/// <summary>
/// Generate the Voronoi diagram from given triangle mesh..
/// </summary>
/// <param name="mesh"></param>
/// <param name="bounded"></param>
protected void Generate(Mesh mesh)
{
mesh.Renumber();
base.edges = new List <HalfEdge>();
this.rays = new List <HalfEdge>();
// Allocate space for Voronoi diagram.
var vertices = new Vertex[mesh.triangles.Count + mesh.hullsize];
var faces = new Face[mesh.vertices.Count];
if (factory == null)
{
factory = new DefaultVoronoiFactory();
}
factory.Initialize(vertices.Length, 2 * mesh.NumberOfEdges, faces.Length);
// Compute triangles circumcenters.
var map = ComputeVertices(mesh, vertices);
// Create all Voronoi faces.
foreach (var vertex in mesh.vertices.Values)
{
faces[vertex.id] = factory.CreateFace(vertex);
}
ComputeEdges(mesh, vertices, faces, map);
// At this point all edges are computed, but the (edge.next) pointers aren't set.
ConnectEdges(map);
base.vertices = new List <Vertex>(vertices);
base.faces = new List <Face>(faces);
}
/// <summary>
/// Generate the Voronoi diagram from given triangle mesh..
/// </summary>
/// <param name="mesh"></param>
/// <param name="bounded"></param>
protected void Generate(Mesh mesh)
{
mesh.Renumber();
base.edges = new List<HalfEdge>();
this.rays = new List<HalfEdge>();
// Allocate space for Voronoi diagram.
var vertices = new Vertex[mesh.triangles.Count + mesh.hullsize];
var faces = new Face[mesh.vertices.Count];
if (factory == null)
{
factory = new DefaultVoronoiFactory();
}
factory.Initialize(vertices.Length, 2 * mesh.NumberOfEdges, faces.Length);
// Compute triangles circumcenters.
var map = ComputeVertices(mesh, vertices);
// Create all Voronoi faces.
foreach (var vertex in mesh.vertices.Values)
{
faces[vertex.id] = factory.CreateFace(vertex);
}
ComputeEdges(mesh, vertices, faces, map);
// At this point all edges are computed, but the (edge.next) pointers aren't set.
ConnectEdges(map);
base.vertices = new List<Vertex>(vertices);
base.faces = new List<Face>(faces);
}
/**
* Iterate over every edge in the voronoi graph building edge objects and connecting centers and corners.
* This method is very important to complete the graph to be used for all later stages!
*/
internal static List <Edge> createEdges(VoronoiBase voronoi, List <Center> centers, List <Corner> corners)
{
List <Edge> edges = new List <Edge>();
List <HalfEdge> halfEdges = voronoi.HalfEdges;
foreach (HalfEdge e0 in halfEdges)
{
HalfEdge e1 = e0.Twin;
if (e1.ID < e0.ID)
{
continue;
}
TriangleNet.Topology.DCEL.Vertex v0 = e0.Origin;
TriangleNet.Topology.DCEL.Vertex v1 = e1.Origin;
Corner corner0 = corners[v0.ID];
Corner corner1 = corners[v1.ID];
Face face0 = e0.Face;
Face face1 = e1.Face;
Center center0 = face0.ID < 0 ? null : centers[face0.ID];
Center center1 = face1.ID < 0 ? null : centers[face1.ID];
bool isBorder = center0 == null || center1 == null;
edges.Add(makeEdge(isBorder, corner0, corner1, center0, center1));
}
return(edges);
}
internal static List <Corner> createCorners(List <TriangleNet.Topology.DCEL.Vertex> vertices)
{
List <Corner> idCorners = new List <Corner>(vertices.Count);
for (int i = 0; i < vertices.Count; i++)
{
TriangleNet.Topology.DCEL.Vertex vertex = vertices[i];
idCorners.Add(new Corner(new Coord((float)vertex.X, 0, (float)vertex.Y)));
}
return(idCorners);
}
/// <summary>
/// Generate the Voronoi diagram from given triangle mesh..
/// </summary>
/// <param name="mesh"></param>
protected void Generate(Mesh mesh)
{
base.edges = new List <HalfEdge>();
this.rays = new List <HalfEdge>();
// Undead vertices cannot be Voronoi cell generators.
int count = mesh.vertices.Count - mesh.undeads;
// Allocate space for Voronoi diagram.
var vertices = new Vertex[mesh.triangles.Count + mesh.hullsize];
var faces = new Face[count];
if (factory == null)
{
factory = new DefaultVoronoiFactory();
}
factory.Initialize(vertices.Length, 2 * mesh.NumberOfEdges, faces.Length);
// Compute triangles circumcenters.
var map = ComputeVertices(mesh, vertices);
// Ensure linear numbering of vertices (excluding undeads).
int vid = 0;
// Create all Voronoi faces, skipping undead vertices.
foreach (var vertex in mesh.vertices.Values)
{
if (vertex.type == VertexType.UndeadVertex)
{
vertex.id = count++;
}
else
{
vertex.id = vid++;
faces[vertex.id] = factory.CreateFace(vertex);
}
}
ComputeEdges(mesh, vertices, faces, map);
// At this point all edges are computed, but the (edge.next) pointers aren't set.
ConnectEdges(map);
base.vertices = new List <Vertex>(vertices);
base.faces = new List <Face>(faces);
}
/// <summary>
/// Compute the Voronoi vertices (the circumcenters of the triangles).
/// </summary>
/// <returns>An empty map, which will map all vertices to a list of leaving edges.</returns>
protected List<HalfEdge>[] ComputeVertices(Mesh mesh, Vertex[] vertices)
{
Otri tri = default(Otri);
double xi = 0, eta = 0;
Vertex vertex;
Point pt;
int id;
// Maps all vertices to a list of leaving edges.
var map = new List<HalfEdge>[mesh.triangles.Count];
// Compue triangle circumcenters
foreach (var t in mesh.triangles)
{
id = t.id;
tri.tri = t;
pt = predicates.FindCircumcenter(tri.Org(), tri.Dest(), tri.Apex(), ref xi, ref eta);
vertex = factory.CreateVertex(pt.x, pt.y);
vertex.id = id;
vertices[id] = vertex;
map[id] = new List<HalfEdge>();
}
return map;
}
/// <summary>
/// Compute the edges of the Voronoi diagram.
/// </summary>
/// <param name="mesh"></param>
/// <param name="vertices"></param>
/// <param name="faces"></param>
/// <param name="map">Empty vertex map.</param>
protected void ComputeEdges(Mesh mesh, Vertex[] vertices, Face[] faces, List<HalfEdge>[] map)
{
Otri tri, neighbor = default(Otri);
TriangleNet.Geometry.Vertex org, dest;
double px, py;
int id, nid, count = mesh.triangles.Count;
Face face, neighborFace;
HalfEdge edge, twin;
Vertex vertex, end;
// Count infinte edges (vertex id for their endpoints).
int j = 0;
// Count half-edges (edge ids).
int k = 0;
// To loop over the set of edges, loop over all triangles, and look at the
// three edges of each triangle. If there isn't another triangle adjacent
// to the edge, operate on the edge. If there is another adjacent triangle,
// operate on the edge only if the current triangle has a smaller id than
// its neighbor. This way, each edge is considered only once.
foreach (var t in mesh.triangles)
{
id = t.id;
tri.tri = t;
for (int i = 0; i < 3; i++)
{
tri.orient = i;
tri.Sym(ref neighbor);
nid = neighbor.tri.id;
if (id < nid || nid < 0)
{
// Get the endpoints of the current triangle edge.
org = tri.Org();
dest = tri.Dest();
face = faces[org.id];
neighborFace = faces[dest.id];
vertex = vertices[id];
// For each edge in the triangle mesh, there's a corresponding edge
// in the Voronoi diagram, i.e. two half-edges will be created.
if (nid < 0)
{
// Unbounded edge, direction perpendicular to the boundary edge,
// pointing outwards.
px = dest.y - org.y;
py = org.x - dest.x;
end = factory.CreateVertex(vertex.x + px, vertex.y + py);
end.id = count + j++;
vertices[end.id] = end;
edge = factory.CreateHalfEdge(end, face);
twin = factory.CreateHalfEdge(vertex, neighborFace);
// Make (face.edge) always point to an edge that starts at an infinite
// vertex. This will allow traversing of unbounded faces.
face.edge = edge;
face.bounded = false;
map[id].Add(twin);
rays.Add(twin);
}
else
{
end = vertices[nid];
// Create half-edges.
edge = factory.CreateHalfEdge(end, face);
twin = factory.CreateHalfEdge(vertex, neighborFace);
// Add to vertex map.
map[nid].Add(edge);
map[id].Add(twin);
}
vertex.leaving = twin;
end.leaving = edge;
edge.twin = twin;
twin.twin = edge;
edge.id = k++;
twin.id = k++;
this.edges.Add(edge);
this.edges.Add(twin);
}
}
}
}
public static DcelMesh ToDCEL(Mesh mesh)
{
var dcel = new DcelMesh();
var vertices = new HVertex[mesh.vertices.Count];
var faces = new Face[mesh.triangles.Count];
dcel.HalfEdges.Capacity = 2 * mesh.NumberOfEdges;
mesh.Renumber();
HVertex vertex;
foreach (var v in mesh.vertices.Values)
{
vertex = new HVertex(v.x, v.y);
vertex.id = v.id;
vertex.label = v.label;
vertices[v.id] = vertex;
}
// Maps a triangle to its 3 edges (used to set next pointers).
var map = new List<HalfEdge>[mesh.triangles.Count];
Face face;
foreach (var t in mesh.triangles)
{
face = new Face(null);
face.id = t.id;
faces[t.id] = face;
map[t.id] = new List<HalfEdge>(3);
}
Otri tri = default(Otri), neighbor = default(Otri);
TriangleNet.Geometry.Vertex org, dest;
int id, nid, count = mesh.triangles.Count;
HalfEdge edge, twin, next;
var edges = dcel.HalfEdges;
// Count half-edges (edge ids).
int k = 0;
// Maps a vertex to its leaving boundary edge.
var boundary = new Dictionary<int, HalfEdge>();
foreach (var t in mesh.triangles)
{
id = t.id;
tri.tri = t;
for (int i = 0; i < 3; i++)
{
tri.orient = i;
tri.Sym(ref neighbor);
nid = neighbor.tri.id;
if (id < nid || nid < 0)
{
face = faces[id];
// Get the endpoints of the current triangle edge.
org = tri.Org();
dest = tri.Dest();
// Create half-edges.
edge = new HalfEdge(vertices[org.id], face);
twin = new HalfEdge(vertices[dest.id], nid < 0 ? Face.Empty : faces[nid]);
map[id].Add(edge);
if (nid >= 0)
{
map[nid].Add(twin);
}
else
{
boundary.Add(dest.id, twin);
}
// Set leaving edges.
edge.origin.leaving = edge;
twin.origin.leaving = twin;
// Set twin edges.
edge.twin = twin;
twin.twin = edge;
edge.id = k++;
twin.id = k++;
edges.Add(edge);
edges.Add(twin);
}
}
}
// Set next pointers for each triangle face.
foreach (var t in map)
{
edge = t[0];
next = t[1];
if (edge.twin.origin.id == next.origin.id)
{
edge.next = next;
next.next = t[2];
t[2].next = edge;
}
else
{
edge.next = t[2];
next.next = edge;
t[2].next = next;
}
}
// Resolve boundary edges.
foreach (var e in boundary.Values)
{
e.next = boundary[e.twin.origin.id];
}
dcel.Vertices.AddRange(vertices);
dcel.Faces.AddRange(faces);
return dcel;
}
public static DcelMesh ToDCEL(Mesh mesh)
{
var dcel = new DcelMesh();
var vertices = new HVertex[mesh.vertices.Count];
var faces = new Face[mesh.triangles.Count];
dcel.HalfEdges.Capacity = 2 * mesh.NumberOfEdges;
mesh.Renumber();
HVertex vertex;
foreach (var v in mesh.vertices.Values)
{
vertex = new HVertex(v.x, v.y);
vertex.id = v.id;
vertex.label = v.label;
vertices[v.id] = vertex;
}
// Maps a triangle to its 3 edges (used to set next pointers).
var map = new List <HalfEdge> [mesh.triangles.Count];
Face face;
foreach (var t in mesh.triangles)
{
face = new Face(null);
face.id = t.id;
faces[t.id] = face;
map[t.id] = new List <HalfEdge>(3);
}
Otri tri = default(Otri), neighbor = default(Otri);
TriangleNet.Geometry.Vertex org, dest;
int id, nid, count = mesh.triangles.Count;
HalfEdge edge, twin, next;
var edges = dcel.HalfEdges;
// Count half-edges (edge ids).
int k = 0;
// Maps a vertex to its leaving boundary edge.
var boundary = new Dictionary <int, HalfEdge>();
foreach (var t in mesh.triangles)
{
id = t.id;
tri.tri = t;
for (int i = 0; i < 3; i++)
{
tri.orient = i;
tri.Sym(ref neighbor);
nid = neighbor.tri.id;
if (id < nid || nid < 0)
{
face = faces[id];
// Get the endpoints of the current triangle edge.
org = tri.Org();
dest = tri.Dest();
// Create half-edges.
edge = new HalfEdge(vertices[org.id], face);
twin = new HalfEdge(vertices[dest.id], nid < 0 ? Face.Empty : faces[nid]);
map[id].Add(edge);
if (nid >= 0)
{
map[nid].Add(twin);
}
else
{
boundary.Add(dest.id, twin);
}
// Set leaving edges.
edge.origin.leaving = edge;
twin.origin.leaving = twin;
// Set twin edges.
edge.twin = twin;
twin.twin = edge;
edge.id = k++;
twin.id = k++;
edges.Add(edge);
edges.Add(twin);
}
}
}
// Set next pointers for each triangle face.
foreach (var t in map)
{
edge = t[0];
next = t[1];
if (edge.twin.origin.id == next.origin.id)
{
edge.next = next;
next.next = t[2];
t[2].next = edge;
}
else
{
edge.next = t[2];
next.next = edge;
t[2].next = next;
}
}
// Resolve boundary edges.
foreach (var e in boundary.Values)
{
e.next = boundary[e.twin.origin.id];
}
dcel.Vertices.AddRange(vertices);
dcel.Faces.AddRange(faces);
return(dcel);
}
public HalfEdge CreateHalfEdge(Vertex origin, Face face)
{
return new HalfEdge(origin, face);
}