//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(HalfEdge e, Vector3 voronoiVertex, List <VoronoiEdge> allEdges)
{
//Ignore if this edge has no neighboring triangle
if (e.oppositeEdge == null)
{
return;
}
//Calculate the circumcenter of the neighbor
HalfEdge eNeighbor = e.oppositeEdge;
Vector3 v1 = eNeighbor.v.position;
Vector3 v2 = eNeighbor.nextEdge.v.position;
Vector3 v3 = eNeighbor.nextEdge.nextEdge.v.position;
//The .XZ() is an extension method that removes the y value of a vector3 so it becomes a vector2
Vector2 center2D = CalculateCircleCenter(new Vector2(v1.x, v1.z), new Vector2(v2.x, v2.z), new Vector2(v3.x, v3.z));
Vector3 voronoiVertexNeighbor = new Vector3(center2D.x, 0f, center2D.y);
//Create a new voronoi edge between the voronoi vertices
VoronoiEdge edge = new VoronoiEdge(voronoiVertex, voronoiVertexNeighbor, e.prevEdge.v.position);
allEdges.Add(edge);
}
//Find the position in the list of all cells that includes this site
//Returns -1 if no cell is found
private static int TryFindCellPos(VoronoiEdge e, List <VoronoiCell> voronoiCells)
{
for (int i = 0; i < voronoiCells.Count; i++)
{
if (e.sitePos == voronoiCells[i].sitePos)
{
return(i);
}
}
return(-1);
}
public static List <VoronoiCell> GenerateVoronoiDiagram(List <Vector3> sites)
{
//First generate the delaunay triangulation
List <Triangle> triangles = TriangulateByFlippingEdges(sites);
//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 <VoronoiEdge> voronoiEdges = new List <VoronoiEdge>();
for (int i = 0; i < triangles.Count; i++)
{
Triangle t = triangles[i];
//Each triangle consists of these edges
HalfEdge e1 = t.halfEdge;
HalfEdge e2 = e1.nextEdge;
HalfEdge e3 = e2.nextEdge;
//Calculate the circumcenter for this triangle
Vector3 v1 = e1.v.position;
Vector3 v2 = e2.v.position;
Vector3 v3 = e3.v.position;
//The circumcenter is the center of a circle where the triangles corners is on the circumference of that circle
//The .XZ() is an extension method that removes the y value of a vector3 so it becomes a vector2
Vector2 center2D = CalculateCircleCenter(new Vector2(v1.x, v1.z), new Vector2(v2.x, v2.z), new Vector2(v3.x, v3.z));
//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
Vector3 voronoiVertex = new Vector3(center2D.x, 0f, center2D.y);
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 <VoronoiCell> voronoiCells = new List <VoronoiCell>();
for (int i = 0; i < voronoiEdges.Count; i++)
{
VoronoiEdge 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)
{
VoronoiCell newCell = new VoronoiCell(e.sitePos);
voronoiCells.Add(newCell);
newCell.edges.Add(e);
}
else
{
voronoiCells[cellPos].edges.Add(e);
}
}
return(voronoiCells);
}
private static void ClipDiagram(List <VoronoiCell> cells, float halfWidth)
{
//Remove the first 4 cells we added in the beginning because they are not needed anymore
//cells.RemoveRange(0, 4);
for (int i = 0; i < cells.Count; i++)
{
//We should move around the cell counter-clockwise so make sure all edges are oriented in that way
List <VoronoiEdge> cellEdges = cells[i].edges;
for (int j = cellEdges.Count - 1; j >= 0; j--)
{
Vector3 edge_v1 = cellEdges[j].v1;
Vector3 edge_v2 = cellEdges[j].v2;
//Remove this edge if it is small
if ((edge_v1 - edge_v2).sqrMagnitude < 0.01f)
{
cellEdges.RemoveAt(j);
continue;
}
Vector3 edgeCenter = (edge_v1 + edge_v2) * 0.5f;
//Now we can make a line between the cell and the edge
Vector2 a = new Vector2(cells[i].sitePos.x, cells[i].sitePos.z);
Vector2 b = new Vector2(edgeCenter.x, edgeCenter.z);
//The point to the left of this line is coming after the other point if we are moving counter-clockwise
if (IsAPointLeftOfVector(a, b, new Vector2(edge_v1.x, edge_v1.z)) < 0f)
{
//Flip because we want to go from v1 to v2
cellEdges[j].v2 = edge_v1;
cellEdges[j].v1 = edge_v2;
}
}
//Connect the edges
VoronoiEdge startEdge = cellEdges[0];
cells[i].borderCoordinates.Add(startEdge.v2);
Vector3 currentVertex = startEdge.v2;
for (int j = 1; j < cellEdges.Count; j++)
{
//Find the next edge
for (int k = 1; k < cellEdges.Count; k++)
{
Vector3 thisEdgeStart = cellEdges[k].v1;
if ((thisEdgeStart - currentVertex).sqrMagnitude < 0.01f)
{
cells[i].borderCoordinates.Add(cellEdges[k].v2);
currentVertex = cellEdges[k].v2;
break;
}
}
}
}
List <Vector3> clipPolygon = new List <Vector3>();
//The positions of the square border
Vector3 TL = new Vector3(-halfWidth, 0f, halfWidth);
Vector3 TR = new Vector3(halfWidth, 0f, halfWidth);
Vector3 BR = new Vector3(halfWidth, 0f, -halfWidth);
Vector3 BL = new Vector3(-halfWidth, 0f, -halfWidth);
clipPolygon.Add(TL);
clipPolygon.Add(BL);
clipPolygon.Add(BR);
clipPolygon.Add(TR);
//Create the clipping planes
List <Plane> clippingPlanes = new List <Plane>();
for (int i = 0; i < clipPolygon.Count; i++)
{
int iPlusOne = ClampListIndex(i + 1, clipPolygon.Count);
Vector3 v1 = clipPolygon[i];
Vector3 v2 = clipPolygon[iPlusOne];
//Doesnt have to be center but easier to debug
Vector3 planePos = (v1 + v2) * 0.5f;
Vector3 planeDir = v2 - v1;
//Should point inwards
Vector3 planeNormal = new Vector3(-planeDir.z, 0f, planeDir.x).normalized;
clippingPlanes.Add(new Plane(planePos, planeNormal));
}
for (int i = 0; i < cells.Count; i++)
{
cells[i].borderCoordinates = ClipPolygon(cells[i].borderCoordinates, clippingPlanes);
}
}