//
// Is a point intersecting with a circle?
//
//Is a point d inside, outside or on the same circle where a, b, c are all on the circle's edge
public static IntersectionCases PointCircle(MyVector2 a, MyVector2 b, MyVector2 c, MyVector2 testPoint)
{
//Center of circle
MyVector2 circleCenter = Geometry.CalculateCircleCenter(a, b, c);
//The radius sqr of the circle
float radiusSqr = MyVector2.SqrDistance(a, circleCenter);
//The distance sqr from the point to the circle center
float distPointCenterSqr = MyVector2.SqrDistance(testPoint, circleCenter);
//Add/remove a small value becuse we will never be exactly on the edge because of floating point precision issues
//Mutiply epsilon by two because we are using sqr root???
if (distPointCenterSqr < radiusSqr - MathUtility.EPSILON * 2f)
{
return(IntersectionCases.IsInside);
}
else if (distPointCenterSqr > radiusSqr + MathUtility.EPSILON * 2f)
{
return(IntersectionCases.NoIntersection);
}
else
{
return(IntersectionCases.IsOnEdge);
}
}
//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 List <VoronoiCell2> GenerateVoronoiDiagram(HashSet <MyVector2> sites)
{
//First generate the delaunay triangulation
HalfEdgeData2 data = _Delaunay.FlippingEdges(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);
}