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// Copyright (C) 2019 Jorgen S. Dokken
//
// This file is part of DOLFINx (https://www.fenicsproject.org)
//
// SPDX-License-Identifier: LGPL-3.0-or-later
#pragma once
#include <array>
#include <cstdint>
#include <dolfinx/mesh/cell_types.h>
#include <span>
#include <vector>
/// @brief Functions for the re-ordering of input mesh topology to the
/// DOLFINx ordering, and transpose orderings for file output.
///
/// Basix ordering is used for the geometry nodes, and is shown below
/// for a range of cell types.
/*!
@verbatim
Triangle: Triangle6: Triangle10:
v
^
|
2 2 2
|`\ |`\ | \
| `\ | `\ 6 4
| `\ 4 `3 | \
| `\ | `\ 5 9 3
| `\ | `\ | \
0----------1 --> u 0-----5----1 0---7---8---1
Quadrilateral: Quadrilateral9: Quadrilateral16:
v
^
|
2-----------3 2-----7-----3 2--10--11---3
| | | | | |
| | | | 7 14 15 9
| | 5 8 6 | |
| | | | 6 12 13 8
| | | | | |
0-----------1 --> u 0-----4-----1 0---4---5---1
Tetrahedron: Tetrahedron10: Tetrahedron20
v
/
2 2 2
,/|`\ ,/\`\ ,/|`\
,/ \ `\ ,/ \ `\. 13 | `9
,/ '. `\ ,8 '. `6 ,/ 4 `\
,/ | `\ ,/ 4 `\ 12 19 | `8
,/ | `\ ,/ | `\ ,/ | `\
0-----------'.--------1 -> u 0--------9--'.--------1 0-----14----'.--15----1
`\. | ,/ `\. | ,/ `\. 17 | 16 ,/
`\. | ,/ `\. | ,5 10. 18 5 ,6
`\. '. ,/ `7. '. ,/ `\. . 7
`\. |/ `\. |/ 11. |/
`3 `3 `3
`\.
w
Hexahedron: Hexahedron27:
w
6----------7 6----19----7
/| ^ v /| /| /|
/ | | / / | 17 | 25 18|
/ | | / / | / 14 24 / 15
4----------5 | 4----16----5 |
| | +--|---|--> u |22 | 26 | 23|
| 2------+---3 | 2----13+---3
| / | / 10 / 21 12 /
| / | / | 9 20 | 11
|/ |/ |/ |/
0----------1 0-----8----1
Prism: Prism15:
w
^
|
3 3
,/|`\ ,/|`\
,/ | `\ 12 | 13
,/ | `\ ,/ | `\
4------+------5 4------14-----5
| | | | 8 |
| ,/|`\ | | | |
| ,/ | `\ | | | |
|,/ 0 `\| 10 0 11
./| ,/ `\ |\ | ,/ `\ |
/ | ,/ `\ | `\ | ,6 `7 |
u |,/ `\| v |,/ `\|
1-------------2 1------9------2
Pyramid: Pyramid13:
4 4
,/|\ ,/|\
,/ .'|\ ,/ .'|\
v ,/ | | \ ,/ | | \
\. ,/ .' | `. ,/ .' | `.
\. | '. \ 11 | 12 \
,/ \. .' w | \ ,/ .' | \
,/ \. | ^ | \ ,/ 7 | 9
2----------\'--|-3 `. 2-------10-.'----3 `.
`\ | \.| `\ \ `\ | `\ \
`\ .' +----`\ - \ -> u `6 .' 8 \
`\ | `\ \ `\ | `\ \
`\.' ` `\ `\.' ` `\
0-----------------1 0--------5--------1
@endverbatim
*/
namespace dolfinx::io::cells
{
/// @brief Get the Lagrange order of a given cell with a given number of
/// nodes.
///
/// @param[in] type Cell shape.
/// @param[in] num_nodes Number of cell 'nodes'
/// @return Lagrange order of the cell type.
int cell_degree(mesh::CellType type, int num_nodes);
/// @brief Permutation array to map from VTK to DOLFINx node ordering.
///
/// @param[in] type Cell shape.
/// @param[in] num_nodes Number of cell 'nodes'
/// @return Permutation array `p` for permuting from VTK ordering to
/// DOLFINx ordering, i.e. `a_dolfin[i] = a_vtk[p[i]]`.
///
/// @details If `p = [0, 2, 1, 3]` and `a = [10, 3, 4, 7]`, then `a_p =
/// [a[p[0]], a[p[1]], a[p[2]], a[p[3]]] = [10, 4, 3, 7]`.
std::vector<std::uint16_t> perm_vtk(mesh::CellType type, int num_nodes);
/// @brief Permutation array to map from Gmsh to DOLFINx node ordering.
///
/// @param[in] type Cell shape.
/// @param[in] num_nodes Number of cell 'nodes'
/// @return Permutation array `p` for permuting from Gmsh ordering to
/// DOLFINx ordering, i.e. `a_dolfin[i] = a_gmsh[p[i]]`.
///
/// @details If `p = [0, 2, 1, 3]` and `a = [10, 3, 4, 7]`, then `a_p
/// =[a[p[0]], a[p[1]], a[p[2]], a[p[3]]] = [10, 4, 3, 7]`.
std::vector<std::uint16_t> perm_gmsh(mesh::CellType type, int num_nodes);
/// @brief Compute the transpose of a re-ordering map.
///
/// @param[in] map A re-ordering map.
/// @return Transpose of the `map`. E.g., is `map = {1, 2, 3, 0}`, the
/// transpose will be `{3 , 0, 1, 2 }`.
std::vector<std::uint16_t> transpose(std::span<const std::uint16_t> map);
/// @brief Permute cell topology by applying a permutation array for
/// each cell.
///
/// @param[in] cells Array of cell topologies, with each row
/// representing a cell (row-major storage).
/// @param[in] shape Shape of the `cells` array.
/// @param[in] p Permutation array that maps `a_p[i] = a[p[i]]`, where
/// `a_p` is the permuted array.
/// @return Permuted cell topology, where for a cell `v_new[i] =
/// v_old[map[i]]`. The storage is row-major and the shape is the same
/// as `cells`.
std::vector<std::int64_t> apply_permutation(std::span<const std::int64_t> cells,
std::array<std::size_t, 2> shape,
std::span<const std::uint16_t> p);
/// @brief Get VTK cell identifier.
///
/// @param[in] cell Cell type.
/// @param[in] dim Topological dimension of the cell.
/// @return VTK cell identifier.
std::int8_t get_vtk_cell_type(mesh::CellType cell, int dim);
} // namespace dolfinx::io::cells
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