Tifa's CP Library

:heavy_check_mark: rel_plp (src/code/geo3d/rel_plp.hpp)

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#ifndef TIFALIBS_GEO3D_REL_PLP
#define TIFALIBS_GEO3D_REL_PLP

#include "planev.hpp"
#include "point3d.hpp"

namespace tifa_libs::geo {

// relation between plane and point3d
enum RELPLP { above_plp,
              in_plp,
              below_plp };

template <class FP>
CEXP RELPLP relation_PlP(planev<FP> CR pl, point3d<FP> CR p) {
  const FP d = (p - *pl.u) * pl.normal();
  if (is_pos(d)) return above_plp;
  if (is_neg(d)) return below_plp;
  return in_plp;
}

}  // namespace tifa_libs::geo

#endif
#line 1 "src/code/geo3d/rel_plp.hpp"



#line 1 "src/code/geo3d/planev.hpp"



#line 1 "src/code/geo2d/cross.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/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/geo3d/point3d.hpp"



#line 5 "src/code/geo3d/point3d.hpp"

namespace tifa_libs::geo {

template <class FP>
struct point3d {
  using FP_t = FP;
  FP x, y, z;
  CEXPE point3d(FP x = FP{}, FP y = FP{}, FP z = FP{}) : x(x), y(y), z(z) {}

  friend std::istream &operator>>(std::istream &is, point3d &p) { return is >> p.x >> p.y >> p.z; }
  friend std::ostream &operator<<(std::ostream &os, point3d CR p) { return os << p.x << ' ' << p.y << ' ' << p.z; }
  // s * r + t * (1 - r)
  friend CEXP point3d lerp(point3d CR s, point3d CR t, FP r) {
    static_assert(std::floating_point<FP>);
    return s * r + t * (1 - r);
  }
  friend CEXP point3d mid_point(point3d CR s, point3d CR t) { return lerp(s, t, .5); }
  CEXP point3d &operator+=(FP n) { return this->x += n, this->y += n, this->z += n, *this; }
  CEXP point3d operator+(FP n) const { return point3d(*this) += n; }
  CEXP point3d &operator-=(FP n) { return this->x -= n, this->y -= n, this->z -= n, *this; }
  CEXP point3d operator-(FP n) const { return point3d(*this) -= n; }
  CEXP point3d &operator*=(FP n) { return this->x *= n, this->y *= n, this->z *= n, *this; }
  CEXP point3d operator*(FP n) const { return point3d(*this) *= n; }
  CEXP point3d &operator/=(FP n) { return this->x /= n, this->y /= n, this->z /= n, *this; }
  CEXP point3d operator/(FP n) const { return point3d(*this) /= n; }
  CEXP point3d &operator+=(point3d CR p) { return this->x += p.x, this->y += p.y, this->z += p.z, *this; }
  CEXP point3d operator+(point3d CR p) const { return point3d(*this) += p; }
  CEXP point3d &operator-=(point3d CR p) { return this->x -= p.x, this->y -= p.y, this->z -= p.z, *this; }
  CEXP point3d operator-(point3d CR p) const { return point3d(*this) -= p; }
  CEXP point3d operator-() const { return point3d{-x, -y, -z}; }
  CEXP auto operator<=>(point3d CR p) const {
    if (auto c = comp(x, p.x); c) return c;
    if (auto c = comp(y, p.y); c) return c;
    return comp(z, p.z);
  }
  CEXP bool operator==(point3d CR p) const { return is_eq(x, p.x) && is_eq(y, p.y) && is_eq(z, p.z); }
  CEXP FP operator*(point3d CR p) const { return x * p.x + y * p.y + z * p.z; }
  CEXP point3d operator^(point3d CR p) const { return point3d{y * p.z - z * p.y, z * p.x - x * p.z, x * p.y - y * p.x}; }
  CEXP auto norm2() const { return x * x + y * y + z * z; }
  CEXP auto norm() const {
    static_assert(std::floating_point<FP>);
    return std::hypot(x, y, z);
  }
  CEXP point3d &do_unit() { return *this /= norm(); }
  CEXP point3d &do_rotx(FP theta) {
    const FP y0 = y, z0 = z, ct = std::cos(theta), st = std::sin(theta);
    return y = y0 * ct - z0 * st, z = y0 * st + z0 * ct, *this;
  }
  CEXP point3d &do_roty(FP theta) {
    const FP x0 = x, z0 = z, ct = std::cos(theta), st = std::sin(theta);
    return z = z0 * ct - x0 * st, x = z0 * st + x0 * ct, *this;
  }
  CEXP point3d &do_rotz(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;
  }
  CEXP point3d &do_rot(point3d e, FP theta) {
    e.do_unit();
    const FP a = e.x, b = e.y, c = e.z, x0 = x, y0 = y, z0 = z, ct = std::cos(theta), st = std::sin(theta);
    x = x0 * (ct + a * a * (1 - ct)) + y0 * (a * b * (1 - ct) - c * st) + z0 * (a * c * (1 - ct) + b * st);
    y = x0 * (a * b * (1 - ct) + c * st) + y0 * (ct + b * b * (1 - ct)) + z0 * (b * c * (1 - ct) - a * st);
    z = x0 * (a * c * (1 - ct) - b * st) + y0 * (b * c * (1 - ct) + a * st) + z0 * (ct + c * c * (1 - ct));
    return *this;
  }
};

}  // namespace tifa_libs::geo


#line 6 "src/code/geo3d/planev.hpp"

namespace tifa_libs::geo {

template <class FP>
struct planev {
  point3d<FP> const *u, *v, *w;
  CEXP planev(point3d<FP> CR a, point3d<FP> CR b, point3d<FP> CR c) : u(&a), v(&b), w(&c) {}

  friend std::ostream &operator<<(std::ostream &os, planev CR pl) { return os << *pl.u << ' ' << *pl.v << ' ' << *pl.w; }
  CEXP point3d<FP> normal() const { return cross(*u, *v, *w); }
  CEXP FP area2() const { return normal().norm(); }
  CEXP FP area() const { return area2() * (FP).5; }
  CEXP point3d<FP> CR get(u32 i) const {
    assert(i < 3);
    return **(&(this->u) + i);
  }
};

}  // namespace tifa_libs::geo


#line 6 "src/code/geo3d/rel_plp.hpp"

namespace tifa_libs::geo {

// relation between plane and point3d
enum RELPLP { above_plp,
              in_plp,
              below_plp };

template <class FP>
CEXP RELPLP relation_PlP(planev<FP> CR pl, point3d<FP> CR p) {
  const FP d = (p - *pl.u) * pl.normal();
  if (is_pos(d)) return above_plp;
  if (is_neg(d)) return below_plp;
  return in_plp;
}

}  // namespace tifa_libs::geo


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