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// Copyright (c) 2020 Chris Richardson
// FEniCS Project
// SPDX-License-Identifier: MIT
#include "cell.h"
#include "lagrange.h"
#include "quadrature.h"
#include <iostream>
#include <map>
using namespace basix;
//-----------------------------------------------------------------------------
Eigen::ArrayXXd cell::geometry(cell::type celltype)
{
Eigen::ArrayXXd geom;
switch (celltype)
{
case cell::type::interval:
geom.resize(2, 1);
geom << 0.0, 1.0;
break;
case cell::type::triangle:
geom.resize(3, 2);
geom << 0.0, 0.0, 1.0, 0.0, 0.0, 1.0;
break;
case cell::type::quadrilateral:
geom.resize(4, 2);
geom << 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0;
break;
case cell::type::tetrahedron:
geom.resize(4, 3);
geom << 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0;
break;
case cell::type::prism:
geom.resize(6, 3);
geom << 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0,
0.0, 1.0, 0.0, 1.0, 1.0;
break;
case cell::type::pyramid:
geom.resize(5, 3);
geom << 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0,
0.0, 1.0;
break;
case cell::type::hexahedron:
geom.resize(8, 3);
geom << 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0,
0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0;
break;
default:
throw std::runtime_error("Unsupported cell type");
}
return geom;
}
//-----------------------------------------------------------------------------
std::vector<std::vector<std::vector<int>>> cell::topology(cell::type celltype)
{
std::vector<std::vector<std::vector<int>>> topo;
switch (celltype)
{
case cell::type::interval:
topo.resize(2);
// Vertices
topo[0] = {{0}, {1}};
// Cell
topo[1] = {{0, 1}};
break;
case cell::type::triangle:
topo.resize(3);
// Vertices
topo[0] = {{0}, {1}, {2}};
// Edges
topo[1] = {{1, 2}, {0, 2}, {0, 1}};
// Cell
topo[2] = {{0, 1, 2}};
break;
case cell::type::quadrilateral:
topo.resize(3);
// FIXME - check all these
// Vertices
topo[0] = {{0}, {1}, {2}, {3}};
// Edges
topo[1] = {{0, 1}, {0, 2}, {1, 3}, {2, 3}};
// Cell
topo[2] = {{0, 1, 2, 3}};
break;
case cell::type::tetrahedron:
topo.resize(4);
// Vertices
topo[0] = {{0}, {1}, {2}, {3}};
// Edges
topo[1] = {{2, 3}, {1, 3}, {1, 2}, {0, 3}, {0, 2}, {0, 1}};
// Faces
topo[2] = {{1, 2, 3}, {0, 2, 3}, {0, 1, 3}, {0, 1, 2}};
// Cell
topo[3] = {{0, 1, 2, 3}};
break;
case cell::type::prism:
// FIXME: check
topo.resize(4);
// Vertices
topo[0] = {{0}, {1}, {2}, {3}, {4}, {5}};
// Edges
topo[1] = {{0, 1}, {1, 2}, {2, 0}, {0, 3}, {1, 4},
{2, 5}, {3, 4}, {4, 5}, {5, 3}};
// Faces
topo[2] = {{0, 1, 2}, {0, 1, 3, 4}, {1, 2, 4, 5}, {2, 0, 5, 3}, {3, 4, 5}};
// Cell
topo[3] = {{0, 1, 2, 3, 4, 5}};
break;
case cell::type::pyramid:
// FIXME: check all these
topo.resize(4);
// Vertices
topo[0] = {{0}, {1}, {2}, {3}, {4}};
// Edges
topo[1] = {{0, 1}, {0, 2}, {2, 3}, {3, 1}, {0, 4}, {1, 4}, {2, 4}, {3, 4}};
// Faces
topo[2] = {{0, 1, 2, 3}, {0, 1, 4}, {0, 2, 4}, {2, 3, 4}, {3, 1, 4}};
// Cell
topo[3] = {{0, 1, 2, 3, 4}};
break;
case cell::type::hexahedron:
topo.resize(4);
// FIXME: check over
// Vertices
topo[0] = {{0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}};
// Edges
topo[1] = {{0, 1}, {0, 2}, {0, 4}, {1, 3}, {1, 5}, {2, 3},
{2, 6}, {3, 7}, {4, 5}, {4, 6}, {5, 7}, {6, 7}};
// Faces
topo[2] = {{0, 1, 2, 3}, {0, 1, 4, 5}, {0, 2, 4, 6},
{1, 3, 5, 7}, {2, 3, 6, 7}, {4, 5, 6, 7}};
// Cell
topo[3] = {{0, 1, 2, 3, 4, 5, 6, 7}};
break;
default:
throw std::runtime_error("Unsupported cell type");
}
return topo;
}
//-----------------------------------------------------------------------------
int cell::topological_dimension(cell::type cell_type)
{
switch (cell_type)
{
case cell::type::interval:
return 1;
case cell::type::triangle:
return 2;
case cell::type::quadrilateral:
return 2;
case cell::type::tetrahedron:
return 3;
case cell::type::hexahedron:
return 3;
case cell::type::prism:
return 3;
case cell::type::pyramid:
return 3;
default:
throw std::runtime_error("Unsupported cell type");
}
return 0;
}
//-----------------------------------------------------------------------------
Eigen::ArrayXXd cell::sub_entity_geometry(cell::type celltype, int dim,
int index)
{
std::vector<std::vector<std::vector<int>>> cell_topology
= cell::topology(celltype);
Eigen::ArrayXXd cell_geometry = cell::geometry(celltype);
if (dim < 0 or dim >= (int)cell_topology.size())
throw std::runtime_error("Invalid dimension for sub-entity");
const std::vector<std::vector<int>>& t = cell_topology[dim];
if (index < 0 or index >= (int)t.size())
throw std::runtime_error("Invalid entity index");
Eigen::ArrayXXd sub_entity(t[index].size(), cell_geometry.cols());
for (int i = 0; i < sub_entity.rows(); ++i)
sub_entity.row(i) = cell_geometry.row(t[index][i]);
return sub_entity;
}
//----------------------------------------------------------------------------
int cell::sub_entity_count(cell::type celltype, int dim)
{
const std::vector<std::vector<std::vector<int>>> cell_topology
= cell::topology(celltype);
return cell_topology.at(dim).size();
}
//----------------------------------------------------------------------------
cell::type cell::sub_entity_type(cell::type celltype, int dim, int index)
{
const int tdim = cell::topological_dimension(celltype);
assert(dim >= 0 and dim <= tdim);
if (dim == 0)
return cell::type::point;
else if (dim == 1)
return cell::type::interval;
else if (dim == tdim)
return celltype;
const std::vector<std::vector<std::vector<int>>> t = cell::topology(celltype);
const std::vector<int>& entity = t[dim][index];
switch (entity.size())
{
case 3:
return cell::type::triangle;
case 4:
return cell::type::quadrilateral;
default:
throw std::runtime_error("Error in sub_entity_type");
}
}
//-----------------------------------------------------------------------------
cell::type cell::str_to_type(std::string name)
{
static const std::map<std::string, cell::type> name_to_type
= {{"point", cell::type::point},
{"interval", cell::type::interval},
{"triangle", cell::type::triangle},
{"tetrahedron", cell::type::tetrahedron},
{"quadrilateral", cell::type::quadrilateral},
{"pyramid", cell::type::pyramid},
{"prism", cell::type::prism},
{"hexahedron", cell::type::hexahedron}};
auto it = name_to_type.find(name);
if (it == name_to_type.end())
throw std::runtime_error("Can't find name " + name);
return it->second;
}
//-----------------------------------------------------------------------------
const std::string& cell::type_to_str(cell::type type)
{
static const std::map<cell::type, std::string> type_to_name
= {{cell::type::point, "point"},
{cell::type::interval, "interval"},
{cell::type::triangle, "triangle"},
{cell::type::tetrahedron, "tetrahedron"},
{cell::type::quadrilateral, "quadrilateral"},
{cell::type::pyramid, "pyramid"},
{cell::type::prism, "prism"},
{cell::type::hexahedron, "hexahedron"}};
auto it = type_to_name.find(type);
if (it == type_to_name.end())
throw std::runtime_error("Can't find type");
return it->second;
}
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