tpl_ca_hex_lattice.H

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
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*/
 
#ifndef TPL_CA_HEX_LATTICE_H
#define TPL_CA_HEX_LATTICE_H
 
#include <array>
#include <cmath>
#include <cstddef>
#include <ostream>
#include <sstream>
#include <string>
 
#include <ah-errors.H>
 
#include <ca-traits.H>
#include <tpl_ca_concepts.H>
#include <tpl_ca_lattice.H>
 
namespace Aleph {
namespace CA {
 
struct Hex_Axial
{
  ca_index_t q = 0;  
  ca_index_t r = 0;  
 
  friend constexpr bool operator==(Hex_Axial a, Hex_Axial b) noexcept
  {
    return a.q == b.q and a.r == b.r;
  }
  friend constexpr bool operator!=(Hex_Axial a, Hex_Axial b) noexcept { return not(a == b); }
};
 
struct Hex_Offset
{
  ca_index_t col = 0;
  ca_index_t row = 0;
 
  friend constexpr bool operator==(Hex_Offset a, Hex_Offset b) noexcept
  {
    return a.col == b.col and a.row == b.row;
  }
  friend constexpr bool operator!=(Hex_Offset a, Hex_Offset b) noexcept { return not(a == b); }
};
 
struct Hex_Cube
{
  ca_index_t x = 0;
  ca_index_t y = 0;
  ca_index_t z = 0;
 
  friend constexpr bool operator==(Hex_Cube a, Hex_Cube b) noexcept
  {
    return a.x == b.x and a.y == b.y and a.z == b.z;
  }
  friend constexpr bool operator!=(Hex_Cube a, Hex_Cube b) noexcept { return not(a == b); }
};
 
// ---------------------------------------------------------------------------
// Coordinate conversions.
// ---------------------------------------------------------------------------
 
[[nodiscard]] inline constexpr Hex_Offset axial_to_offset_even_r(Hex_Axial a) noexcept
{
  // even-r: col = q + (r + (r & 1)) / 2
  const ca_index_t col = a.q + (a.r + (a.r & 1)) / 2;
  return Hex_Offset{col, a.r};
}
 
[[nodiscard]] inline constexpr Hex_Axial offset_to_axial_even_r(Hex_Offset o) noexcept
{
  const ca_index_t q = o.col - (o.row + (o.row & 1)) / 2;
  return Hex_Axial{q, o.row};
}
 
[[nodiscard]] inline constexpr Hex_Offset axial_to_offset_odd_r(Hex_Axial a) noexcept
{
  const ca_index_t col = a.q + (a.r - (a.r & 1)) / 2;
  return Hex_Offset{col, a.r};
}
 
[[nodiscard]] inline constexpr Hex_Axial offset_to_axial_odd_r(Hex_Offset o) noexcept
{
  const ca_index_t q = o.col - (o.row - (o.row & 1)) / 2;
  return Hex_Axial{q, o.row};
}
 
[[nodiscard]] inline constexpr Hex_Cube axial_to_cube(Hex_Axial a) noexcept
{
  const ca_index_t x = a.q;
  const ca_index_t z = a.r;
  return Hex_Cube{x, -x - z, z};
}
 
[[nodiscard]] inline constexpr Hex_Axial cube_to_axial(Hex_Cube c) noexcept
{
  return Hex_Axial{c.x, c.z};
}
 
[[nodiscard]] inline constexpr ca_size_t hex_distance(Hex_Axial a, Hex_Axial b) noexcept
{
  const Hex_Cube ca = axial_to_cube(a);
  const Hex_Cube cb = axial_to_cube(b);
  auto absv = [](ca_index_t v) noexcept -> ca_index_t { return v < 0 ? -v : v; };
  const ca_index_t d = absv(ca.x - cb.x) + absv(ca.y - cb.y) + absv(ca.z - cb.z);
  return static_cast<ca_size_t>(d / 2);
}
 
[[nodiscard]] inline std::array<double, 2> axial_to_pixel_pointy(Hex_Axial a,
                                                                 double radius) noexcept
{
  const double sqrt3 = 1.7320508075688772;
  const double x = radius * (sqrt3 * static_cast<double>(a.q)
                             + (sqrt3 / 2.0) * static_cast<double>(a.r));
  const double y = radius * (3.0 / 2.0) * static_cast<double>(a.r);
  return {x, y};
}
 
[[nodiscard]] inline std::array<double, 2> axial_to_pixel_flat(Hex_Axial a,
                                                               double radius) noexcept
{
  const double sqrt3 = 1.7320508075688772;
  const double x = radius * (3.0 / 2.0) * static_cast<double>(a.q);
  const double y = radius * (sqrt3 * static_cast<double>(a.r)
                             + (sqrt3 / 2.0) * static_cast<double>(a.q));
  return {x, y};
}
 
template <typename Storage, typename Boundary = OpenBoundary>
class Hex_Lattice : public Lattice<Storage, Boundary>
{
  static_assert(Storage::rank == 2, "Hex_Lattice requires a 2D storage");
 
public:
  using base_type = Lattice<Storage, Boundary>;
  using state_type = typename base_type::state_type;
  using coord_type = typename base_type::coord_type;
  using extents_type = typename base_type::extents_type;
  static constexpr std::size_t rank = base_type::rank;
 
  using base_type::base_type;  
 
  [[nodiscard]] ca_size_t rows() const noexcept { return this->size(0); }
 
  [[nodiscard]] ca_size_t cols() const noexcept { return this->size(1); }
 
  [[nodiscard]] state_type at_axial(Hex_Axial a) const
  {
    return this->at(coord_type{a.r, a.q});
  }
 
  void set_axial(Hex_Axial a, const state_type &v)
  {
    this->set(coord_type{a.r, a.q}, v);
  }
 
  [[nodiscard]] state_type at_axial_safe(Hex_Axial a) const
  {
    return this->at_safe(coord_type{a.r, a.q});
  }
 
  [[nodiscard]] state_type at_offset_even_r(Hex_Offset o) const
  {
    return at_axial(offset_to_axial_even_r(o));
  }
 
  void set_offset_even_r(Hex_Offset o, const state_type &v)
  {
    set_axial(offset_to_axial_even_r(o), v);
  }
};
 
template <typename Lattice, typename Palette>
inline void render_hex_lattice_tikz(std::ostream &os,
                                    const Lattice &lat,
                                    Palette &&palette,
                                    double radius = 0.5,
                                    bool pointy_top = true)
{
  os << "% Aleph::CA::render_hex_lattice_tikz\n";
  os << "\\begin{tikzpicture}[x=1cm, y=-1cm]\n";
  for (ca_size_t r = 0; r < lat.rows(); ++r)
    for (ca_size_t q = 0; q < lat.cols(); ++q)
      {
        const Hex_Axial a{static_cast<ca_index_t>(q), static_cast<ca_index_t>(r)};
        const auto px
          = pointy_top ? axial_to_pixel_pointy(a, radius) : axial_to_pixel_flat(a, radius);
        const std::string colour = palette(lat.at_axial(a));
        const double rotation = pointy_top ? 30.0 : 0.0;
        os << "  \\node[regular polygon, regular polygon sides=6, draw, fill="
           << colour << ", inner sep=0pt, minimum size=" << (2 * radius)
           << "cm, rotate=" << rotation << "] at (" << px[0] << ", " << px[1] << ") {};\n";
      }
  os << "\\end{tikzpicture}\n";
}
 
template <typename Lattice, typename Palette>
[[nodiscard]] inline std::string render_hex_lattice_tikz(const Lattice &lat,
                                                         Palette &&palette,
                                                         double radius = 0.5,
                                                         bool pointy_top = true)
{
  std::ostringstream oss;
  render_hex_lattice_tikz(oss, lat, std::forward<Palette>(palette), radius, pointy_top);
  return oss.str();
}
 
}  // namespace CA
}  // namespace Aleph
 
#endif  // TPL_CA_HEX_LATTICE_H