public static Voronoi FromDelaunay(Adjacency adjacency)
{
Voronoi v = new Voronoi();
int[] triangleRemapping = new int[adjacency.triangles.Count];
for (int i = 0; i < adjacency.triangles.Count; i++)
{
Adjacency.Triangle t = adjacency.triangles[i];
if (!t.valid)
{
triangleRemapping[i] = -1;
continue;
}
Vertex c; float r;
t.CircumCircle(adjacency.vertices, out c, out r);
triangleRemapping[i] = v.vertices.Count;
v.vertices.Add(c);
}
for (int i = 0; i < adjacency.triangles.Count; i++)
{
Adjacency.Triangle t = adjacency.triangles[i];
if (!t.valid)
{
continue;
}
for (int e = 0; e < 3; e++)
{
int adjT = adjacency.AdjacentTriangle(i, e);
if (adjT < 0 || adjacency.triangles[adjT].valid == false)
{
continue;
}
if (triangleRemapping[adjT] < 0)
{
continue; // already processed
}
int voronoiV0 = triangleRemapping[i];
int voronoiV1 = triangleRemapping[adjT];
Debug.Assert(voronoiV0 >= 0 && voronoiV1 >= 0);
// the 2 vertices shared by the adjacent triangles will become
// the voronoi cells divided by the edge we're creating
int cellA = adjacency.edges[Math.Abs(t.edges[e]) - 1].vertices[0];
int cellB = adjacency.edges[Math.Abs(t.edges[e]) - 1].vertices[1];
v.edges.Add(new Edge(voronoiV0, voronoiV1, cellA, cellB));
}
triangleRemapping[i] = -1;
}
return(v);
}
public static Voronoi FromDelaunay(Adjacency adjacency)
{
Voronoi v = new Voronoi();
int[] triangleRemapping = new int[adjacency.triangles.Count];
for (int i = 0; i < adjacency.triangles.Count; i++)
{
Adjacency.Triangle t = adjacency.triangles[i];
if (!t.valid)
{
triangleRemapping[i] = -1;
continue;
}
Vertex c; float r;
t.CircumCircle( adjacency.vertices, out c, out r);
triangleRemapping[i] = v.vertices.Count;
v.vertices.Add(c);
}
for (int i = 0; i < adjacency.triangles.Count; i++)
{
Adjacency.Triangle t = adjacency.triangles[i];
if (!t.valid)
{
continue;
}
for (int e = 0; e < 3; e++)
{
int adjT = adjacency.AdjacentTriangle(i, e);
if (adjT < 0 || adjacency.triangles[adjT].valid == false) continue;
if (triangleRemapping[adjT] < 0) continue; // already processed
int voronoiV0 = triangleRemapping[i];
int voronoiV1 = triangleRemapping[adjT];
Debug.Assert(voronoiV0 >= 0 && voronoiV1 >= 0);
// the 2 vertices shared by the adjacent triangles will become
// the voronoi cells divided by the edge we're creating
int cellA = adjacency.edges[Math.Abs(t.edges[e]) - 1].vertices[0];
int cellB = adjacency.edges[Math.Abs(t.edges[e]) - 1].vertices[1];
v.edges.Add(new Edge(voronoiV0, voronoiV1, cellA, cellB));
}
triangleRemapping[i] = -1;
}
return v;
}
private static bool Delaunay2DInsertPoints(List<Vertex> vertices, Adjacency adjacency)
{
// Insert points
HashSet<int> toCheck = new HashSet<int>();
for (int i = 0; i < vertices.Count; i++)
{
// Insert Vi
Vertex Vi = vertices[i];
bool skip = false;
for (int j = 0; j < adjacency.vertices.Count; j++)
{
if ((Vi - adjacency.vertices[j]).Length() <= COINCIDENT_POINTS_DISTANCE_EPSILON)
{
// the point has already been inserted. Skip it
skip = true;
break;
}
}
if (skip)
{
continue;
}
if (OnDelaunayInsertPoint != null)
OnDelaunayInsertPoint(adjacency, Vi);
int tri = adjacency.PointInTriangle(Vi);
if (tri < 0)
{
Debug.Assert(false);
return false;
}
// check whether the point lies exactly on one edge of the triangle
int edgeIdx = adjacency.PointInTriangleEdge(Vi, tri);
if (edgeIdx >= 0)
{
// split the edge by Vi
int[] result;
adjacency.SplitEdge(edgeIdx, Vi, out result);
for (int j = 0; j < 4; j++)
{
if (result[j] >= 0)
{
toCheck.Add(result[j]);
}
}
}
else
{
// split the triangle in 3
int[] result;
adjacency.SplitTriangle(tri, Vi, out result);
for (int j = 0; j < 3; j++)
{
toCheck.Add(result[j]);
}
}
while (toCheck.Count > 0)
{
int t = toCheck.Last<int>();
toCheck.Remove(t);
Adjacency.Triangle triangle = adjacency.triangles[t];
if (!triangle.valid)
{
continue;
}
if (OnDelaunayTriangleCheck != null)
OnDelaunayTriangleCheck(adjacency, t);
// check Delaunay condition
for (int e = 0; e < 3; e++)
{
if (!adjacency.triangles[t].valid) continue;
int adjacentIdx = adjacency.AdjacentTriangle(t, e);
if (adjacentIdx < 0)
{
continue;
}
int globalEdgeIndex = Math.Abs(triangle.edges[e]) - 1;
Adjacency.Triangle adjacent = adjacency.triangles[adjacentIdx];
if (!adjacent.valid)
{
continue;
}
Debug.Assert(adjacent.valid);
int edgeFromAdjacent = adjacent.LocalEdgeIndex(globalEdgeIndex);
Debug.Assert(edgeFromAdjacent >= 0);
int v = adjacency.VertexOutOfTriEdge(adjacentIdx, edgeFromAdjacent);
Debug.Assert(v >= 0);
Debug.Assert(!triangle.Contains(v));
if (triangle.InsideCircumcircle(adjacency.vertices[v], adjacency.vertices) > INSIDE_CIRCUMCIRCLE_EPSILON)
{
int[] result;
if (adjacency.FlipTriangles(t, adjacentIdx, out result))
{
toCheck.Add(result[0]);
toCheck.Add(result[1]);
//break;
}
}
}
}
if (OnDelaunayStep != null)
OnDelaunayStep(adjacency);
}
return true;
}
private static bool Delaunay2DInsertPoints(List <Vertex> vertices, Adjacency adjacency)
{
// Insert points
HashSet <int> toCheck = new HashSet <int>();
for (int i = 0; i < vertices.Count; i++)
{
// Insert Vi
Vertex Vi = vertices[i];
bool skip = false;
for (int j = 0; j < adjacency.vertices.Count; j++)
{
if ((Vi - adjacency.vertices[j]).Length() <= COINCIDENT_POINTS_DISTANCE_EPSILON)
{
// the point has already been inserted. Skip it
skip = true;
break;
}
}
if (skip)
{
continue;
}
if (OnDelaunayInsertPoint != null)
{
OnDelaunayInsertPoint(adjacency, Vi);
}
int tri = adjacency.PointInTriangle(Vi);
if (tri < 0)
{
Debug.Assert(false);
return(false);
}
// check whether the point lies exactly on one edge of the triangle
int edgeIdx = adjacency.PointInTriangleEdge(Vi, tri);
if (edgeIdx >= 0)
{
// split the edge by Vi
int[] result;
adjacency.SplitEdge(edgeIdx, Vi, out result);
for (int j = 0; j < 4; j++)
{
if (result[j] >= 0)
{
toCheck.Add(result[j]);
}
}
}
else
{
// split the triangle in 3
int[] result;
adjacency.SplitTriangle(tri, Vi, out result);
for (int j = 0; j < 3; j++)
{
toCheck.Add(result[j]);
}
}
while (toCheck.Count > 0)
{
int t = toCheck.Last <int>();
toCheck.Remove(t);
Adjacency.Triangle triangle = adjacency.triangles[t];
if (!triangle.valid)
{
continue;
}
if (OnDelaunayTriangleCheck != null)
{
OnDelaunayTriangleCheck(adjacency, t);
}
// check Delaunay condition
for (int e = 0; e < 3; e++)
{
if (!adjacency.triangles[t].valid)
{
continue;
}
int adjacentIdx = adjacency.AdjacentTriangle(t, e);
if (adjacentIdx < 0)
{
continue;
}
int globalEdgeIndex = Math.Abs(triangle.edges[e]) - 1;
Adjacency.Triangle adjacent = adjacency.triangles[adjacentIdx];
if (!adjacent.valid)
{
continue;
}
Debug.Assert(adjacent.valid);
int edgeFromAdjacent = adjacent.LocalEdgeIndex(globalEdgeIndex);
Debug.Assert(edgeFromAdjacent >= 0);
int v = adjacency.VertexOutOfTriEdge(adjacentIdx, edgeFromAdjacent);
Debug.Assert(v >= 0);
Debug.Assert(!triangle.Contains(v));
if (triangle.InsideCircumcircle(adjacency.vertices[v], adjacency.vertices) > INSIDE_CIRCUMCIRCLE_EPSILON)
{
int[] result;
if (adjacency.FlipTriangles(t, adjacentIdx, out result))
{
toCheck.Add(result[0]);
toCheck.Add(result[1]);
//break;
}
}
}
}
if (OnDelaunayStep != null)
{
OnDelaunayStep(adjacency);
}
}
return(true);
}