internal void OnDelaunayTriangleCheck(Adjacency adjacency, int triangle)
{
Bitmap img = new Bitmap(800, 800);
Random random = new Random();
float scale = 1000.0f;
for (int j = 0; j < adjacency.vertices.Count; j++)
{
adjacency.vertices[j].x /= scale;
adjacency.vertices[j].y /= scale;
}
adjacency.ToImage(img);
Graphics g = Graphics.FromImage(img);
PointF[] points = new PointF[3];
for (int i = 0; i < 3; i++)
{
Vertex v = adjacency.vertices[adjacency.triangles[triangle].vertices[i]];
points[i] = new PointF(v.x * img.Width, v.y * img.Height);
}
g.FillPolygon(new SolidBrush(Color.FromArgb(random.Next(255), random.Next(255), random.Next(255))), points);
for (int j = 0; j < adjacency.vertices.Count; j++)
{
adjacency.vertices[j].x *= scale;
adjacency.vertices[j].y *= scale;
}
QueueDebugImage(img);
}
public void ToImage(Image img, Adjacency adjacency)
{
SolidBrush vertexColor = new SolidBrush(Color.Green);
Pen boundaryColor = new Pen(Color.Blue);
Pen cellColor = new Pen(Color.Gray);
Graphics g = Graphics.FromImage(img);
g.Clear(Color.White);
for (int e = 0; e < edges.Count; e++)
{
Vertex v0 = vertices[edges[e].v[0]];
Vertex v1 = vertices[edges[e].v[1]];
g.DrawLine(boundaryColor, v0.x * img.Width, v0.y * img.Height, v1.x * img.Width, v1.y * img.Height);
Vertex cellA = adjacency.vertices[edges[e].cell[0]];
Vertex cellB = adjacency.vertices[edges[e].cell[1]];
Vertex centerV = new Vertex((v0.x + v1.x) * 0.5f, (v0.y + v1.y) * 0.5f);
g.DrawLine(cellColor, centerV.x * img.Width, centerV.y * img.Height, cellA.x * img.Width, cellA.y * img.Height);
g.DrawLine(cellColor, centerV.x * img.Width, centerV.y * img.Height, cellB.x * img.Width, cellB.y * img.Height);
}
for (int v = 0; v < vertices.Count; v++)
{
const float r = 3;
g.FillEllipse(vertexColor, new RectangleF(vertices[v].x * img.Width - r, vertices[v].y * img.Height - r, 2 * r, 2 * r));
}
}
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;
}
internal void OnDelaunayStep(Adjacency adjacency)
{
Bitmap bmp = new Bitmap(800, 800);
float scale = 1000.0f;
for (int j = 0; j < adjacency.vertices.Count; j++)
{
adjacency.vertices[j].x /= scale;
adjacency.vertices[j].y /= scale;
}
adjacency.ToImage(bmp);
for (int j = 0; j < adjacency.vertices.Count; j++)
{
adjacency.vertices[j].x *= scale;
adjacency.vertices[j].y *= scale;
}
QueueDebugImage(bmp);
}
private static void Delaunay2DCreateSuperTriangle(List <Vertex> vertices, Adjacency adjacency,
out int stIdx1, out int stIdx2, out int stIdx3)
{
// Calculate super triangle
Bounds2D bounds = new Bounds2D();
for (int i = 0; i < vertices.Count; i++)
{
bounds.AddPoint(vertices[i]);
}
Vertex center;
float radius;
bounds.BoundingCircunference(out center, out radius);
Vertex st1 = new Vertex();
Vertex st2 = new Vertex();
Vertex st3 = new Vertex();
const float DEG2RAD = (float)Math.PI / 180.0f;
st1.x = center.x + 2.0f * radius * (float)Math.Cos(0.0f * DEG2RAD);
st1.y = center.y + 2.0f * radius * (float)Math.Sin(0.0f * DEG2RAD);
st2.x = center.x + 2.0f * radius * (float)Math.Cos(120.0f * DEG2RAD);
st2.y = center.y + 2.0f * radius * (float)Math.Sin(120.0f * DEG2RAD);
st3.x = center.x + 2.0f * radius * (float)Math.Cos(240.0f * DEG2RAD);
st3.y = center.y + 2.0f * radius * (float)Math.Sin(240.0f * DEG2RAD);
adjacency.vertices.Add(st1);
adjacency.vertices.Add(st2);
adjacency.vertices.Add(st3);
stIdx1 = adjacency.vertices.Count - 3;
stIdx2 = adjacency.vertices.Count - 2;
stIdx3 = adjacency.vertices.Count - 1;
adjacency.CreateTriangle(stIdx1, stIdx2, stIdx3);
}
public Graph(Voronoi voronoi, Adjacency adjacency, List <WangTile.MergeCandidate> candidates)
{
vertices = voronoi.vertices;
this.candidates = candidates;
edges = new List <Edge>();
float maxCellDist = float.MinValue;
for (int i = 0; i < voronoi.edges.Count; i++)
{
Voronoi.Edge edge = voronoi.edges[i];
bool found = false;
foreach (Edge e in edges)
{
if (e.v[0] == edge.v[0] && e.v[1] == edge.v[1] ||
e.v[0] == edge.v[1] && e.v[1] == edge.v[0])
{
found = true;
break;
}
}
if (!found)
{
Vertex cellA = edge.cell[0] < adjacency.vertices.Count ? adjacency.vertices[edge.cell[0]] : null;
Vertex cellB = edge.cell[1] < adjacency.vertices.Count ? adjacency.vertices[edge.cell[1]] : null;
float cellDist = (cellA != null & cellB != null) ? (cellA - cellB).Length() : float.MaxValue;
if (cellDist < float.MaxValue)
{
maxCellDist = Math.Max(maxCellDist, cellDist);
}
Graph.Edge gEdge = new Graph.Edge(edge.v[0], edge.v[1], cellDist);
edges.Add(gEdge);
}
}
for (int i = 0; i < edges.Count; i++)
{
float dist = edges[i].cost;
edges[i].cost = dist < float.MaxValue ? (float)Math.Pow(1.0f - dist / maxCellDist, 100.0f) : INFINITY_COST; // the exponent value is suggested in the paper
}
}
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);
}
public static bool Delaunay2DTriangulate(List <Vertex> vertices, bool removeSurroundingTriangle, out List <int> outTriangles, ref Adjacency adjacencyInfo)
{
/* Implements Lawson algorithm:
* http://www.henrikzimmer.com/VoronoiDelaunay.pdf
*
* Unlike the Watson algorithm the Lawson algorithm is not based finding circumcircles and deleting
* triangles to obtain an insertion polygon. Lawson's incremental insertion algorithm utilizes edge
* flippings to achieve the same result and thus avoids a possibly faulty, degenerate mesh which can
* occur using Watsons method.
* In the same way as before, if we are not given a start triangulation we use a super triangle
* enclosing all vertices in V . In every insertion step a vertex p belonging to V is inserted.
* A simple retriangulation is made where the edges are inserted between p and the corner vertices of
* the triangle containing p (fig.11). For all new triangles formed the circumcircles are checked, if they contain
* any neighbouring vertex the edge between them is flipped. This process is executed recursively
* until there are no more faulty triangles and no more flips are required (fig.12). The algorithm then
* moves on, inserting another vertex from V until they have all been triangulated into a mesh, then,
* like before the super triangle and its edge are removed.
*/
if (vertices.Count < 3)
{
outTriangles = new List <int>();
return(false);
}
Adjacency adjacency = adjacencyInfo;
if (adjacencyInfo == null)
{
adjacency = new Adjacency();
}
;
int stIdx1, stIdx2, stIdx3;
Delaunay2DCreateSuperTriangle(vertices, adjacency, out stIdx1, out stIdx2, out stIdx3);
if (!Delaunay2DInsertPoints(vertices, adjacency))
{
outTriangles = new List <int>();
return(false);
}
if (removeSurroundingTriangle)
{
Delaunay2DRemoveSuperTriangle(adjacency, stIdx1, stIdx2, stIdx3, out outTriangles, vertices);
}
else
{
// move the 3 vertices from the supertriangle right to the end of
// the array instead of the beginning, so that the N first vertices
// match with the point insertion order
foreach (Adjacency.Edge e in adjacency.edges)
{
for (int i = 0; i < 2; i++)
{
e.vertices[i] -= 3;
if (e.vertices[i] < 0)
{
e.vertices[i] += adjacency.vertices.Count;
}
}
}
foreach (Adjacency.Triangle t in adjacency.triangles)
{
for (int i = 0; i < 3; i++)
{
t.vertices[i] -= 3;
if (t.vertices[i] < 0)
{
t.vertices[i] += adjacency.vertices.Count;
}
}
}
adjacency.vertices.Add(adjacency.vertices[0]);
adjacency.vertices.Add(adjacency.vertices[1]);
adjacency.vertices.Add(adjacency.vertices[2]);
adjacency.vertices.RemoveAt(0);
adjacency.vertices.RemoveAt(0);
adjacency.vertices.RemoveAt(0);
//
outTriangles = new List <int>();
for (int i = 0; i < adjacency.triangles.Count; i++)
{
if (adjacency.triangles[i].valid)
{
outTriangles.Add(adjacency.triangles[i].vertices[0]);
outTriangles.Add(adjacency.triangles[i].vertices[1]);
outTriangles.Add(adjacency.triangles[i].vertices[2]);
}
}
}
return(true);
}
private static void Delaunay2DCreateSuperTriangle(List<Vertex> vertices, Adjacency adjacency,
out int stIdx1, out int stIdx2, out int stIdx3)
{
// Calculate super triangle
Bounds2D bounds = new Bounds2D();
for (int i = 0; i < vertices.Count; i++)
{
bounds.AddPoint(vertices[i]);
}
Vertex center;
float radius;
bounds.BoundingCircunference(out center, out radius);
Vertex st1 = new Vertex();
Vertex st2 = new Vertex();
Vertex st3 = new Vertex();
const float DEG2RAD = (float)Math.PI / 180.0f;
st1.x = center.x + 2.0f * radius * (float)Math.Cos(0.0f * DEG2RAD);
st1.y = center.y + 2.0f * radius * (float)Math.Sin(0.0f * DEG2RAD);
st2.x = center.x + 2.0f * radius * (float)Math.Cos(120.0f * DEG2RAD);
st2.y = center.y + 2.0f * radius * (float)Math.Sin(120.0f * DEG2RAD);
st3.x = center.x + 2.0f * radius * (float)Math.Cos(240.0f * DEG2RAD);
st3.y = center.y + 2.0f * radius * (float)Math.Sin(240.0f * DEG2RAD);
adjacency.vertices.Add(st1);
adjacency.vertices.Add(st2);
adjacency.vertices.Add(st3);
stIdx1 = adjacency.vertices.Count - 3;
stIdx2 = adjacency.vertices.Count - 2;
stIdx3 = adjacency.vertices.Count - 1;
adjacency.CreateTriangle(stIdx1, stIdx2, stIdx3);
}
public void ToImage(Image img, Adjacency adjacency)
{
SolidBrush vertexColor = new SolidBrush(Color.Green);
Pen boundaryColor = new Pen(Color.Blue);
Pen cellColor = new Pen(Color.Gray);
Graphics g = Graphics.FromImage(img);
g.Clear(Color.White);
for (int e = 0; e < edges.Count; e++)
{
Vertex v0 = vertices[ edges[e].v[0] ];
Vertex v1 = vertices[ edges[e].v[1] ];
g.DrawLine(boundaryColor, v0.x * img.Width, v0.y * img.Height, v1.x * img.Width, v1.y * img.Height);
Vertex cellA = adjacency.vertices[edges[e].cell[0]];
Vertex cellB = adjacency.vertices[edges[e].cell[1]];
Vertex centerV = new Vertex((v0.x + v1.x) * 0.5f, (v0.y + v1.y) * 0.5f);
g.DrawLine(cellColor, centerV.x * img.Width, centerV.y * img.Height, cellA.x * img.Width, cellA.y * img.Height);
g.DrawLine(cellColor, centerV.x * img.Width, centerV.y * img.Height, cellB.x * img.Width, cellB.y * img.Height);
}
for (int v = 0; v < vertices.Count; v++)
{
const float r = 3;
g.FillEllipse(vertexColor, new RectangleF(vertices[v].x * img.Width - r, vertices[v].y * img.Height - r, 2 * r, 2 * r));
}
}
private static void MergeTiles(List <PoissonSample> source, List <PoissonSample> toMerge,
neighbour_e side,
out List <PoissonSample> result)
{
List <MergeCandidate> candidates = new List <MergeCandidate>();
foreach (PoissonSample s in source)
{
candidates.Add(new MergeCandidate(s, 0));
}
foreach (PoissonSample s in toMerge)
{
candidates.Add(new MergeCandidate(s, 1));
}
const float scale = 1000.0f; // apply a temporary scaling to the Poisson points (in 0-1 range)
// before Delaunay triangulation (we'll undo this later) to avoid
// requiring very small epsilons for point snapping etc which
// may lead to numeric issues.
List <Vertex> vertices = new List <Vertex>();
for (int i = 0; i < candidates.Count; i++)
{
vertices.Add(new Vertex(candidates[i].sample.x * scale, candidates[i].sample.y * scale));
}
List <int> outTriangles;
Adjacency adjacency = new Adjacency();
Delaunay2D.Delaunay2DTriangulate(vertices, false, out outTriangles, ref adjacency);
for (int j = 0; j < adjacency.vertices.Count; j++)
{
adjacency.vertices[j].x /= scale;
adjacency.vertices[j].y /= scale;
}
Image debugImage = null;
if (OnDebugStep != null)
{
debugImage = new Bitmap(800, 800);
}
Voronoi v = Voronoi.FromDelaunay(adjacency);
#if DEBUG
if (debugImage != null)
{
v.ToImage(debugImage, adjacency);
OnDebugStep(debugImage, "Voronoi diagram generated from Delaunay Triangulation");
}
#endif
Graph g = new Graph(v, adjacency, candidates);
if (debugImage != null)
{
g.ToImage(debugImage);
OnDebugStep(debugImage, "Merging " + NeighbourName(side) + " tile: Convert voronoi diagram into a graph");
}
int v0, v1;
for (int i = 0; i < 4; i++)
{
if (i != (int)side)
{
g.Clip((WangTile.neighbour_e)i, out v0, out v1);
}
}
g.Clip(side, out v0, out v1);
#if DEBUG
if (debugImage != null)
{
g.ToImage(debugImage);
OnDebugStep(debugImage, "Graph generated from Voronoi Diagram");
}
#endif
List <int> path;
g.ShortestPath(v0, v1, out path);
List <Vertex> shape;
g.GenerateShape(path, out shape);
for (int i = 0; i < shape.Count - 1; i++) // skip last one as it is the same as the first element (they're references)
{
shape[i].x *= scale;
shape[i].y *= scale;
}
if (debugImage != null)
{
Graphics grph = Graphics.FromImage(debugImage);
Pen sp = new Pen(Color.Orange, 2);
for (int i = 0; i < shape.Count - 1; i++)
{
grph.DrawLine(sp,
shape[i].x / scale * debugImage.Width,
shape[i].y / scale * debugImage.Height,
shape[i + 1].x / scale * debugImage.Width,
shape[i + 1].y / scale * debugImage.Height);
}
OnDebugStep(debugImage, "Merging " + NeighbourName(side) + " tile: Orange line displays the lowest cost seam");
}
result = new List <PoissonSample>();
for (int i = 0; i < candidates.Count; i++)
{
bool insideSeam = GeomUtils.PointInPolygon(new Vertex(candidates[i].sample.x * scale, candidates[i].sample.y * scale), shape);
if ((insideSeam && candidates[i].sourceDist == 1) ||
(!insideSeam && candidates[i].sourceDist == 0))
{
result.Add(candidates[i].sample);
}
}
if (debugImage != null)
{
Graphics grph = Graphics.FromImage(debugImage);
grph.Clear(Color.White);
SolidBrush brushInside = new SolidBrush(Color.Red);
SolidBrush brushOutside = new SolidBrush(Color.Gray);
for (int i = 0; i < result.Count; i++)
{
bool insideSeam = GeomUtils.PointInPolygon(new Vertex(result[i].x * scale, result[i].y * scale), shape);
float r = (float)debugImage.Width * 0.01f;
RectangleF rect = new RectangleF(result[i].x * debugImage.Width - r, result[i].y * debugImage.Height - r, 2.0f * r, 2.0f * r);
if (insideSeam)
{
grph.FillEllipse(brushInside, rect);
}
else
{
grph.FillEllipse(brushOutside, rect);
}
}
OnDebugStep(debugImage, "Merging " + NeighbourName(side) + " tile: gray dots = base tile, red dots = merged points");
}
}
internal void OnDelaunayStep(Adjacency adjacency)
{
Bitmap bmp = new Bitmap(800, 800);
float scale = 1000.0f;
for (int j = 0; j < adjacency.vertices.Count; j++)
{
adjacency.vertices[j].x /= scale;
adjacency.vertices[j].y /= scale;
}
adjacency.ToImage(bmp);
for (int j = 0; j < adjacency.vertices.Count; j++)
{
adjacency.vertices[j].x *= scale;
adjacency.vertices[j].y *= scale;
}
QueueDebugImage(bmp);
}
internal void OnDelaunayTriangleCheck(Adjacency adjacency, int triangle)
{
Bitmap img = new Bitmap(800,800);
Random random = new Random();
float scale = 1000.0f;
for (int j = 0; j < adjacency.vertices.Count; j++)
{
adjacency.vertices[j].x /= scale;
adjacency.vertices[j].y /= scale;
}
adjacency.ToImage(img);
Graphics g = Graphics.FromImage(img);
PointF[] points = new PointF[3];
for (int i = 0; i < 3; i++)
{
Vertex v = adjacency.vertices[adjacency.triangles[triangle].vertices[i]];
points[i] = new PointF(v.x * img.Width, v.y * img.Height);
}
g.FillPolygon(new SolidBrush(Color.FromArgb(random.Next(255), random.Next(255), random.Next(255))), points);
for (int j = 0; j < adjacency.vertices.Count; j++)
{
adjacency.vertices[j].x *= scale;
adjacency.vertices[j].y *= scale;
}
QueueDebugImage(img);
}
private static void Delaunay2DRemoveSuperTriangle(Adjacency adjacency, int stIdx1, int stIdx2, int stIdx3, out List<int> outTriangles, List<Vertex> vertices)
{
outTriangles = new List<int>();
// remove triangles containing vertices from the supertriangle
for (int i = 0; i < adjacency.triangles.Count; i++)
{
Adjacency.Triangle triangle = adjacency.triangles[i];
if (!triangle.valid)
{
continue;
}
if (triangle.Contains(stIdx1) || triangle.Contains(stIdx2) || triangle.Contains(stIdx3))
{
adjacency.RemoveTriangle(i);
}
else
{
for (int j = 0; j < 3; j++)
{
Debug.Assert(triangle.vertices[j] >= 0 && triangle.vertices[j] < adjacency.vertices.Count);
outTriangles.Add(triangle.vertices[j]);
}
}
}
adjacency.invalidTriangles.Clear();
// remove first 3 vertices (belonging to the supertriangle) and remap all remaining tris
for (int i = 0; i < outTriangles.Count; i++)
{
outTriangles[i] -= 3;
}
int numTris = adjacency.triangles.Count;
for (int i = 0; i < numTris; i++)
{
if (!adjacency.triangles[i].valid)
{
int remappedTriangle = numTris - 1;
if (remappedTriangle > i)
{
adjacency.triangles[i] = adjacency.triangles[remappedTriangle];
numTris--;
// remap edges pointing to this triangle
for (int e = 0; e < 3; e++)
{
int edgeIndex = Math.Abs(adjacency.triangles[i].edges[e]) - 1;
if (adjacency.edges[edgeIndex].triangles[0] == remappedTriangle)
adjacency.edges[edgeIndex].triangles[0] = i;
if (adjacency.edges[edgeIndex].triangles[1] == remappedTriangle)
adjacency.edges[edgeIndex].triangles[1] = i;
}
#if false
for (int e = 0; e < adjacency.edges.Count; e++)
{
Adjacency.Edge edge = adjacency.edges[e];
for (int et = 0; et < 2; et++)
{
Debug.Assert(edge.triangles[et] != i);
if (edge.triangles[et] == remappedTriangle)
{
edge.triangles[et] = i;
}
}
}
#endif
i--;
}
}
else
{
Adjacency.Triangle t = adjacency.triangles[i];
t.vertices[0] -= 3;
t.vertices[1] -= 3;
t.vertices[2] -= 3;
}
}
adjacency.triangles.RemoveRange(numTris, adjacency.triangles.Count - numTris);
adjacency.vertices = vertices;
for (int i = 0; i < adjacency.edges.Count; i++)
{
adjacency.edges[i].vertices[0] -= 3;
adjacency.edges[i].vertices[1] -= 3;
}
}
public static bool Delaunay2DTriangulate( List<Vertex> vertices, bool removeSurroundingTriangle, out List<int> outTriangles, ref Adjacency adjacencyInfo )
{
/* Implements Lawson algorithm:
http://www.henrikzimmer.com/VoronoiDelaunay.pdf
Unlike the Watson algorithm the Lawson algorithm is not based finding circumcircles and deleting
triangles to obtain an insertion polygon. Lawson's incremental insertion algorithm utilizes edge
flippings to achieve the same result and thus avoids a possibly faulty, degenerate mesh which can
occur using Watsons method.
In the same way as before, if we are not given a start triangulation we use a super triangle
enclosing all vertices in V . In every insertion step a vertex p belonging to V is inserted.
A simple retriangulation is made where the edges are inserted between p and the corner vertices of
the triangle containing p (fig.11). For all new triangles formed the circumcircles are checked, if they contain
any neighbouring vertex the edge between them is flipped. This process is executed recursively
until there are no more faulty triangles and no more flips are required (fig.12). The algorithm then
moves on, inserting another vertex from V until they have all been triangulated into a mesh, then,
like before the super triangle and its edge are removed.
*/
if ( vertices.Count < 3 )
{
outTriangles = new List<int>();
return false;
}
Adjacency adjacency = adjacencyInfo;
if ( adjacencyInfo == null ) {
adjacency = new Adjacency();
};
int stIdx1, stIdx2, stIdx3;
Delaunay2DCreateSuperTriangle(vertices, adjacency, out stIdx1, out stIdx2, out stIdx3 );
if (!Delaunay2DInsertPoints(vertices, adjacency))
{
outTriangles = new List<int>();
return false;
}
if (removeSurroundingTriangle)
{
Delaunay2DRemoveSuperTriangle(adjacency, stIdx1, stIdx2, stIdx3, out outTriangles, vertices);
}
else
{
// move the 3 vertices from the supertriangle right to the end of
// the array instead of the beginning, so that the N first vertices
// match with the point insertion order
foreach (Adjacency.Edge e in adjacency.edges)
{
for (int i = 0; i < 2; i++)
{
e.vertices[i] -= 3;
if (e.vertices[i] < 0) e.vertices[i] += adjacency.vertices.Count;
}
}
foreach (Adjacency.Triangle t in adjacency.triangles)
{
for (int i = 0; i < 3; i++)
{
t.vertices[i] -= 3;
if (t.vertices[i] < 0) t.vertices[i] += adjacency.vertices.Count;
}
}
adjacency.vertices.Add(adjacency.vertices[0]);
adjacency.vertices.Add(adjacency.vertices[1]);
adjacency.vertices.Add(adjacency.vertices[2]);
adjacency.vertices.RemoveAt(0);
adjacency.vertices.RemoveAt(0);
adjacency.vertices.RemoveAt(0);
//
outTriangles = new List<int>();
for (int i = 0; i < adjacency.triangles.Count; i++)
{
if (adjacency.triangles[i].valid)
{
outTriangles.Add(adjacency.triangles[i].vertices[0]);
outTriangles.Add(adjacency.triangles[i].vertices[1]);
outTriangles.Add(adjacency.triangles[i].vertices[2]);
}
}
}
return true;
}
private static void MergeTiles(List<PoissonSample> source, List<PoissonSample> toMerge,
neighbour_e side,
out List<PoissonSample> result)
{
List<MergeCandidate> candidates = new List<MergeCandidate>();
foreach (PoissonSample s in source) candidates.Add(new MergeCandidate(s, 0));
foreach (PoissonSample s in toMerge) candidates.Add(new MergeCandidate(s, 1));
const float scale = 1000.0f; // apply a temporary scaling to the Poisson points (in 0-1 range)
// before Delaunay triangulation (we'll undo this later) to avoid
// requiring very small epsilons for point snapping etc which
// may lead to numeric issues.
List<Vertex> vertices = new List<Vertex>();
for (int i = 0; i < candidates.Count; i++)
{
vertices.Add(new Vertex(candidates[i].sample.x * scale, candidates[i].sample.y * scale));
}
List<int> outTriangles;
Adjacency adjacency = new Adjacency();
Delaunay2D.Delaunay2DTriangulate(vertices, false, out outTriangles, ref adjacency);
for (int j = 0; j < adjacency.vertices.Count; j++)
{
adjacency.vertices[j].x /= scale;
adjacency.vertices[j].y /= scale;
}
Image debugImage = null;
if (OnDebugStep != null) debugImage = new Bitmap(800, 800);
Voronoi v = Voronoi.FromDelaunay(adjacency);
#if DEBUG
if (debugImage != null)
{
v.ToImage(debugImage, adjacency);
OnDebugStep(debugImage, "Voronoi diagram generated from Delaunay Triangulation");
}
#endif
Graph g = new Graph(v, adjacency, candidates);
if (debugImage != null)
{
g.ToImage(debugImage);
OnDebugStep(debugImage, "Merging " + NeighbourName(side) + " tile: Convert voronoi diagram into a graph");
}
int v0, v1;
for (int i = 0; i < 4; i++)
if (i != (int)side) g.Clip((WangTile.neighbour_e)i, out v0, out v1);
g.Clip(side, out v0, out v1);
#if DEBUG
if (debugImage != null)
{
g.ToImage(debugImage);
OnDebugStep(debugImage, "Graph generated from Voronoi Diagram");
}
#endif
List<int> path;
g.ShortestPath(v0, v1, out path);
List<Vertex> shape;
g.GenerateShape(path, out shape);
for (int i = 0; i < shape.Count - 1; i++) // skip last one as it is the same as the first element (they're references)
{
shape[i].x *= scale;
shape[i].y *= scale;
}
if (debugImage != null)
{
Graphics grph = Graphics.FromImage(debugImage);
Pen sp = new Pen(Color.Orange, 2);
for (int i = 0; i < shape.Count - 1; i++)
{
grph.DrawLine(sp,
shape[i].x / scale * debugImage.Width,
shape[i].y / scale * debugImage.Height,
shape[i + 1].x / scale * debugImage.Width,
shape[i + 1].y / scale * debugImage.Height);
}
OnDebugStep(debugImage, "Merging " + NeighbourName(side) + " tile: Orange line displays the lowest cost seam");
}
result = new List<PoissonSample>();
for (int i = 0; i < candidates.Count; i++)
{
bool insideSeam = GeomUtils.PointInPolygon(new Vertex(candidates[i].sample.x * scale, candidates[i].sample.y * scale), shape);
if ((insideSeam && candidates[i].sourceDist == 1) ||
(!insideSeam && candidates[i].sourceDist == 0))
result.Add(candidates[i].sample);
}
if (debugImage != null)
{
Graphics grph = Graphics.FromImage(debugImage);
grph.Clear(Color.White);
SolidBrush brushInside = new SolidBrush(Color.Red);
SolidBrush brushOutside = new SolidBrush(Color.Gray);
for (int i = 0; i < result.Count; i++)
{
bool insideSeam = GeomUtils.PointInPolygon(new Vertex(result[i].x * scale, result[i].y * scale), shape);
float r = (float)debugImage.Width * 0.01f;
RectangleF rect = new RectangleF(result[i].x * debugImage.Width - r, result[i].y * debugImage.Height - r, 2.0f * r, 2.0f * r);
if (insideSeam)
grph.FillEllipse(brushInside, rect);
else
grph.FillEllipse(brushOutside, rect);
}
OnDebugStep(debugImage, "Merging " + NeighbourName(side) + " tile: gray dots = base tile, red dots = merged points");
}
}
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 void Delaunay2DRemoveSuperTriangle(Adjacency adjacency, int stIdx1, int stIdx2, int stIdx3, out List <int> outTriangles, List <Vertex> vertices)
{
outTriangles = new List <int>();
// remove triangles containing vertices from the supertriangle
for (int i = 0; i < adjacency.triangles.Count; i++)
{
Adjacency.Triangle triangle = adjacency.triangles[i];
if (!triangle.valid)
{
continue;
}
if (triangle.Contains(stIdx1) || triangle.Contains(stIdx2) || triangle.Contains(stIdx3))
{
adjacency.RemoveTriangle(i);
}
else
{
for (int j = 0; j < 3; j++)
{
Debug.Assert(triangle.vertices[j] >= 0 && triangle.vertices[j] < adjacency.vertices.Count);
outTriangles.Add(triangle.vertices[j]);
}
}
}
adjacency.invalidTriangles.Clear();
// remove first 3 vertices (belonging to the supertriangle) and remap all remaining tris
for (int i = 0; i < outTriangles.Count; i++)
{
outTriangles[i] -= 3;
}
int numTris = adjacency.triangles.Count;
for (int i = 0; i < numTris; i++)
{
if (!adjacency.triangles[i].valid)
{
int remappedTriangle = numTris - 1;
if (remappedTriangle > i)
{
adjacency.triangles[i] = adjacency.triangles[remappedTriangle];
numTris--;
// remap edges pointing to this triangle
for (int e = 0; e < 3; e++)
{
int edgeIndex = Math.Abs(adjacency.triangles[i].edges[e]) - 1;
if (adjacency.edges[edgeIndex].triangles[0] == remappedTriangle)
{
adjacency.edges[edgeIndex].triangles[0] = i;
}
if (adjacency.edges[edgeIndex].triangles[1] == remappedTriangle)
{
adjacency.edges[edgeIndex].triangles[1] = i;
}
}
#if false
for (int e = 0; e < adjacency.edges.Count; e++)
{
Adjacency.Edge edge = adjacency.edges[e];
for (int et = 0; et < 2; et++)
{
Debug.Assert(edge.triangles[et] != i);
if (edge.triangles[et] == remappedTriangle)
{
edge.triangles[et] = i;
}
}
}
#endif
i--;
}
}
else
{
Adjacency.Triangle t = adjacency.triangles[i];
t.vertices[0] -= 3;
t.vertices[1] -= 3;
t.vertices[2] -= 3;
}
}
adjacency.triangles.RemoveRange(numTris, adjacency.triangles.Count - numTris);
adjacency.vertices = vertices;
for (int i = 0; i < adjacency.edges.Count; i++)
{
adjacency.edges[i].vertices[0] -= 3;
adjacency.edges[i].vertices[1] -= 3;
}
}