/// <summary>
/// Constructs a table of the neighbours of each face.
/// Neighbours are listed in the same order as given by surface.NeighboursOf.
/// </summary>
public static int[][] Neighbours(IPolyhedron surface)
{
var neighbours = new int[surface.Faces.Count][];
foreach (var face in surface.Faces)
{
var indicesOfNeighbours = surface.NeighboursOf(face).Select(neighbour => surface.IndexOf(neighbour));
neighbours[surface.IndexOf(face)] = indicesOfNeighbours.ToArray();
}
return(neighbours);
}
/// <summary>
/// Constructs a table of the directions towards the faces neighbours in the face's tangent space.
/// </summary>
public static Vector[][] Directions(IPolyhedron surface)
{
var directions = new Vector[surface.Faces.Count][];
foreach (var face in surface.Faces)
{
var neighboursOfFace = surface.NeighboursOf(face);
var localDirections = neighboursOfFace.Select(neighbour => Direction(face, neighbour));
directions[surface.IndexOf(face)] = localDirections.ToArray();
}
return(directions);
}
// Gets the neighbours of a face which are within radius steps of it.
private IEnumerable <Face> GetNearbyFaces(Face center, int radius)
{
var faces = new HashSet <Face> {
center
};
for (int i = 1; i < radius; i++)
{
var neighbours = faces.SelectMany(face => _polyhedron.NeighboursOf(face)).ToList();
faces.UnionWith(neighbours);
}
return(faces);
}
/// <summary>
/// Constructs a table of the vectors perpendicular to a vertex and normal to each adjoining edge.
///
/// Normals point anticlockwise around the vertex.
/// </summary>
public static Vector[][] EdgeNormals(IPolyhedron surface)
{
var edgeNormalsTable = new Vector[surface.Vertices.Count][];
foreach (var vertex in surface.Vertices)
{
var vertexVector = vertex.Position;
var edgeVectors = surface.NeighboursOf(vertex).Select(neighbour => (neighbour.Position - vertexVector));
var edgeNormals = edgeVectors.Select(edgeVector => Vector.CrossProduct(vertexVector, edgeVector).Normalize()).ToArray();
edgeNormalsTable[surface.IndexOf(vertex)] = edgeNormals;
}
return(edgeNormalsTable);
}
/// <summary>
/// Constructs a table of the distances from each face's center to it's neighbour's centers.
/// Neighbours are listed in the same order as given by surface.NeighboursOf.
/// </summary>
public static double[][] Distances(IPolyhedron surface)
{
var edgeLengths = new double[surface.Faces.Count][];
foreach (var face in surface.Faces)
{
var distances =
surface.
NeighboursOf(face).
Select(neighbour => VectorUtilities.GeodesicDistance(face.SphericalCenter(), neighbour.SphericalCenter()));
edgeLengths[surface.IndexOf(face)] = distances.ToArray();
}
//TODO: Work out how to turn this into spherical area.
return(edgeLengths);
}