Tifa's CP Library

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

Depends on

Required by

Verified with

Code

#ifndef TIFALIBS_GEO2D_POINT
#define TIFALIBS_GEO2D_POINT

#include "../util/fp_comp.hpp"

namespace tifa_libs::geo {

template <class FP>
struct point {
  FP x, y;
  explicit constexpr 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 const &p) { return os << p.x << ' ' << p.y; }

  // s * r + t * (1 - r)
  friend constexpr point lerp(point const &s, point const &t, FP r) { return s * r + t * (1 - r); }
  friend constexpr point mid_point(point const &s, point const &t) { return lerp(s, t, .5); }

  constexpr point &operator+=(FP n) {
    this->x += n;
    this->y += n;
    return *this;
  }
  constexpr point &operator-=(FP n) {
    this->x -= n;
    this->y -= n;
    return *this;
  }
  constexpr point &operator*=(FP n) {
    this->x *= n;
    this->y *= n;
    return *this;
  }
  constexpr point &operator/=(FP n) {
    this->x /= n;
    this->y /= n;
    return *this;
  }
  friend constexpr point operator+(point x, FP n) { return x += n; }
  friend constexpr point operator+(FP n, point x) { return x += n; }
  friend constexpr point operator-(point x, FP n) { return x -= n; }
  friend constexpr point operator-(FP n, point x) { return x -= n; }
  friend constexpr point operator*(point x, FP n) { return x *= n; }
  friend constexpr point operator*(FP n, point x) { return x *= n; }
  friend constexpr point operator/(point x, FP n) { return x /= n; }
  friend constexpr point operator/(FP n, point x) { return x /= n; }

  constexpr point &operator+=(point const &p) {
    this->x += p.x;
    this->y += p.y;
    return *this;
  }
  constexpr point &operator-=(point const &p) {
    this->x -= p.x;
    this->y -= p.y;
    return *this;
  }
  constexpr point operator+(point const &p) const { return point(*this) += p; }
  constexpr point operator-(point const &p) const { return point(*this) -= p; }

  constexpr point operator-() const { return point{-x, -y}; }
  constexpr auto operator<=>(point const &p) const {
    if (auto c = comp(x, p.x); c) return c;
    return comp(y, p.y);
  }
  constexpr bool operator==(point const &p) const { return is_eq(x, p.x) && is_eq(y, p.y); }

  constexpr FP operator*(point const &p) const { return x * p.x + y * p.y; }
  constexpr FP operator^(point const &p) const { return x * p.y - y * p.x; }

  constexpr auto arg() const { return std::atan2(y, x); }
  constexpr FP norm2() const { return x * x + y * y; }
  constexpr FP norm() const { return std::hypot(x, y); }
  constexpr point &do_unit() { return *this /= norm(); }

  static constexpr u32 QUAD__[9] = {6, 7, 8, 5, 0, 1, 4, 3, 2};
  // 4 3 2
  // 5 0 1
  // 6 7 8
  constexpr u32 quad() const { return QUAD__[(sgn(y) + 1) * 3 + sgn(x) + 1]; }

  constexpr point &do_rot(FP theta) {
    FP x0 = x, y0 = y, ct = std::cos(theta), st = std::sin(theta);
    x = x0 * ct - y0 * st;
    y = x0 * st + y0 * ct;
    return *this;
  }
  constexpr point &do_rot90() {
    FP tmp = x;
    x = -y;
    y = tmp;
    return *this;
  }
  friend constexpr point rot90(point p) { return p.do_rot90(); }
  constexpr point &do_rot270() {
    FP tmp = y;
    y = -x;
    x = tmp;
    return *this;
  }
  friend constexpr point rot270(point p) { return p.do_rot270(); }
};

}  // namespace tifa_libs::geo

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



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



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



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



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

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;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
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 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>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<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>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

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

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};


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

namespace tifa_libs {

using namespace std::numbers;

// std::sqrt(std::numeric_limits<FP>::epsilon())
template <std::floating_point FP>
constexpr inline FP eps_v = FP(1e-8L);

}  // namespace tifa_libs


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



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

namespace tifa_libs {

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

template <class T>
concept container_c = iterable_c<T> && !std::derived_from<T, std::basic_string<typename T::value_type>>;

template <class T>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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 = typename 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 = typename to_uint<T>::type;

}  // namespace tifa_libs


#line 6 "src/code/util/fp_comp.hpp"

namespace tifa_libs {

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

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

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

template <class FP>
constexpr bool is_lt(FP l, FP r) { return comp(l, r) < 0; }
template <class FP>
constexpr bool is_eq(FP l, FP r) { return !comp(l, r); }
template <class FP>
constexpr 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 {
  FP x, y;
  explicit constexpr 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 const &p) { return os << p.x << ' ' << p.y; }

  // s * r + t * (1 - r)
  friend constexpr point lerp(point const &s, point const &t, FP r) { return s * r + t * (1 - r); }
  friend constexpr point mid_point(point const &s, point const &t) { return lerp(s, t, .5); }

  constexpr point &operator+=(FP n) {
    this->x += n;
    this->y += n;
    return *this;
  }
  constexpr point &operator-=(FP n) {
    this->x -= n;
    this->y -= n;
    return *this;
  }
  constexpr point &operator*=(FP n) {
    this->x *= n;
    this->y *= n;
    return *this;
  }
  constexpr point &operator/=(FP n) {
    this->x /= n;
    this->y /= n;
    return *this;
  }
  friend constexpr point operator+(point x, FP n) { return x += n; }
  friend constexpr point operator+(FP n, point x) { return x += n; }
  friend constexpr point operator-(point x, FP n) { return x -= n; }
  friend constexpr point operator-(FP n, point x) { return x -= n; }
  friend constexpr point operator*(point x, FP n) { return x *= n; }
  friend constexpr point operator*(FP n, point x) { return x *= n; }
  friend constexpr point operator/(point x, FP n) { return x /= n; }
  friend constexpr point operator/(FP n, point x) { return x /= n; }

  constexpr point &operator+=(point const &p) {
    this->x += p.x;
    this->y += p.y;
    return *this;
  }
  constexpr point &operator-=(point const &p) {
    this->x -= p.x;
    this->y -= p.y;
    return *this;
  }
  constexpr point operator+(point const &p) const { return point(*this) += p; }
  constexpr point operator-(point const &p) const { return point(*this) -= p; }

  constexpr point operator-() const { return point{-x, -y}; }
  constexpr auto operator<=>(point const &p) const {
    if (auto c = comp(x, p.x); c) return c;
    return comp(y, p.y);
  }
  constexpr bool operator==(point const &p) const { return is_eq(x, p.x) && is_eq(y, p.y); }

  constexpr FP operator*(point const &p) const { return x * p.x + y * p.y; }
  constexpr FP operator^(point const &p) const { return x * p.y - y * p.x; }

  constexpr auto arg() const { return std::atan2(y, x); }
  constexpr FP norm2() const { return x * x + y * y; }
  constexpr FP norm() const { return std::hypot(x, y); }
  constexpr point &do_unit() { return *this /= norm(); }

  static constexpr u32 QUAD__[9] = {6, 7, 8, 5, 0, 1, 4, 3, 2};
  // 4 3 2
  // 5 0 1
  // 6 7 8
  constexpr u32 quad() const { return QUAD__[(sgn(y) + 1) * 3 + sgn(x) + 1]; }

  constexpr point &do_rot(FP theta) {
    FP x0 = x, y0 = y, ct = std::cos(theta), st = std::sin(theta);
    x = x0 * ct - y0 * st;
    y = x0 * st + y0 * ct;
    return *this;
  }
  constexpr point &do_rot90() {
    FP tmp = x;
    x = -y;
    y = tmp;
    return *this;
  }
  friend constexpr point rot90(point p) { return p.do_rot90(); }
  constexpr point &do_rot270() {
    FP tmp = y;
    y = -x;
    x = tmp;
    return *this;
  }
  friend constexpr point rot270(point p) { return p.do_rot270(); }
};

}  // namespace tifa_libs::geo


Back to top page