tpl_ca_triangular_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_TRIANGULAR_LATTICE_H
#define TPL_CA_TRIANGULAR_LATTICE_H
 
#include <array>
#include <cstddef>
#include <ostream>
#include <sstream>
#include <string>
#include <utility>
 
#include <ah-errors.H>
 
#include <ca-traits.H>
#include <tpl_ca_concepts.H>
#include <tpl_ca_lattice.H>
 
namespace Aleph {
namespace CA {
 
struct Tri_Coord
{
  ca_index_t i = 0;
  ca_index_t j = 0;
 
  friend constexpr bool operator==(const Tri_Coord & a, const Tri_Coord & b) noexcept
  {
    return a.i == b.i and a.j == b.j;
  }
  friend constexpr bool operator!=(const Tri_Coord & a, const Tri_Coord & b) noexcept { return not(a == b); }
};
 
[[nodiscard]] inline constexpr int tri_parity(const Tri_Coord & c) noexcept
{
  using unsigned_t = std::make_unsigned_t<ca_index_t>;
  return static_cast<int>((static_cast<unsigned_t>(c.i) + static_cast<unsigned_t>(c.j)) & 1u);
}
 
[[nodiscard]] inline constexpr bool tri_is_up(const Tri_Coord & c) noexcept
{
  return tri_parity(c) == 0;
}
 
[[nodiscard]] inline constexpr bool tri_is_down(const Tri_Coord & c) noexcept
{
  return tri_parity(c) == 1;
}
 
[[nodiscard]] inline std::array<double, 2> tri_pixel_centre(const Tri_Coord & c,
                                                            const double side) noexcept
{
  constexpr double sqrt3 = 1.7320508075688772;
  const double height = side * sqrt3 / 2.0;
  const double x = (static_cast<double>(c.j) + 1.0) * (side / 2.0);
  const double y_base = static_cast<double>(c.i) * height + height / 2.0;
  const double y = tri_is_up(c) ? y_base - height / 6.0 : y_base + height / 6.0;
  return {x, y};
}
 
template <typename Storage, typename Boundary = OpenBoundary>
class Triangular_Lattice : public Lattice<Storage, Boundary>
{
  static_assert(Storage::rank == 2, "Triangular_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_tri(Tri_Coord c) const
  {
    return this->at(coord_type{c.i, c.j});
  }
 
  void set_tri(Tri_Coord c, const state_type &v)
  {
    this->set(coord_type{c.i, c.j}, v);
  }
 
  [[nodiscard]] state_type at_tri_safe(Tri_Coord c) const
  {
    return this->at_safe(coord_type{c.i, c.j});
  }
};
 
template <typename Lattice, typename Palette>
inline void render_triangular_lattice_tikz(std::ostream &os,
                                           const Lattice &lat,
                                           Palette &&palette,
                                           const double side = 1.0)
{
  os << "% Aleph::CA::render_triangular_lattice_tikz\n";
  os << "\\begin{tikzpicture}[x=1cm, y=-1cm]\n";
  for (ca_size_t i = 0; i < lat.rows(); ++i)
    for (ca_size_t j = 0; j < lat.cols(); ++j)
      {
        const Tri_Coord c{static_cast<ca_index_t>(i), static_cast<ca_index_t>(j)};
        const auto px = tri_pixel_centre(c, side);
        const std::string colour = palette(lat.at_tri(c));
        const double rotation = tri_is_up(c) ? 0.0 : 180.0;
        os << "  \\node[regular polygon, regular polygon sides=3, draw, fill=" << colour
           << ", inner sep=0pt, minimum size=" << side
           << "cm, rotate=" << rotation << "] at (" << px[0] << ", " << px[1] << ") {};\n";
      }
  os << "\\end{tikzpicture}\n";
}
 
template <typename Lattice, typename Palette>
[[nodiscard]] inline std::string render_triangular_lattice_tikz(const Lattice &lat,
                                                                Palette &&palette,
                                                                double side = 1.0)
{
  std::ostringstream oss;
  render_triangular_lattice_tikz(oss, lat, std::forward<Palette>(palette), side);
  return oss.str();
}
 
}  // namespace CA
}  // namespace Aleph
 
#endif  // TPL_CA_TRIANGULAR_LATTICE_H