//Take a LatticeGeometry and return the polygons that spatially make it up
//This is useful for display purposes, each lattice element then corresponds to a polygon element
public static void calculate_polygon_tiling(List <List <Vector2D> > polygon_list, Lattice_Geometry lattice_geometry)
{
Lattice_Graph lattice_graph = lattice_geometry.Lattice;
List <List <int> > graph = lattice_graph.GetVertices();
List <Vector2D> geometry = lattice_geometry.GeometryPoints;
int p = lattice_graph.P;
int q = lattice_graph.Q;
double base_length = lattice_geometry.LengthScale * EuclideanTransversalLength(p, q);
if (lattice_graph.GetCurvatureSign() == -1)
{
base_length = HyperbolicToPpoincare(HyperbolicTransversalLength(p, q));
}
Vector2D base_vector = new Gyrovector2D(base_length, 0.0);
double dt = 2 * Math.PI / p;
base_vector = base_vector.Rotate(Math.PI / p);
if (lattice_graph.Size == 1)
{
List <Vector2D> poly = new List <Vector2D>();
for (int i = 0; i < p; i++)
{
poly.Add(base_vector.Rotate(i * dt));
}
polygon_list.Add(poly);
return;
}
for (int i = 0; i < lattice_graph.Size; i++)
{
List <Vector2D> poly = new List <Vector2D>(p);
Vector2D current = geometry[i];
Vector2D neighbor = geometry[graph[i][0]];
double guide_direction = ((-current) + neighbor).Phase();
Vector2D offset = base_vector.Rotate(guide_direction);
for (int k = 0; k < p; k++)
{
poly.Add(current + offset.Rotate(k * dt));
}
polygon_list.Add(poly);
}
}
public Lattice_Geometry(int p, int q, int r, double spacing)
{
Lattice = new Lattice_Graph(p, q, r, false);
if (Lattice.GetCurvatureSign() == 0)
{
GuideVector = new Euclvector2D(spacing, 0.0);
}
else if (Lattice.GetCurvatureSign() == -1)
{
GuideVector = new Gyrovector2D(spacing, 0.0);
}
valid = new List <bool>(4000);
GeometryPoints = new List <Vector2D>(4000);
LengthScale = spacing;
Compose();
}
public Lattice_Geometry(Lattice_Graph lat, double spacing)
{
Lattice = lat;
if (lat.GetCurvatureSign() == 0)
{
GuideVector = new Euclvector2D(spacing, 0.0);
}
else if (lat.GetCurvatureSign() == -1)
{
GuideVector = new Gyrovector2D(spacing, 0.0);
}
valid = new List <bool>(4000);
GeometryPoints = new List <Vector2D>(4000);
LengthScale = spacing;
Compose();
}
//Take a polygon list and generate a list of edges, useful for display purposes
public static void graph_to_edge_list(Lattice_Graph lattice, List <Edge <int> > edge_list)
{
List <List <int> > graph = lattice.GetVertices();
for (int i = 0; i < graph.Count; i++)
{
List <int> vertex = graph[i];
for (int j = 0; j < vertex.Count; j++)
{
Edge <int> edge = new Edge <int>(i, vertex[j]);
if (!edge_list.Contains(edge))
{
edge_list.Add(edge);
}
}
}
}
