16(unsigned long long x) { return (i16)x; }
CEXP i32 operator""_i32(unsigned long long x) { return (i32)x; }
CEXP i64 operator""_i64(unsigned long long x) { return (i64)x; }
CEXP isz operator""_iz(unsigned long long x) { return (isz)x; }
CEXP u8 operator""_u8(unsigned long long x) { return (u8)x; }
CEXP u16 operator""_u16(unsigned long long x) { return (u16)x; }
CEXP u32 operator""_u32(unsigned long long x) { return (u32)x; }
CEXP u64 operator""_u64(unsigned long long x) { return (u64)x; }
CEXP usz operator""_uz(unsigned long long x) { return (usz)x; }

using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) { eps_v<FP> = v; }

inline const auto fn_0 = [](auto&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };

namespace tifa_libs {
using std::min, std::max, std::swap;
template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }
}  // namespace tifa_libs


#line 5 "src/code/util/traits.hpp"

namespace tifa_libs {

template <class T>
concept iterable_c = requires(T v) {
  { v.begin() } -> std::same_as<TPN T::iterator>;
  { v.end() } -> std::same_as<TPN T::iterator>;
};

template <class T>
concept container_c = iterable_c<T> && !std::same_as<std::remove_cvref_t<T>, strn> && !std::same_as<std::remove_cvref_t<T>, strnv>;

template <class T>
CEXP bool is_char_v = std::is_same_v<T, char> || std::is_same_v<T, signed char> || std::is_same_v<T, unsigned char>;
template <class T>
concept char_c = is_char_v<T>;

template <class T>
CEXP bool is_s128_v = std::is_same_v<T, __int128_t> || std::is_same_v<T, __int128>;
template <class T>
concept s128_c = is_s128_v<T>;

template <class T>
CEXP bool is_u128_v = std::is_same_v<T, __uint128_t> || std::is_same_v<T, unsigned __int128>;
template <class T>
concept u128_c = is_u128_v<T>;

template <class T>
CEXP bool is_i128_v = is_s128_v<T> || is_u128_v<T>;
template <class T>
concept i128_c = is_u128_v<T>;

template <class T>
CEXP bool is_int_v = std::is_integral_v<T> || is_i128_v<T>;
template <class T>
concept int_c = is_int_v<T>;

template <class T>
CEXP bool is_sint_v = is_s128_v<T> || (is_int_v<T> && std::is_signed_v<T>);
template <class T>
concept sint_c = is_sint_v<T>;

template <class T>
CEXP bool is_uint_v = is_u128_v<T> || (is_int_v<T> && std::is_unsigned_v<T>);
template <class T>
concept uint_c = is_uint_v<T>;

template <class T>
concept mint_c = requires(T x) {
  { x.mod() } -> uint_c;
  { x.val() } -> uint_c;
};

template <class T>
concept dft_c = requires(T x, vec<TPN T::data_t> v, u32 n) {
  { x.size() } -> std::same_as<u32>;
  x.bzr(n);
  x.dif(v, n);
  x.dit(v, n);
};

template <class T>
concept ntt_c = dft_c<T> && requires(T x) {
  T::max_size;
  T::G;
};

template <class T>
CEXP bool is_arithm_v = std::is_arithmetic_v<T> || is_int_v<T>;
template <class T>
concept arithm_c = is_arithm_v<T>;

template <class T>
struct to_sint : std::make_signed<T> {};
template <>
struct to_sint<u128> {
  using type = u128;
};
template <>
struct to_sint<i128> {
  using type = u128;
};
template <class T>
using to_sint_t = TPN to_sint<T>::type;

template <class T>
struct to_uint : std::make_unsigned<T> {};
template <>
struct to_uint<u128> {
  using type = u128;
};
template <>
struct to_uint<i128> {
  using type = u128;
};
template <class T>
using to_uint_t = TPN to_uint<T>::type;

}  // namespace tifa_libs


#line 5 "src/code/util/fp_comp.hpp"

namespace tifa_libs {

template <sint_c T>
CEXP int sgn(T x) { return (!!x) | (x >> (sizeof(T) * 8 - 1)); }
template <uint_c T>
CEXP int sgn(T x) { return !!x; }
template <std::floating_point FP>
CEXP int sgn(FP x) { return (x > eps_v<FP>)-(x < -eps_v<FP>); }

template <class FP>
CEXP bool is_neg(FP x) { return sgn(x) < 0; }
template <class FP>
CEXP bool is_zero(FP x) { return !sgn(x); }
template <class FP>
CEXP bool is_pos(FP x) { return sgn(x) > 0; }

template <int_c T>
CEXP int comp(T l, T r) { return sgn(l - r); }
template <std::floating_point FP>
CEXP int comp(FP l, FP r) { return sgn((l - r) / max({abs(l), abs(r), FP(1)})); }

template <class FP>
CEXP bool is_lt(FP l, FP r) { return comp(l, r) < 0; }
template <class FP>
CEXP bool is_eq(FP l, FP r) { return !comp(l, r); }
template <class FP>
CEXP bool is_gt(FP l, FP r) { return comp(l, r) > 0; }

}  // namespace tifa_libs


#line 5 "src/code/geo2d/point.hpp"

namespace tifa_libs::geo {

template <class FP>
struct point {
  using FP_t = FP;

  FP x, y;
  CEXPE point(FP x = FP{}, FP y = FP{}) : x(x), y(y) {}

  friend std::istream &operator>>(std::istream &is, point &p) { return is >> p.x >> p.y; }
  friend std::ostream &operator<<(std::ostream &os, point CR p) { return os << p.x << ' ' << p.y; }
  // s * r + t * (1 - r)
  template <std::floating_point T>
  friend CEXP point lerp(point CR s, point CR t, T r) { return s * r + t * (1 - r); }
  friend CEXP point mid_point(point CR s, point CR t) { return lerp(s, t, .5); }
  template <arithm_c T>
  CEXP point &operator+=(T n) { return this->x += n, this->y += n, *this; }
  template <arithm_c T>
  CEXP point &operator-=(T n) { return this->x -= n, this->y -= n, *this; }
  template <arithm_c T>
  CEXP point &operator*=(T n) { return this->x *= n, this->y *= n, *this; }
  template <arithm_c T>
  CEXP point &operator/=(T n) { return this->x /= n, this->y /= n, *this; }
  template <arithm_c T>
  friend CEXP point operator+(point x, T n) { return x += n; }
  template <arithm_c T>
  friend CEXP point operator+(T n, point x) { return x += n; }
  template <arithm_c T>
  friend CEXP point operator-(point x, T n) { return x -= n; }
  template <arithm_c T>
  friend CEXP point operator-(T n, point x) { return x -= n; }
  template <arithm_c T>
  friend CEXP point operator*(point x, T n) { return x *= n; }
  template <arithm_c T>
  friend CEXP point operator*(T n, point x) { return x *= n; }
  template <arithm_c T>
  friend CEXP point operator/(point x, T n) { return x /= n; }
  template <arithm_c T>
  friend CEXP point operator/(T n, point x) { return x /= n; }
  CEXP point &operator+=(point CR p) { return this->x += p.x, this->y += p.y, *this; }
  CEXP point &operator-=(point CR p) { return this->x -= p.x, this->y -= p.y, *this; }
  CEXP point operator+(point CR p) const { return point(*this) += p; }
  CEXP point operator-(point CR p) const { return point(*this) -= p; }
  CEXP point operator-() const { return point{-x, -y}; }
  CEXP auto operator<=>(point CR p) const {
    if (auto CR c = comp(x, p.x); c) return c;
    return comp(y, p.y);
  }
  CEXP bool operator==(point CR p) const { return is_eq(x, p.x) && is_eq(y, p.y); }
  CEXP FP operator*(point CR p) const { return x * p.x + y * p.y; }
  CEXP FP operator^(point CR p) const { return x * p.y - y * p.x; }
  CEXP FP arg() const {
    static_assert(std::is_floating_point_v<FP>);
    return std::atan2(y, x);
  }
  CEXP FP arg_2pi() const {
    FP res = arg();
    return is_neg(res) ? res + 2 * pi_v<FP> : res;
  }
  CEXP FP norm2() const { return x * x + y * y; }
  CEXP FP norm() const {
    static_assert(std::is_floating_point_v<FP>);
    return std::hypot(x, y);
  }
  CEXP point &do_unit() {
    static_assert(std::is_floating_point_v<FP>);
    return *this /= norm();
  }
  static CEXP u32 QUAD__[9] = {6, 7, 8, 5, 0, 1, 4, 3, 2};
  // 4 3 2
  // 5 0 1
  // 6 7 8
  CEXP u32 quad() const { return QUAD__[(sgn(y) + 1) * 3 + sgn(x) + 1]; }
  CEXP int toleft(point CR p) const { return sgn(*this ^ p); }
  CEXP point &do_rot(FP theta) {
    const FP x0 = x, y0 = y, ct = std::cos(theta), st = std::sin(theta);
    return x = x0 * ct - y0 * st, y = x0 * st + y0 * ct, *this;
  }
  friend CEXP point rot(point p, FP theta) { return p.do_rot(theta); }
  CEXP point &do_rot90() {
    const FP _ = x;
    return x = -y, y = _, *this;
  }
  friend CEXP point rot90(point p) { return p.do_rot90(); }
  CEXP point &do_rot270() {
    const FP _ = y;
    return y = -x, x = _, *this;
  }
  friend CEXP point rot270(point p) { return p.do_rot270(); }
};

}  // namespace tifa_libs::geo


#line 5 "src/code/geo2d/ang_pp.hpp"

namespace tifa_libs::geo {

// clamp angle of two points, result in $(-\pi,\pi]$
template <class FP>
CEXP FP ang_PP(point<FP> CR p1, point<FP> CR p2) { return std::atan2(p1 ^ p2, p1 * p2); }
// clamp angle of two points, result in $[0,2\pi)$
template <class FP>
CEXP FP ang2pi_PP(point<FP> CR p1, point<FP> CR p2) {
  const FP res = ang_PP(p1, p2);
  return is_neg(res) ? res + 2 * pi_v<FP> : res;
}

}  // namespace tifa_libs::geo


#line 1 "src/code/geo2d/cross.hpp"



#line 5 "src/code/geo2d/cross.hpp"

namespace tifa_libs::geo {

template <class P>
CEXP auto cross(P CR o, P CR a, P CR b) { return (a - o) ^ (b - o); }
template <class P>
requires std::floating_point<typename P::FP_t>
CEXP auto cross_unit(P CR o, P CR a, P CR b) { return (a - o).do_unit() ^ (b - o).do_unit(); }
template <class P>
requires std::floating_point<typename P::FP_t>
CEXP int sgn_cross(P CR o, P CR a, P CR b) { return sgn(cross_unit(o, a, b)); }
template <class P>
CEXP int sgn_cross(P CR o, P CR a, P CR b) { return sgn(cross(o, a, b)); }

}  // namespace tifa_libs::geo


#line 1 "src/code/geo2d/dist_pp.hpp"



#line 5 "src/code/geo2d/dist_pp.hpp"

namespace tifa_libs::geo {

// distance of two points (Manhattan)
template <class FP>
CEXP FP dist_PP_Ma(point<FP> CR p1, point<FP> CR p2) { return abs(p1.x - p2.x) + abs(p1.y - p2.y); }
// distance of two points (Euclidian)
template <class FP>
CEXP FP dist_PP(point<FP> CR p1, point<FP> CR p2) { return (p1 - p2).norm(); }
// distance of two points (Chebyshev)
template <class FP>
CEXP FP dist_PP_Ch(point<FP> CR p1, point<FP> CR p2) { return max(abs(p1.x - p2.x), abs(p1.y - p2.y)); }

}  // namespace tifa_libs::geo


#line 1 "src/code/geo2d/dot.hpp"



#line 5 "src/code/geo2d/dot.hpp"

namespace tifa_libs::geo {

template <class P>
CEXP typename P::FP_t dot(P CR o, P CR a, P CR b) { return (a - o) * (b - o); }
template <class P>
CEXP int sgn_dot(P CR o, P CR a, P CR b) { return sgn(dot(o, a, b)); }

}  // namespace tifa_libs::geo


#line 8 "src/code/geo2d/triangle.hpp"

namespace tifa_libs::geo {

template <class FP>
struct triangle {
  point<FP> A, B, C;

  CEXP triangle() {}
  CEXP triangle(point<FP> CR a, point<FP> CR b, point<FP> CR c) : A(a), B(b), C(c) {}
  CEXP triangle(FP a_x, FP a_y, FP b_x, FP b_y, FP c_x, FP c_y) : A(a_x, a_y), B(b_x, b_y), C(c_x, c_y) {}

  friend std::istream &operator>>(std::istream &is, triangle &t) { return is >> t.A >> t.B >> t.C; }
  friend std::ostream &operator<<(std::ostream &os, triangle CR t) { return os << t.A << ' ' << t.B << ' ' << t.C; }
  friend CEXP bool operator==(triangle CR l, triangle CR r) { return l.A == r.A && l.B == r.B && l.C == r.C; }
  // (a, b, c)
  CEXP pt3<FP> edges() const { return {dist_PP(B, C), dist_PP(C, A), dist_PP(A, B)}; }
  // (A, B, C)
  CEXP pt3<FP> angles() const { return {abs(ang_PP(C - A, B - A)), abs(ang_PP(A - B, C - B)), abs(ang_PP(A - C, B - C))}; }
  CEXP point<FP> trilinears(FP x, FP y, FP z) const {
    auto [a, b, c] = edges();
    return x *= a, y *= b, z *= c, (A * x + B * y + C * z) / (x + y + z);
  }
  CEXP point<FP> barycentrics(FP u, FP v, FP w) const { return (A * u + B * v + C * w) / (u + v + w); }
  CEXP FP area() const { return abs(cross(A, B, C)) / 2; }
  CEXP bool is_acute() const { return is_pos(dot(A, B, C)) && is_pos(dot(B, C, A)) && is_pos(dot(C, A, B)); }
  CEXP bool is_right() const { return is_zero(dot(A, B, C)) || is_zero(dot(B, C, A)) || is_zero(dot(C, A, B)); }
  CEXP bool is_obtuse() const { return is_neg(dot(A, B, C)) || is_neg(dot(B, C, A)) || is_neg(dot(C, A, B)); }
};

}  // namespace tifa_libs::geo


#line 5 "src/code/geo2d/tcenter_x.hpp"

namespace tifa_libs::geo {

// fermat center (X13)
template <class FP>
CEXP point<FP> center_X(triangle<FP> CR t) {
  auto [A, B, C] = t.angles();
  return t.trilinears(1 / std::sin(A + pi_v<FP> / 3), 1 / std::sin(B + pi_v<FP> / 3), 1 / std::sin(C + pi_v<FP> / 3));
}

}  // namespace tifa_libs::geo


Back to top page