comp-geometry

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:heavy_check_mark: src/real-geometry/point-cloud/convex-hull-with-index.hpp

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Code

#pragma once

#include "src/real-geometry/common/size-alias.hpp"
#include "src/real-geometry/class/point.hpp"
#include "src/real-geometry/class/polygon.hpp"
#include "src/real-geometry/compare/compare-x.hpp"
#include "src/real-geometry/operation/cross-product.hpp"

#include <algorithm>
#include <numeric>
#include <tuple>
#include <utility>
#include <vector>

namespace geometry {

  template< typename R >
  std::pair< polygon<R>, std::vector< usize > > convex_hull_with_index(const points<R> &pts) {
    usize n = pts.size();
    if (n <= 2) {
      std::vector< usize > idxs(n);
      std::iota(idxs.begin(), idxs.end(), 0);
      return {pts, idxs};
    }

    std::vector< std::pair< point<R>, usize > > ps;
    ps.reserve(n);
    for (usize i = 0; i < n; i++) {
      ps.emplace_back(pts[i], i);
    }

    auto cmp = [](const std::pair<point<R>, usize> &a, const std::pair<point<R>, usize> &b) {
      return compare_x(a.first, b.first);
    };
    std::sort(ps.begin(), ps.end(), cmp);

    std::vector< usize > idxs(2 * n);
    polygon<R> poly(2 * n);
    usize k = 0, i = 0;

    auto check = [&](usize i) {
      return sign(cross_product<R>(poly[k - 1] - poly[k - 2], ps[i].first - poly[k - 1])) == -1;
    };

    while (i < n) {
      while (k >= 2 and check(i)) k--;

      std::tie(poly[k], idxs[k]) = ps[i];
      k++; i++;
    }

    i = n - 2;
    usize t = k + 1;
    while (true) {
      while (k >= t and check(i)) k--;

      std::tie(poly[k], idxs[k]) = ps[i];
      k++;
      if (not i) break;
      i--;
    }

    poly.resize(k - 1);
    idxs.resize(k - 1);
    return {poly, idxs};
  }

}
#line 2 "src/real-geometry/point-cloud/convex-hull-with-index.hpp"

#line 2 "src/real-geometry/common/size-alias.hpp"

#include <cstddef>

namespace geometry {

  using isize = std::ptrdiff_t;
  using usize = std::size_t;

}
#line 2 "src/real-geometry/class/point.hpp"

#line 2 "src/real-geometry/class/vector.hpp"

#include <complex>
#include <iostream>

namespace geometry {

  template< typename R >
  class vec2d : public std::complex< R > {
    using complex = std::complex< R >;

   public:
    using complex::complex;

    vec2d(const complex &c): complex::complex(c) {}

    const R x() const { return this->real(); }
    const R y() const { return this->imag(); }

    friend vec2d operator*(const vec2d &v, const R &k) {
      return vec2d(v.x() * k, v.y() * k);
    }

    friend vec2d operator*(const R &k, const vec2d &v) {
      return vec2d(v.x() * k, v.y() * k);
    }

    friend std::istream &operator>>(std::istream &is, vec2d &v) {
      R x, y;
      is >> x >> y;
      v = vec2d(x, y);
      return is;
    }
 
  };

}
#line 4 "src/real-geometry/class/point.hpp"

#include <vector>

namespace geometry {

  template< typename R >
  using point = vec2d<R>;

  template< typename R >
  using points = std::vector< point< R > >;

}
#line 2 "src/real-geometry/class/polygon.hpp"

#line 4 "src/real-geometry/class/polygon.hpp"

#line 6 "src/real-geometry/class/polygon.hpp"

namespace geometry {

  template< typename R >
  using polygon = std::vector< point<R> >;

  template< typename R >
  using polygons = std::vector< polygon<R> >;

}
#line 2 "src/real-geometry/compare/compare-x.hpp"

#line 2 "src/real-geometry/utility/equals/real-number.hpp"

#line 2 "src/real-geometry/utility/sign.hpp"

#line 2 "src/real-geometry/common/const/eps.hpp"

#line 2 "src/real-geometry/common/float-alias.hpp"

namespace geometry {

  using f80 = long double;
  using f64 = double;

}
#line 4 "src/real-geometry/common/const/eps.hpp"

namespace geometry {

  inline static f80 &eps() {
    static f80 EPS = 1e-10;
    return EPS;
  }

  void set_eps(f80 EPS) {
    eps() = EPS;
  }

}
#line 2 "src/real-geometry/numbers/sign.hpp"

#line 2 "src/real-geometry/common/int-alias.hpp"

namespace geometry {

  using i32 = int;
  using i64 = long long;

}
#line 4 "src/real-geometry/numbers/sign.hpp"

namespace geometry::number::sign {

  constexpr i32 PLUS  = +1;
  constexpr i32 ZERO  =  0;
  constexpr i32 MINUS = -1;

}
#line 5 "src/real-geometry/utility/sign.hpp"

namespace geometry {

  using namespace geometry::number::sign;

  template< typename R >
  inline int sign(R r) {
    if (r < -eps()) return MINUS;
    if (r > +eps()) return PLUS;
    return ZERO;
  }

}
#line 4 "src/real-geometry/utility/equals/real-number.hpp"

namespace geometry {

  template< typename R >
  bool equals(R a, R b) {
    return sign(a - b) == 0;
  }

}
#line 5 "src/real-geometry/compare/compare-x.hpp"

namespace geometry {

  template< typename R >
  bool compare_x(const point<R> &a, const point<R> &b) {
    return not equals(a.x(), b.x()) ? a.x() < b.x() : a.y() < b.y();
  }

}
#line 2 "src/real-geometry/operation/cross-product.hpp"

#line 4 "src/real-geometry/operation/cross-product.hpp"

namespace geometry {

  template< typename R >
  R cross_product(const vec2d<R> &a, const vec2d<R> &b) {
    return a.x() * b.y() - a.y() * b.x();
  }

}
#line 8 "src/real-geometry/point-cloud/convex-hull-with-index.hpp"

#include <algorithm>
#include <numeric>
#include <tuple>
#include <utility>
#line 14 "src/real-geometry/point-cloud/convex-hull-with-index.hpp"

namespace geometry {

  template< typename R >
  std::pair< polygon<R>, std::vector< usize > > convex_hull_with_index(const points<R> &pts) {
    usize n = pts.size();
    if (n <= 2) {
      std::vector< usize > idxs(n);
      std::iota(idxs.begin(), idxs.end(), 0);
      return {pts, idxs};
    }

    std::vector< std::pair< point<R>, usize > > ps;
    ps.reserve(n);
    for (usize i = 0; i < n; i++) {
      ps.emplace_back(pts[i], i);
    }

    auto cmp = [](const std::pair<point<R>, usize> &a, const std::pair<point<R>, usize> &b) {
      return compare_x(a.first, b.first);
    };
    std::sort(ps.begin(), ps.end(), cmp);

    std::vector< usize > idxs(2 * n);
    polygon<R> poly(2 * n);
    usize k = 0, i = 0;

    auto check = [&](usize i) {
      return sign(cross_product<R>(poly[k - 1] - poly[k - 2], ps[i].first - poly[k - 1])) == -1;
    };

    while (i < n) {
      while (k >= 2 and check(i)) k--;

      std::tie(poly[k], idxs[k]) = ps[i];
      k++; i++;
    }

    i = n - 2;
    usize t = k + 1;
    while (true) {
      while (k >= t and check(i)) k--;

      std::tie(poly[k], idxs[k]) = ps[i];
      k++;
      if (not i) break;
      i--;
    }

    poly.resize(k - 1);
    idxs.resize(k - 1);
    return {poly, idxs};
  }

}
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