tpl_ca_hex_lattice.H File Reference

Hexagonal lattice with axial / offset / cube coordinate conversions and a TikZ-compatible pixel mapping. More...

#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>

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Classes
struct	Aleph::CA::Hex_Axial
	Axial integer coordinates (q, r) of a hex cell. More...
struct	Aleph::CA::Hex_Offset
	Offset coordinates (col, row) for visualisation. More...
struct	Aleph::CA::Hex_Cube
	Cube coordinates (x, y, z) with the constraint x+y+z = 0. More...
class	Aleph::CA::Hex_Lattice< Storage, Boundary >
	Hexagonal lattice with axial accessors over a 2D storage. More...

Namespaces
namespace	Aleph
	Main namespace for Aleph-w library functions.
namespace	Aleph::CA

Functions
constexpr Hex_Offset	Aleph::CA::axial_to_offset_even_r (Hex_Axial a) noexcept
	Axial -> offset (even-r convention: even rows are shifted right).
constexpr Hex_Axial	Aleph::CA::offset_to_axial_even_r (Hex_Offset o) noexcept
	Offset (even-r) -> axial.
constexpr Hex_Offset	Aleph::CA::axial_to_offset_odd_r (Hex_Axial a) noexcept
	Axial -> offset (odd-r convention: odd rows are shifted right).
constexpr Hex_Axial	Aleph::CA::offset_to_axial_odd_r (Hex_Offset o) noexcept
	Offset (odd-r) -> axial.
constexpr Hex_Cube	Aleph::CA::axial_to_cube (Hex_Axial a) noexcept
	Axial -> cube.
constexpr Hex_Axial	Aleph::CA::cube_to_axial (Hex_Cube c) noexcept
	Cube -> axial.
constexpr ca_size_t	Aleph::CA::hex_distance (Hex_Axial a, Hex_Axial b) noexcept
	Hex distance between two axial coordinates.
std::array< double, 2 >	Aleph::CA::axial_to_pixel_pointy (Hex_Axial a, double radius) noexcept
	Pointy-top pixel coordinates of an axial cell.
std::array< double, 2 >	Aleph::CA::axial_to_pixel_flat (Hex_Axial a, double radius) noexcept
	Flat-top pixel coordinates of an axial cell.
template<typename Lattice , typename Palette >
void	Aleph::CA::render_hex_lattice_tikz (std::ostream &os, const Lattice &lat, Palette &&palette, double radius=0.5, bool pointy_top=true)
	Render a hex frame as a stand-alone TikZ picture.
template<typename Lattice , typename Palette >
std::string	Aleph::CA::render_hex_lattice_tikz (const Lattice &lat, Palette &&palette, double radius=0.5, bool pointy_top=true)
	Returns a std::string instead of writing to a stream.

Detailed Description

Hexagonal lattice with axial / offset / cube coordinate conversions and a TikZ-compatible pixel mapping.

Hexagonal CAs are conventionally described in axial coordinates (q, r): two integer axes selected so that neighbour offsets are symmetric (six unit steps, including two diagonals). Storing the cells as a regular 2D row-major buffer indexed by (r, q) matches the rectangular bounding parallelogram of the hex grid; visualizers switch to offset coordinates (col, row) (even-r or odd-r) where alternate rows are shifted by half a hex.

This header does three things:

• Defines Hex_Axial, Hex_Offset, Hex_Cube value types and free functions to convert between them. All conversions are lossless and round-trip exactly for valid inputs.
• Provides Hex_Lattice<Storage, Boundary>, a thin subclass of Lattice<Storage, Boundary> that adds axial/offset accessors and a hexagonal pixel mapping. The 2D rank is preserved, so the same Synchronous_Engine / Parallel_Synchronous_Engine and the existing Hex_Neighborhood (six axial offsets) work unchanged.
• Provides render_hex_lattice_tikz to dump a frame as a TikZ picture for inclusion in reports / papers.

Storage convention: coord c = {r, q}. Axis 0 stores r (axial row), axis 1 stores q (axial column). This matches the standard CA convention where axis 0 is the slowest-varying axis, and keeps the data layout cache-friendly for row-by-row iteration.

Author

Leandro Rabindranath Leon

Definition in file tpl_ca_hex_lattice.H.