//HashSet<VoronoiCell2>
public HashSet <VoronoiCell2> UnNormalize(HashSet <VoronoiCell2> data)
{
HashSet <VoronoiCell2> unNormalizedData = new HashSet <VoronoiCell2>();
foreach (VoronoiCell2 cell in data)
{
MyVector2 sitePosUnNormalized = UnNormalize(cell.sitePos);
VoronoiCell2 cellUnNormalized = new VoronoiCell2(sitePosUnNormalized);
foreach (VoronoiEdge2 e in cell.edges)
{
MyVector2 p1UnNormalized = UnNormalize(e.p1);
MyVector2 p2UnNormalized = UnNormalize(e.p2);
VoronoiEdge2 eUnNormalized = new VoronoiEdge2(p1UnNormalized, p2UnNormalized, sitePosUnNormalized);
cellUnNormalized.edges.Add(eUnNormalized);
}
unNormalizedData.Add(cellUnNormalized);
}
return(unNormalizedData);
}
//Try to add a voronoi edge. Not all edges have a neighboring triangle, and if it hasnt we cant add a voronoi edge
private static void TryAddVoronoiEdgeFromTriangleEdge(HalfEdge2 e, MyVector2 voronoiVertex, List <VoronoiEdge2> allEdges)
{
//Ignore if this edge has no neighboring triangle
//If no opposite exists, we could maybe add a fake opposite to get an edge far away
if (e.oppositeEdge == null)
{
return;
}
//Calculate the circumcenter of the neighbor
HalfEdge2 eNeighbor = e.oppositeEdge;
MyVector2 v1 = eNeighbor.v.position;
MyVector2 v2 = eNeighbor.nextEdge.v.position;
MyVector2 v3 = eNeighbor.nextEdge.nextEdge.v.position;
MyVector2 voronoiVertexNeighbor = _Geometry.CalculateCircleCenter(v1, v2, v3);
//Create a new voronoi edge between the voronoi vertices
//Each edge in the half-edge data structure points TO a vertex, so this edge will be associated
//with the vertex the edge is going from
VoronoiEdge2 edge = new VoronoiEdge2(voronoiVertex, voronoiVertexNeighbor, sitePos: e.prevEdge.v.position);
allEdges.Add(edge);
}
//List<VoronoiCell2>
public static List <VoronoiCell2> UnNormalize(List <VoronoiCell2> data, AABB2 aabb, float dMax)
{
List <VoronoiCell2> unNormalizedData = new List <VoronoiCell2>();
foreach (VoronoiCell2 cell in data)
{
MyVector2 sitePosUnNormalized = HelpMethods.UnNormalize(cell.sitePos, aabb, dMax);
VoronoiCell2 cellUnNormalized = new VoronoiCell2(sitePosUnNormalized);
foreach (VoronoiEdge2 e in cell.edges)
{
MyVector2 p1UnNormalized = HelpMethods.UnNormalize(e.p1, aabb, dMax);
MyVector2 p2UnNormalized = HelpMethods.UnNormalize(e.p2, aabb, dMax);
VoronoiEdge2 eUnNormalized = new VoronoiEdge2(p1UnNormalized, p2UnNormalized, sitePosUnNormalized);
cellUnNormalized.edges.Add(eUnNormalized);
}
unNormalizedData.Add(cellUnNormalized);
}
return(unNormalizedData);
}
//Find the cell in the list of all cells that includes this site
private static VoronoiCell2 TryFindCell(VoronoiEdge2 e, HashSet <VoronoiCell2> voronoiCells)
{
foreach (VoronoiCell2 cell in voronoiCells)
{
if (e.sitePos.Equals(cell.sitePos))
{
return(cell);
}
}
return(null);
}
//Find the position in the list of all cells that includes this site
//Returns -1 if no cell is found
private static int TryFindCellPos(VoronoiEdge2 e, List <VoronoiCell2> voronoiCells)
{
for (int i = 0; i < voronoiCells.Count; i++)
{
if (e.sitePos.Equals(voronoiCells[i].sitePos))
{
return(i);
}
}
return(-1);
}
//Try to add a voronoi edge. Not all edges have a neighboring triangle, and if it hasnt we cant add a voronoi edge
private static void TryAddVoronoiEdgeFromTriangleEdge(HalfEdge2 e, MyVector2 voronoiVertex, List <VoronoiEdge2> allEdges)
{
//Ignore if this edge has no neighboring triangle
if (e.oppositeEdge == null)
{
return;
}
//Calculate the circumcenter of the neighbor
HalfEdge2 eNeighbor = e.oppositeEdge;
MyVector2 v1 = eNeighbor.v.position;
MyVector2 v2 = eNeighbor.nextEdge.v.position;
MyVector2 v3 = eNeighbor.nextEdge.nextEdge.v.position;
MyVector2 voronoiVertexNeighbor = _Geometry.CalculateCircleCenter(v1, v2, v3);
//Create a new vornoi edge between the voronoi vertices
VoronoiEdge2 edge = new VoronoiEdge2(voronoiVertex, voronoiVertexNeighbor, sitePos: e.prevEdge.v.position);
allEdges.Add(edge);
}
public static HashSet <VoronoiCell2> GenerateVoronoiDiagram(HashSet <MyVector2> sites)
{
//First generate the delaunay triangulation
//This one has caused a bug so should be avoided
//HalfEdgeData2 data = _Delaunay.FlippingEdges(sites, new HalfEdgeData2());
//This one is faster and more accurate, so use it. But if you are using it, make sure to normalize the sites!
HalfEdgeData2 delaunayTriangulation = _Delaunay.PointByPoint(sites, new HalfEdgeData2());
//Generate the voronoi diagram
//Step 1. For every delaunay edge, compute a voronoi edge
//The voronoi edge is the edge connecting the circumcenters of two neighboring delaunay triangles
List <VoronoiEdge2> voronoiEdges = new List <VoronoiEdge2>();
HashSet <HalfEdgeFace2> triangles = delaunayTriangulation.faces;
//Loop through each triangle
foreach (HalfEdgeFace2 t in triangles)
{
//Each triangle consists of these edges
HalfEdge2 e1 = t.edge;
HalfEdge2 e2 = e1.nextEdge;
HalfEdge2 e3 = e2.nextEdge;
//Calculate the circumcenter for this triangle
MyVector2 v1 = e1.v.position;
MyVector2 v2 = e2.v.position;
MyVector2 v3 = e3.v.position;
//The circumcenter is the center of a circle where the triangles corners is on the circumference of that circle
//The circumcenter is also known as a voronoi vertex, which is a position in the diagram where we are equally
//close to the surrounding sites (= the corners ina voronoi cell)
MyVector2 voronoiVertex = _Geometry.CalculateCircleCenter(v1, v2, v3);
//Debug.Log(voronoiVertex.x + " " + voronoiVertex.y);
//We will generate a single edge belonging to this site
//Try means that this edge might not have an opposite and then we can't generate an edge
TryAddVoronoiEdgeFromTriangleEdge(e1, voronoiVertex, voronoiEdges);
TryAddVoronoiEdgeFromTriangleEdge(e2, voronoiVertex, voronoiEdges);
TryAddVoronoiEdgeFromTriangleEdge(e3, voronoiVertex, voronoiEdges);
}
//Step 2. Find the voronoi cells where each cell is a list of all edges belonging to a site
//So we have a lot of edges and now each edge should get a cell
//These edges are not sorted, so they are added as we find them
HashSet <VoronoiCell2> voronoiCells = new HashSet <VoronoiCell2>();
for (int i = 0; i < voronoiEdges.Count; i++)
{
VoronoiEdge2 e = voronoiEdges[i];
//Find the cell in the list of all cells that includes this site
VoronoiCell2 cell = TryFindCell(e, voronoiCells);
//No cell was found so we need to create a new cell
if (cell == null)
{
VoronoiCell2 newCell = new VoronoiCell2(e.sitePos);
voronoiCells.Add(newCell);
newCell.edges.Add(e);
}
else
{
cell.edges.Add(e);
}
}
return(voronoiCells);
}
public static List <VoronoiCell2> GenerateVoronoiDiagram(HashSet <MyVector2> sites)
{
//First generate the delaunay triangulation
//This one has caused a bug so should be avoided
//HalfEdgeData2 data = _Delaunay.FlippingEdges(sites, new HalfEdgeData2());
//This one is faster and more accurate, so use it. But if you are using it, make sure to normalize the sites!
HalfEdgeData2 data = _Delaunay.PointByPoint(sites, new HalfEdgeData2());
//Generate the voronoi diagram
//Step 1. For every delaunay edge, compute a voronoi edge
//The voronoi edge is the edge connecting the circumcenters of two neighboring delaunay triangles
List <VoronoiEdge2> voronoiEdges = new List <VoronoiEdge2>();
HashSet <HalfEdgeFace2> triangles = data.faces;
foreach (HalfEdgeFace2 t in triangles)
{
//Each triangle consists of these edges
HalfEdge2 e1 = t.edge;
HalfEdge2 e2 = e1.nextEdge;
HalfEdge2 e3 = e2.nextEdge;
//Calculate the circumcenter for this triangle
MyVector2 v1 = e1.v.position;
MyVector2 v2 = e2.v.position;
MyVector2 v3 = e3.v.position;
//The circumcenter is the center of a circle where the triangles corners is on the circumference of that circle
//The circumcenter is also known as a voronoi vertex, which is a position in the diagram where we are equally
//close to the surrounding sites
MyVector2 voronoiVertex = _Geometry.CalculateCircleCenter(v1, v2, v3);
//This will generate double edges - one belonging to each site, and could maybe be improved in the future
//by using the half-edge data structure
TryAddVoronoiEdgeFromTriangleEdge(e1, voronoiVertex, voronoiEdges);
TryAddVoronoiEdgeFromTriangleEdge(e2, voronoiVertex, voronoiEdges);
TryAddVoronoiEdgeFromTriangleEdge(e3, voronoiVertex, voronoiEdges);
}
//Step 2. Find the voronoi cells where each cell is a list of all edges belonging to a site
List <VoronoiCell2> voronoiCells = new List <VoronoiCell2>();
for (int i = 0; i < voronoiEdges.Count; i++)
{
VoronoiEdge2 e = voronoiEdges[i];
//Find the position in the list of all cells that includes this site
int cellPos = TryFindCellPos(e, voronoiCells);
//No cell was found so we need to create a new cell
if (cellPos == -1)
{
VoronoiCell2 newCell = new VoronoiCell2(e.sitePos);
voronoiCells.Add(newCell);
newCell.edges.Add(e);
}
else
{
voronoiCells[cellPos].edges.Add(e);
}
}
return(voronoiCells);
}
