protected List <Vertex2D> GetSpinePoints(Chord2D chord)
{
var points = new List <Vertex2D>();
GetSpinePointsRoutine(points, chord, null);
return(points);
}
// triangles are divided at the spine
protected void Subdivide(Chord2D root)
{
var rTriangles = new List <Triangle2D>();
var rSegments = new List <Segment2D>();
SubdivideRoutine(rTriangles, rSegments, root, null);
rTriangles.ForEach(t => triangulation.RemoveTriangle(t));
rSegments.ForEach(s => triangulation.RemoveTriangle(s));
}
protected void GetSpinePointsRoutine(List <Vertex2D> points, Chord2D current, Chord2D from)
{
if (!current.Pruned)
{
points.Add(current.Src);
}
current.Connection.ForEach(to =>
{
if (to != from)
{
GetSpinePointsRoutine(points, to, current);
}
});
}
protected void Sew(Triangulation2D triangulation, Chord2D chord, Dictionary <Vertex2D, float> heightTable, int division)
{
var triangles = triangulation.Triangles.ToList();
Dictionary <Triangle2D, bool> flags = new Dictionary <Triangle2D, bool>();
// 既にSew済みのTriangle2Dを再度Sewする必要があるケースが存在する
// 特定のChord2DのSrcとDstを含むTriangle2Dなのに，それ以外のChord2Dと共通点を持っているがために
// Spineと共通エッジを持つ場合のSewの処理がかけられず適切な分割ができていないケース
Dictionary <Triangle2D, List <Triangle2D> > sews = new Dictionary <Triangle2D, List <Triangle2D> >();
triangles.ForEach(t => flags.Add(t, false));
SewRoutine(triangles, flags, sews, chord, null, division);
}
protected List <Chord2D> Traverse(Chord2D cur, Chord2D from, Func <Chord2D, bool> check)
{
var chords = new List <Chord2D>();
if (check(cur))
{
chords.Add(cur);
}
cur.Connection.ForEach(to => {
if (to != from)
{
chords.AddRange(Traverse(to, cur, check));
}
});
return(chords);
}
List <Vertex2D> GetSpinePoints(Chord2D chord)
{
var points = new List <Vertex2D>();
Action <Chord2D, Chord2D> Recursion;
Recursion = (Chord2D current, Chord2D from) => {
if (!current.Pruned)
{
points.Add(current.Src);
}
current.Connection.ForEach(to => {
if (to != from)
{
Recursion(to, current);
}
});
};
Recursion(chord, null);
return(points);
}
/*
* The chordal axis is obtained by connecting the midpoints of the internal edges.
*/
protected Chord2D GetChordalAxis(Face2D external, List <Face2D> faces)
{
var t = external.Triangle;
Vertex2D src, dst;
Segment2D dstEdge;
bool e0 = ExternalSegment(t.s0);
bool e1 = ExternalSegment(t.s1);
bool e2 = ExternalSegment(t.s2);
if (e0 && e1)
{
src = t.s0.HasPoint(t.s1.a) ? t.s1.a : t.s1.b;
dst = triangulation.CheckAndAddVertex(t.s2.Midpoint());
dstEdge = t.s2;
}
else if (e1 && e2)
{
src = t.s1.HasPoint(t.s2.a) ? t.s2.a : t.s2.b;
dst = triangulation.CheckAndAddVertex(t.s0.Midpoint());
dstEdge = t.s0;
}
else
{
src = t.s2.HasPoint(t.s0.a) ? t.s0.a : t.s0.b;
dst = triangulation.CheckAndAddVertex(t.s1.Midpoint());
dstEdge = t.s1;
}
var chord = new Chord2D(src, dst, external);
chord.SetDstEdge(dstEdge);
var connection = new Connection2D(faces);
ChordalAxisRoutine(chord, connection);
return(chord);
}
void Init(Triangulation2D triangulation)
{
contourSegments = BuildContourSegments(triangulation);
var triangles = triangulation.Triangles.ToList();
faces = Categorize(triangles);
var terminal = faces.Find(f => f.Type == Face2DType.Terminal);
chord = GetChordalAxis(terminal, faces);
var terminalChords = Traverse(chord, null, (Chord2D c) => {
return(c.Face.Type == Face2DType.Terminal);
});
var convergence = new List <Vertex2D>();
terminalChords.ForEach(c => {
Prune(c, convergence);
});
Subdivide(chord);
// var spine = GetSpinePoints(chord);
var networkTable = BuildTable(triangulation);
networks = BuildNetworks(triangulation, networkTable);
Elevate(networks);
heightTable = new Dictionary <Vertex2D, float>();
foreach (Vertex2D v in networkTable.Keys)
{
heightTable.Add(v, networkTable[v].Height);
}
Sew(triangulation, chord, heightTable, 3);
}
protected void SewRoutine(List <Triangle2D> triangles, Dictionary <Triangle2D, bool> flags, Dictionary <Triangle2D, List <Triangle2D> > sews, Chord2D current, Chord2D from, int division)
{
if (!current.Pruned)
{
triangles.FindAll(t =>
{
return(t.HasPoint(current.Src) && (t.HasPoint(current.Dst) || !sews.ContainsKey(t)));
}).ForEach(t =>
{
Segment2D[] segments;
if (sews.ContainsKey(t))
{
foreach (Triangle2D st in sews[t])
{
triangulation.RemoveTriangle(st);
}
sews.Remove(t);
}
if (t.HasPoint(current.Dst))
{
Segment2D s = t.CommonSegment(current.Src, current.Dst);
segments = t.ExcludeSegment(s);
}
else
{
segments = t.CommonSegments(current.Src);
}
SewTriangle(flags, sews, t, segments, division);
});
}
var next = current.Connection.FindAll(con => con != from);
// Prune後のSpineで末端にあたる頂点
bool terminal = next.All(con => con.Pruned);
if (terminal && !current.Pruned)
{
triangles.FindAll(t =>
{
return(!sews.ContainsKey(t) && t.HasPoint(current.Dst));
}).ForEach(t =>
{
var segments = t.CommonSegments(current.Dst);
SewTriangle(flags, sews, t, segments, division);
});
}
next.ForEach(to =>
{
SewRoutine(triangles, flags, sews, to, current, division);
});
}
protected void SubdivideRoutine(List <Triangle2D> rTriangles, List <Segment2D> rSegments, Chord2D chord, Chord2D from)
{
switch (chord.Face.Type)
{
case Face2DType.Sleeve:
if (!chord.Pruned)
{
Vertex2D top, lb, rb;
Segment2D s0 = chord.SrcEdge, s1 = chord.DstEdge;
if (s0.a == s1.a || s0.a == s1.b)
{
top = s0.a;
lb = s0.b;
}
else
{
top = s0.b;
lb = s0.a;
}
rb = (s1.a == top) ? s1.b : s1.a;
Vertex2D tl = chord.Src, tr = chord.Dst, bottom = triangulation.CheckAndAddVertex((lb.Coordinate + rb.Coordinate) * 0.5f);
// triangulation.RemoveTriangle(chord.Face.Triangle);
rTriangles.Add(chord.Face.Triangle);
triangulation.AddTriangle(top, tl, tr);
triangulation.AddTriangle(tl, lb, bottom);
triangulation.AddTriangle(tr, bottom, rb);
triangulation.AddTriangle(tl, bottom, tr);
}
break;
case Face2DType.Junction:
if (!chord.Pruned)
{
Vertex2D top, lb, rb, bottom;
if (chord.SrcEdge != null)
{
top = chord.Dst;
lb = chord.SrcEdge.a;
rb = chord.SrcEdge.b;
bottom = chord.Src;
// triangulation.RemoveTriangle(chord.SrcEdge);
rSegments.Add(chord.SrcEdge);
}
else
{
top = chord.Src;
lb = chord.DstEdge.a;
rb = chord.DstEdge.b;
bottom = chord.Dst;
// triangulation.RemoveTriangle(chord.DstEdge);
rSegments.Add(chord.DstEdge);
}
// triangulation.RemoveTriangle(chord.Face.Triangle);
triangulation.AddTriangle(top, lb, bottom);
triangulation.AddTriangle(top, rb, bottom);
}
break;
}
chord.Connection.ForEach(to => {
if (to != from)
{
SubdivideRoutine(rTriangles, rSegments, to, chord);
}
});
}
/*
* BUG
* 既にPrune済みのJunctionを再度Pruneしてしまうバグ
*/
protected void Prune(Chord2D chord, List <Vertex2D> convergence, Chord2D from = null, List <Chord2D> past = null)
{
if (chord.Face.Type == Face2DType.Junction)
{
past.Add(chord);
var centroid = chord.Face.Centroid();
var points = new List <Vertex2D>();
var ignores = new List <Vertex2D>();
for (int i = 0, n = past.Count - 1; i < n; i++)
{
var c0 = past[i];
var c1 = past[i + 1];
points.Add(c0.Face.GetUncommonPoint(c1.Face));
}
var t = chord.Face.Triangle;
Vertex2D dividePoint = null;
if (!chord.Face.Pruned)
{
points.Add(t.a); points.Add(t.b); points.Add(t.c);
var coord = chord.Src.Coordinate;
if (coord == (t.a.Coordinate + t.b.Coordinate) * 0.5f)
{
dividePoint = t.c;
}
else if (coord == (t.b.Coordinate + t.c.Coordinate) * 0.5f)
{
dividePoint = t.a;
}
else
{
dividePoint = t.b;
}
}
else
{
points.Add(t.a); points.Add(t.b); points.Add(t.c);
var divides = chord.Face.Divides;
Triangle2D t0 = divides[0], t1 = divides[1];
Vertex2D[] ps0 = t0.ExcludePoint(centroid), ps1 = t1.ExcludePoint(centroid);
if (chord.Dst.Coordinate == (ps0[0].Coordinate + ps0[1].Coordinate) * 0.5f)
{
triangulation.RemoveTriangle(t0);
if (t.a != ps0[0] && t.a != ps0[1])
{
ignores.Add(t.a);
}
else if (t.b != ps0[0] && t.b != ps0[1])
{
ignores.Add(t.b);
}
else
{
ignores.Add(t.c);
}
}
else if (chord.Dst.Coordinate == (ps1[0].Coordinate + ps1[1].Coordinate) * 0.5f)
{
triangulation.RemoveTriangle(t1);
if (t.a != ps1[0] && t.a != ps1[1])
{
ignores.Add(t.a);
}
else if (t.b != ps1[0] && t.b != ps1[1])
{
ignores.Add(t.b);
}
else
{
ignores.Add(t.c);
}
}
else
{
// Debug.LogWarning("error!");
return;
}
}
var vertices = points.OrderBy(p => Angle(centroid, p.Coordinate)).ToList();
var cv = triangulation.CheckAndAddVertex(centroid);
var newTriangles = new List <Triangle2D>();
for (int i = 0, n = vertices.Count; i < n; i++)
{
Vertex2D a = cv, b = vertices[i], c = vertices[(i + 1) % n];
if (ignores.Contains(b) || ignores.Contains(c))
{
continue;
}
var nt = triangulation.AddTriangle(a, b, c);
newTriangles.Add(nt);
}
if (!chord.Face.Pruned && dividePoint != null)
{
var divides = newTriangles.FindAll(nt => nt.HasPoint(dividePoint));
chord.Face.SetDivides(divides.ToList());
}
// finish current loop
convergence.Add(cv);
Prune(past);
return;
}
Segment2D diameter;
if (chord.Face.Type == Face2DType.Terminal)
{
var t = chord.Face.Triangle;
if (!ExternalSegment(t.s0))
{
diameter = t.s0;
}
else if (!ExternalSegment(t.s1))
{
diameter = t.s1;
}
else
{
diameter = t.s2;
}
}
else
{
var segments = chord.Face.GetUncommonSegments(from.Face);
if (!ExternalSegment(segments[0]))
{
diameter = segments[0];
}
else
{
diameter = segments[1];
}
}
if (past == null)
{
past = new List <Chord2D>();
}
past.Add(chord);
Vector2 center = diameter.Midpoint();
float radius = Vector2.Distance(center, diameter.a.Coordinate);
var found = past.Find(ch => {
var t = ch.Face.Triangle;
Vector2 a = t.a.Coordinate, b = t.b.Coordinate, c = t.c.Coordinate;
return
((!diameter.HasPoint(a) && Vector2.Distance(a, center) - radius > float.Epsilon) ||
(!diameter.HasPoint(b) && Vector2.Distance(b, center) - radius > float.Epsilon) ||
(!diameter.HasPoint(c) && Vector2.Distance(c, center) - radius > float.Epsilon));
});
if (found != null)
{
var points = new List <Vertex2D>();
for (int i = 0, n = past.Count - 1; i < n; i++)
{
var c0 = past[i];
var c1 = past[i + 1];
points.Add(c0.Face.GetUncommonPoint(c1.Face));
}
points.Add(chord.Face.GetUncommonPoint(diameter));
var basis = diameter.a.Coordinate;
var vertices = points.OrderBy(p => Angle(center, basis, p.Coordinate)).ToList();
vertices.Insert(0, diameter.a);
vertices.Add(diameter.b);
var cv = triangulation.CheckAndAddVertex(center);
for (int i = 0, n = vertices.Count - 1; i < n; i++)
{
Vertex2D a = cv, b = vertices[i], c = vertices[i + 1];
triangulation.AddTriangle(a, b, c);
}
convergence.Add(cv);
Prune(past);
return;
}
chord.Connection.ForEach(to => {
if (to != from)
{
Prune(to, convergence, chord, past.ToList());
}
});
}
protected void ChordalAxisRoutine(Chord2D chord, Connection2D connection)
{
var origin = chord.Face;
var neighbors = connection.GetNeighbors(origin);
connection.Remove(origin); // prevent overlaping to traverse
neighbors.ForEach(neighbor => {
var face = neighbor.face;
var segment = neighbor.joint;
Vertex2D destination;
Segment2D destinationEdge = null;
switch (face.Type)
{
case Face2DType.Junction:
destination = triangulation.CheckAndAddVertex(face.Centroid());
break;
case Face2DType.Sleeve:
var others = face.Triangle.ExcludeSegment(segment);
if (!ExternalSegment(others[0]))
{
destination = triangulation.CheckAndAddVertex(others[0].Midpoint());
destinationEdge = others[0];
}
else
{
destination = triangulation.CheckAndAddVertex(others[1].Midpoint());
destinationEdge = others[1];
}
break;
// case Face2DType.Terminal:
default:
destination = face.GetUncommonPoint(origin);
break;
}
Chord2D nextChord;
if (origin.Type == Face2DType.Junction)
{
var interval = new Chord2D(chord.Dst, triangulation.CheckAndAddVertex(segment.Midpoint()), origin);
interval.SetSrcEdge(chord.DstEdge); // maybe null
interval.SetDstEdge(segment);
nextChord = new Chord2D(interval.Dst, destination, face);
nextChord.SetSrcEdge(segment);
nextChord.SetDstEdge(destinationEdge); // null or exist
chord.Connect(interval);
interval.Connect(nextChord);
}
else
{
nextChord = new Chord2D(chord.Dst, destination, face);
nextChord.SetSrcEdge(chord.DstEdge);
nextChord.SetDstEdge(destinationEdge); // null or exist
chord.Connect(nextChord);
}
ChordalAxisRoutine(nextChord, connection);
});
}
void Sew(Triangulation2D triangulation, Chord2D chord, Dictionary <Vertex2D, float> heightTable, int division)
{
var triangles = triangulation.Triangles.ToList();
Dictionary <Triangle2D, bool> flags = new Dictionary <Triangle2D, bool>();
// 既にSew済みのTriangle2Dを再度Sewする必要があるケースが存在する
// 特定のChord2DのSrcとDstを含むTriangle2Dなのに，それ以外のChord2Dと共通点を持っているがために
// Spineと共通エッジを持つ場合のSewの処理がかけられず適切な分割ができていないケース
Dictionary <Triangle2D, List <Triangle2D> > sews = new Dictionary <Triangle2D, List <Triangle2D> >();
triangles.ForEach(t => flags.Add(t, false));
Action <Triangle2D, Segment2D[]> SewTriangle = (Triangle2D t, Segment2D[] segments) => {
triangulation.RemoveTriangle(t);
var sewTriangles = Sew(heightTable, triangulation, segments[0], segments[1], division);
sews.Add(t, sewTriangles);
flags[t] = true;
};
Action <Chord2D, Chord2D> SewRoutine;
SewRoutine = (Chord2D current, Chord2D from) => {
if (!current.Pruned)
{
triangles.FindAll(t => {
return(t.HasPoint(current.Src) && (t.HasPoint(current.Dst) || !sews.ContainsKey(t)));
}).ForEach(t => {
Segment2D[] segments;
if (sews.ContainsKey(t))
{
foreach (Triangle2D st in sews[t])
{
triangulation.RemoveTriangle(st);
}
sews.Remove(t);
}
if (t.HasPoint(current.Dst))
{
Segment2D s = t.CommonSegment(current.Src, current.Dst);
segments = t.ExcludeSegment(s);
}
else
{
segments = t.CommonSegments(current.Src);
}
SewTriangle(t, segments);
});
}
var next = current.Connection.FindAll(con => con != from);
// Prune後のSpineで末端にあたる頂点
bool terminal = next.All(con => con.Pruned);
if (terminal && !current.Pruned)
{
triangles.FindAll(t => {
return(!sews.ContainsKey(t) && t.HasPoint(current.Dst));
}).ForEach(t => {
var segments = t.CommonSegments(current.Dst);
SewTriangle(t, segments);
});
}
next.ForEach(to => {
SewRoutine(to, current);
});
};
SewRoutine(chord, null);
}
public void Disconnect(Chord2D c)
{
this.connection.Remove(c);
c.connection.Remove(this);
}
public void Connect(Chord2D c)
{
this.connection.Add(c);
c.connection.Add(this);
}