/// <summary>
/// Construit une représentation graphique du Diagramme de Voronoi de la triangulation
/// </summary>
public void BuildVoronoi(WingedEdgeMesh mesh)
{
List <StandardVertex> lines = new List <StandardVertex>();
// On va commencer par construire les sommets correspondant aux centre des faces de la triangulation
// qui sont les noeuds du diagramme de voronoir
CleanVoronoi();
for (int i = 0; i < mesh.Faces.Count; i++)
{
// On récupère le centre de la face (barycentre)
List <VertexWE> vertices = mesh.GetFaceVertices(mesh.Faces[i]);
Vector3 center = vertices[0].Position + vertices[1].Position + vertices[2].Position;
center = center / 3.0f;
Troll3D.Entity entity = new Troll3D.Entity(Entity);
entity.transform_.SetPosition(
center.X,
center.Y,
0.0f);
entity.transform_.SetScale(0.02f, 0.02f, 1.0f);
MaterialDX11 material = new MaterialDX11();
material.SetMainColor(0.0f, 1.0f, 1.0f, 1.0f);
MeshRenderer meshrenderer = entity.AddComponent <MeshRenderer>();
meshrenderer.material_ = material;
meshrenderer.model_ = Quad.GetMesh();
// On récupère les voisins
List <FaceWE> neighbours = mesh.GetFaceNeighbours(mesh.Faces[i]);
for (int j = 0; j < neighbours.Count; j++)
{
// On récupère le centre de la face (barycentre)
List <VertexWE> verticesNeighbour = mesh.GetFaceVertices(neighbours[j]);
Vector3 centerNeighbour = verticesNeighbour[0].Position + verticesNeighbour[1].Position + verticesNeighbour[2].Position;
centerNeighbour = centerNeighbour / 3.0f;
lines.Add(new StandardVertex(center));
lines.Add(new StandardVertex(centerNeighbour));
}
VoronoiPoints.Add(entity);
}
if (lines.Count > 0)
{
(( LineRenderer )VoronoiLines.GetComponent(ComponentType.LineRenderer)).Display = true;
(( LineRenderer )VoronoiLines.GetComponent(ComponentType.LineRenderer)).Vertices = lines;
(( LineRenderer )VoronoiLines.GetComponent(ComponentType.LineRenderer)).UpdateRenderer();
}
}
public void BuildVoronoi(WingedEdgeMesh mesh)
{
List <StandardVertex> lines = new List <StandardVertex>();
// We start by building the vertices corresponding to the face's center of the triangulation who are node of the Voronoi diagram
CleanVoronoi();
for (int i = 0; i < mesh.Faces.Count; i++)
{
// We get back the face's center (barycentre)
List <VertexWE> vertices = mesh.GetFaceVertices(mesh.Faces[i]);
Vector3 center = vertices[0].Position + vertices[1].Position + vertices[2].Position;
center = center / 3.0f;
Troll3D.Entity entity = new Troll3D.Entity(Entity);
entity.transform_.SetPosition(
center.X,
center.Y,
0.0f);
entity.transform_.SetScale(0.02f, 0.02f, 1.0f);
MaterialDX11 material = new MaterialDX11();
material.SetMainColor(0.0f, 1.0f, 1.0f, 1.0f);
MeshRenderer meshrenderer = entity.AddComponent <MeshRenderer>();
meshrenderer.material_ = material;
meshrenderer.model_ = Quad.GetMesh();
// We get back the neighbours
List <FaceWE> neighbours = mesh.GetFaceNeighbours(mesh.Faces[i]);
for (int j = 0; j < neighbours.Count; j++)
{
// On récupère le centre de la face (barycentre)
List <VertexWE> verticesNeighbour = mesh.GetFaceVertices(neighbours[j]);
Vector3 centerNeighbour = verticesNeighbour[0].Position + verticesNeighbour[1].Position + verticesNeighbour[2].Position;
centerNeighbour = centerNeighbour / 3.0f;
lines.Add(new StandardVertex(center));
lines.Add(new StandardVertex(centerNeighbour));
}
VoronoiPoints.Add(entity);
}
if (lines.Count > 0)
{
(( LineRenderer )VoronoiLines.GetComponent(ComponentType.LineRenderer)).Display = true;
(( LineRenderer )VoronoiLines.GetComponent(ComponentType.LineRenderer)).Vertices = lines;
(( LineRenderer )VoronoiLines.GetComponent(ComponentType.LineRenderer)).UpdateRenderer();
}
}
public void DelaunayIncremental()
{
List <Entity> p = new List <Entity>();
List <Entity> currentPoints = new List <Entity>();
p.AddRange(Points);
WingedEdgeMesh mesh = new WingedEdgeMesh();
// We start by making a first triangle
mesh.AddVertex(-2.0f, -1.0f, 0.0f);
mesh.AddVertex(-2.0f, 5.0f, 0.0f);
mesh.AddVertex(2.0f, -1.0f, 0.0f);
mesh.AddFace(mesh.Vertices[0], mesh.Vertices[1], mesh.Vertices[2]);
// Now, we're going to triangulate vertex per vertex
// We get back 1 vertex from the set of vertices, we look for the triangle containing it, then,
// we subdivide it in 3 triangles. We then check that every new triangle is Delaunay. If not, we flip/switchover the
// opposite edge of the new vertex
while (p.Count > 0)
{
// We start by extracting a point from the set of vertices
Entity point = p[0];
p.RemoveAt(0);
FaceWE f = null;
int findex = 0;
// Looking for the triangle that contains the dot
for (int i = 0; i < mesh.Faces.Count; i++)
{
FaceWE currentFace = mesh.Faces[i];
List <VertexWE> vertices = mesh.GetFaceVertices(currentFace);
bool isIn = Troll3D.TRaycast.PointInTriangle(vertices[0].Position, vertices[1].Position, vertices[2].Position, point.transform_.position_);
if (isIn)
{
f = currentFace;
findex = i;
}
}
// In theory, we should have get back a triangle that contains the vertex. We're now going to divide that
// in 3 triangles using the current vertex
List <FaceWE> faces = mesh.AddVertex(f, point.transform_.position_.X, point.transform_.position_.Y, point.transform_.position_.Z);
// Now we must check that the triangles we found are Delaunay. Meaning that the
// circumscribed circle of the triangle must contains only points of the triangle.
// Checking the faces created
for (int i = 0; i < faces.Count; i++)
{
InspectEdge(faces[i].Edges, mesh);
}
}
//Removing mesh thing used for triangulation
List <FaceWE> faceToRemove = new List <FaceWE>();
for (int i = mesh.Faces.Count - 1; i >= 0; i--)
{
if (mesh.IsFaceBorder(mesh.Faces[i]))
{
faceToRemove.Add(mesh.Faces[i]);
}
}
for (int i = 0; i < faceToRemove.Count; i++)
{
mesh.RemoveFace(faceToRemove[i]);
}
for (int i = 0; i < CircleCenter.Count; i++)
{
Scene.CurrentScene.RemoveRenderable(( MeshRenderer )CircleCenter[i].GetComponent(ComponentType.MeshRenderer));
}
if (DisplayCenters)
{
for (int i = 0; i < Circles.Count; i++)
{
Scene.CurrentScene.RemoveRenderable(( LineRenderer )Circles[i].GetComponent(ComponentType.LineRenderer));
}
CircleCenter.Clear();
for (int i = 0; i < mesh.Faces.Count; i++)
{
List <VertexWE> vertices = mesh.GetFaceVertices(mesh.Faces[i]);
Vector3 circleCenter = GetCircleCenter(vertices[0].Position, vertices[1].Position, vertices[2].Position);
float radius = GetCircleRadius(vertices[0].Position, vertices[1].Position, vertices[2].Position, circleCenter);
AddCircleCenter(circleCenter.X, circleCenter.Y, radius);
}
}
else
{
for (int i = 0; i < Circles.Count; i++)
{
Scene.CurrentScene.RemoveRenderable(( LineRenderer )Circles[i].GetComponent(ComponentType.LineRenderer));
}
CircleCenter.Clear();
}
if (mesh.MakeMesh() != null)
{
meshRenderer.model_ = mesh.MakeMesh();
meshRenderer.SetFillMode(SharpDX.Direct3D11.FillMode.Wireframe);
meshRenderer.material_.SetMainColor(1.0f, 0.0f, 0.0f, 1.0f);
}
else
{
}
if (DisplayVoronoi)
{
BuildVoronoi(mesh);
}
else
{
CleanVoronoi();
}
}
/// <summary>
/// Check an edge and determine if it needs to be change? If yes the function call itself again
/// </summary>
/// <param name="e"></param>
private void InspectEdge(List <EdgeWE> edges, WingedEdgeMesh mesh)
{
foreach (EdgeWE e in edges)
{
// Wefirstcheck that the edge connect 2 triangles
if (e.LeftFace != null && e.RightFace != null)
{
List <VertexWE> v1 = mesh.GetFaceVertices(e.LeftFace);
List <VertexWE> v2 = mesh.GetFaceVertices(e.RightFace);
// We get the opposite side of the left face
VertexWE leftOppositeVertex = null;
for (int i = 0; i < v1.Count; i++)
{
if ((v1[i] != e.Vertex1) && (v1[i] != e.Vertex2))
{
leftOppositeVertex = v1[i];
}
}
//We get the opposite side of the right face
VertexWE rightOppositeVertex = null;
for (int i = 0; i < v2.Count; i++)
{
if ((v2[i] != e.Vertex1) && (v2[i] != e.Vertex2))
{
rightOppositeVertex = v1[i];
}
}
// We get back informations about the circles from the left and right face
Vector3 leftCircleCenter = GetCircleCenter(v1[0].Position, v1[1].Position, v1[2].Position);
float leftCircleRadius = GetCircleRadius(v1[0].Position, v1[1].Position, v1[2].Position, leftCircleCenter);
Vector3 rightCircleCenter = GetCircleCenter(v2[0].Position, v2[1].Position, v2[2].Position);
float rightCircleRadius = GetCircleRadius(v2[0].Position, v2[1].Position, v2[2].Position, rightCircleCenter);
// We check if one of the opposite side can fit in the circle of the opposite face
if (IsPointInCircle(leftOppositeVertex.Position, rightCircleCenter, rightCircleRadius) || IsPointInCircle(rightOppositeVertex.Position, leftCircleCenter, leftCircleRadius))
{
// We switchover the edge
List <FaceWE> newfaces = mesh.FlipEdge(e);
// We inspect the new edges
List <EdgeWE> newEdges = new List <EdgeWE>();
for (int i = 0; i < newfaces.Count; i++)
{
for (int j = 0; j < newfaces[i].Edges.Count; j++)
{
if (newEdges.Contains(newfaces[i].Edges[j]))
{
newEdges.Add(newfaces[i].Edges[j]);
}
}
}
InspectEdge(newEdges, mesh);
return;
}
}
}
return;
}
/// <summary>
/// Implémentation de l'algorithme de triangulation de Delaunay incremental
/// </summary>
public void DelaunayIncremental()
{
List <Entity> p = new List <Entity>();
List <Entity> currentPoints = new List <Entity>();
p.AddRange(Points);
WingedEdgeMesh mesh = new WingedEdgeMesh();
// On commence par créer un big triangle capable de contenir tout les autres
mesh.AddVertex(-2.0f, -1.0f, 0.0f);
mesh.AddVertex(-2.0f, 5.0f, 0.0f);
mesh.AddVertex(2.0f, -1.0f, 0.0f);
mesh.AddFace(mesh.Vertices[0], mesh.Vertices[1], mesh.Vertices[2]);
// Maintenant, on va trianguler point par point
// On récupère un point de l'ensemble de point, on cherche le triangle qui le contient,
// puis, on subdivise en 3 triangles. On vérifie ensuite que chacun des triangles crée est
// Delaunay, si ce n'est pas le cas, on flip l'arrête "opposé" au sommet rajouté
while (p.Count > 0)
{
// On commence par extraire le point
Entity point = p[0];
p.RemoveAt(0);
FaceWE f = null;
int findex = 0;
// On cherche le triangle qui contient le point
for (int i = 0; i < mesh.Faces.Count; i++)
{
FaceWE currentFace = mesh.Faces[i];
List <VertexWE> vertices = mesh.GetFaceVertices(currentFace);
bool isIn = Troll3D.TRaycast.PointInTriangle(vertices[0].Position, vertices[1].Position, vertices[2].Position, point.transform_.position_);
if (isIn)
{
f = currentFace;
findex = i;
}
}
// En théorie, on a récupéré le triangle qui contient le point, on va désormais diviser
// ce triangle en 3 en utilisant le point actuel
List <FaceWE> faces = mesh.AddVertex(f, point.transform_.position_.X, point.transform_.position_.Y, point.transform_.position_.Z);
// Maintenant, on doit vérifier que les triangles obtenus sont delaunay, c'est à dire
// que le cercle circonscrit au triangle ne contienne que des points du triangle
// On inspecte les faces crées
for (int i = 0; i < faces.Count; i++)
{
InspectEdge(faces[i].Edges, mesh);
}
}
// Je retire les parties du maillage qui sont utilisé pour construire la triangulation
List <FaceWE> faceToRemove = new List <FaceWE>();
for (int i = mesh.Faces.Count - 1; i >= 0; i--)
{
if (mesh.IsFaceBorder(mesh.Faces[i]))
{
faceToRemove.Add(mesh.Faces[i]);
}
}
for (int i = 0; i < faceToRemove.Count; i++)
{
mesh.RemoveFace(faceToRemove[i]);
}
for (int i = 0; i < CircleCenter.Count; i++)
{
Scene.CurrentScene.RemoveRenderable(( MeshRenderer )CircleCenter[i].GetComponent(ComponentType.MeshRenderer));
}
if (DisplayCenters)
{
for (int i = 0; i < Circles.Count; i++)
{
Scene.CurrentScene.RemoveRenderable(( LineRenderer )Circles[i].GetComponent(ComponentType.LineRenderer));
}
CircleCenter.Clear();
for (int i = 0; i < mesh.Faces.Count; i++)
{
List <VertexWE> vertices = mesh.GetFaceVertices(mesh.Faces[i]);
Vector3 circleCenter = GetCircleCenter(vertices[0].Position, vertices[1].Position, vertices[2].Position);
float radius = GetCircleRadius(vertices[0].Position, vertices[1].Position, vertices[2].Position, circleCenter);
AddCircleCenter(circleCenter.X, circleCenter.Y, radius);
}
}
else
{
for (int i = 0; i < Circles.Count; i++)
{
Scene.CurrentScene.RemoveRenderable(( LineRenderer )Circles[i].GetComponent(ComponentType.LineRenderer));
}
CircleCenter.Clear();
}
if (mesh.MakeMesh() != null)
{
meshRenderer.model_ = mesh.MakeMesh();
meshRenderer.SetFillMode(SharpDX.Direct3D11.FillMode.Wireframe);
meshRenderer.material_.SetMainColor(1.0f, 0.0f, 0.0f, 1.0f);
}
else
{
}
if (DisplayVoronoi)
{
BuildVoronoi(mesh);
}
else
{
CleanVoronoi();
}
}
/// <summary>
/// Inspecte une edge et détermine si un basculement est nécéssaire
/// Si un basculement a eu lieu, réinvoque la fonction
/// </summary>
/// <param name="e"></param>
private void InspectEdge(List <EdgeWE> edges, WingedEdgeMesh mesh)
{
foreach (EdgeWE e in edges)
{
// On vérifie d'abord que l'arrête relie 2 triangles
if (e.LeftFace != null && e.RightFace != null)
{
List <VertexWE> v1 = mesh.GetFaceVertices(e.LeftFace);
List <VertexWE> v2 = mesh.GetFaceVertices(e.RightFace);
// Récupère le coté opposé à la face gauche
VertexWE leftOppositeVertex = null;
for (int i = 0; i < v1.Count; i++)
{
if ((v1[i] != e.Vertex1) && (v1[i] != e.Vertex2))
{
leftOppositeVertex = v1[i];
}
}
// Récupère le coté opposé à la face droite
VertexWE rightOppositeVertex = null;
for (int i = 0; i < v2.Count; i++)
{
if ((v2[i] != e.Vertex1) && (v2[i] != e.Vertex2))
{
rightOppositeVertex = v1[i];
}
}
// On récupère les informations sur les cercle Right et Left Face
Vector3 leftCircleCenter = GetCircleCenter(v1[0].Position, v1[1].Position, v1[2].Position);
float leftCircleRadius = GetCircleRadius(v1[0].Position, v1[1].Position, v1[2].Position, leftCircleCenter);
Vector3 rightCircleCenter = GetCircleCenter(v2[0].Position, v2[1].Position, v2[2].Position);
float rightCircleRadius = GetCircleRadius(v2[0].Position, v2[1].Position, v2[2].Position, rightCircleCenter);
// On vérifie si un des coté opposé ne rentre pas dans le cercle de la face opposé
if (IsPointInCircle(leftOppositeVertex.Position, rightCircleCenter, rightCircleRadius) || IsPointInCircle(rightOppositeVertex.Position, leftCircleCenter, leftCircleRadius))
{
// On bascule l'arrête
List <FaceWE> newfaces = mesh.FlipEdge(e);
// On inspecte les nouvelles arrêtes
List <EdgeWE> newEdges = new List <EdgeWE>();
for (int i = 0; i < newfaces.Count; i++)
{
for (int j = 0; j < newfaces[i].Edges.Count; j++)
{
if (newEdges.Contains(newfaces[i].Edges[j]))
{
newEdges.Add(newfaces[i].Edges[j]);
}
}
}
InspectEdge(newEdges, mesh);
return;
}
}
}
return;
}
