/// <summary>
/// Compute the convex hull in 3-D space
/// </summary>
/// <returns>surfaces of the convex hull</returns>
public List <TriangularFace> Compute()
{
NumFace = 0;
if (NumVertex < 4)
{
return(null);
}
Prepare();
for (int i = 4; i < NumVertex; i++)
{
for (int j = 0; j < NumFace; j++)
{
if (HullFace[j].Valid && HullFace[j].VOutFace(Vertices[i]))
{
Horizon.Clear();
ComputeHorizon(HullFace[j], Vertices[i]);
SortHorizons();
TriangularFace first = null;
TriangularFace last = null;
DualSite v = Vertices[i];
for (int ii = 0; ii < Horizon.Count; ii++)
{
Edge e = Horizon[ii];
TriangularFace f = e.NeighborFace;
TriangularFace add = new TriangularFace(e.Vertex0, e.Vertex1, v);
HullFace.Add(add);
NumFace++;
f.SetNeighbor(add, e.Vertex0, e.Vertex1);
if (first == null)
{
first = add;
}
else
{
add.SetNeighbor(last, e.Vertex0, v);
}
last = add;
}
last.SetNeighbor(first, last.Edge0.Vertex1, Vertices[i]);
break;
}
}
}
List <TriangularFace> result = new List <TriangularFace>();
for (int i = 0; i < HullFace.Count; i++)
{
if (HullFace[i].Valid)
{
result.Add(HullFace[i]);
}
}
return(result);
}
/// <summary>
/// let the first three vertices noncollinear and the first four vertices noncoplanar
/// </summary>
private void Prepare()
{
Vector3D tmp_vector = new Vector3D();
for (int i = 2; i < NumVertex; i++)
{
tmp_vector = Vector3D.CrossProduct(Vertices[1].Coordinate - Vertices[0].Coordinate, Vertices[i].Coordinate - Vertices[0].Coordinate);
if (tmp_vector.LengthSquared > Eps)//三点不共线
{
if (i != 2)
{
DualSite tmp = Vertices[i];
Vertices[i] = Vertices[2];
Vertices[2] = tmp;
}
break;
}
}
for (int i = 3; i < NumVertex; i++)
{
if (Math.Abs(Vector3D.DotProduct(tmp_vector, Vertices[i].Coordinate - Vertices[0].Coordinate)) > Eps)//四点不共面
{
if (i != 3)
{
DualSite tmp = Vertices[i];
Vertices[i] = Vertices[3];
Vertices[3] = tmp;
}
break;
}
}
//为使面法向量方向指向凸包外
TriangularFace tmp_face = new TriangularFace(Vertices[0], Vertices[1], Vertices[2]);
if (tmp_face.VOutFace(Vertices[3]))
{
DualSite tmp = Vertices[2];
Vertices[2] = Vertices[3];
Vertices[3] = tmp;
}
HullFace.Add(new TriangularFace(Vertices[0], Vertices[1], Vertices[2]));
HullFace.Add(new TriangularFace(Vertices[1], Vertices[3], Vertices[2]));
HullFace.Add(new TriangularFace(Vertices[0], Vertices[2], Vertices[3]));
HullFace.Add(new TriangularFace(Vertices[0], Vertices[3], Vertices[1]));
HullFace[0].SetNeighbor(HullFace[1], Vertices[1], Vertices[2]);
HullFace[0].SetNeighbor(HullFace[2], Vertices[0], Vertices[2]);
HullFace[0].SetNeighbor(HullFace[3], Vertices[0], Vertices[1]);
HullFace[1].SetNeighbor(HullFace[2], Vertices[2], Vertices[3]);
HullFace[1].SetNeighbor(HullFace[3], Vertices[1], Vertices[3]);
HullFace[2].SetNeighbor(HullFace[3], Vertices[0], Vertices[3]);
NumFace = 4;
}
private void MainLoop()
{
int count = 0;
while (faceQueue.Count > 0)
{
count++;
HullFace face = faceQueue.Dequeue();
if (face.active == false)
{
continue;
}
if (face.furthestIndex != -1)
{
int p0 = face.furthestIndex;
this.hullVertices.Add(p0);
// collect visible faces, boundary edges and assoicated vertices
List <HullFace> holeFace = new List <HullFace>();
HashSet <EdgeRecord> holeBoundary = new HashSet <EdgeRecord>();
HashSet <int> assoicatedVertex = new HashSet <int>();
foreach (HullFace f in this.surfaceSet)
{
Vector3d v = this.p[p0] - this.p[f.p1];
if (v.Dot(f.normal) > 0)
{
holeFace.Add(f);
int p1 = f.p1;
int p2 = f.p2;
int p3 = f.p3;
EdgeRecord r1 = new EdgeRecord(p1, p2);
EdgeRecord r2 = new EdgeRecord(p2, p3);
EdgeRecord r3 = new EdgeRecord(p3, p1);
if (holeBoundary.Contains(r1))
{
holeBoundary.Remove(r1);
}
else
{
holeBoundary.Add(r1);
}
if (holeBoundary.Contains(r2))
{
holeBoundary.Remove(r2);
}
else
{
holeBoundary.Add(r2);
}
if (holeBoundary.Contains(r3))
{
holeBoundary.Remove(r3);
}
else
{
holeBoundary.Add(r3);
}
foreach (int index in f.associatedPoints)
{
assoicatedVertex.Add(index);
}
}
}
if (holeFace.Count == 0)
{
throw new Exception();
}
// remove add visible faces
foreach (HullFace f in holeFace)
{
this.surfaceSet.Remove(f);
f.active = false;
}
// add new faces
foreach (EdgeRecord edge in holeBoundary)
{
HullFace newFace = new HullFace(p0, edge.p1, edge.p2);
newFace.normal = ((p[edge.p1] - p[p0]).Cross(p[edge.p2] - p[p0])).normalize();
this.surfaceSet.Add(newFace);
this.faceQueue.Enqueue(newFace);
// add assoicated vertices
foreach (int index in assoicatedVertex)
{
if (index == p0)
{
continue;
}
double dis = (p[index] - p[p0]).Dot(newFace.normal);
if (dis > 0)
{
newFace.AddPoint(index, dis);
}
}
}
}
}
computeCenter();
}
private void InitHullFaces()
{
// get init points
int[] initPts = FindInitPoints();
this.initIndex = initPts;
int p0 = initPts[0];
int p1 = initPts[1];
int p2 = initPts[2];
int p3 = initPts[3];
double vol = (p[p1] - p[p0]).Dot((p[p2] - p[p0]).Cross(p[p3] - p[p0]));
if (vol > 0)
{
int t = p0; p0 = p1; p1 = t;
}
this.hullVertices.Add(p0);
this.hullVertices.Add(p1);
this.hullVertices.Add(p2);
this.hullVertices.Add(p3);
// create hull faces
HullFace f1 = new HullFace(p0, p1, p2); this.faceQueue.Enqueue(f1);
HullFace f2 = new HullFace(p3, p1, p0); this.faceQueue.Enqueue(f2);
HullFace f3 = new HullFace(p3, p2, p1); this.faceQueue.Enqueue(f3);
HullFace f4 = new HullFace(p3, p0, p2); this.faceQueue.Enqueue(f4);
f1.normal = ((p[p1] - p[p0]).Cross(p[p2] - p[p0])).normalize();
f2.normal = ((p[p1] - p[p3]).Cross(p[p0] - p[p3])).normalize();
f3.normal = ((p[p2] - p[p3]).Cross(p[p1] - p[p3])).normalize();
f4.normal = ((p[p0] - p[p3]).Cross(p[p2] - p[p3])).normalize();
this.surfaceSet.Add(f1);
this.surfaceSet.Add(f2);
this.surfaceSet.Add(f3);
this.surfaceSet.Add(f4);
// assoicate vertices outside current hull
foreach (int i in this.pointIndex)
{
if (i == p0 || i == p1 || i == p2 || i == p3)
{
continue;
}
double d1 = (p[i] - p[p0]).Dot(f1.normal);
double d2 = (p[i] - p[p3]).Dot(f2.normal);
double d3 = (p[i] - p[p3]).Dot(f3.normal);
double d4 = (p[i] - p[p3]).Dot(f4.normal);
if (d1 < 0 && d2 < 0 && d3 < 0 && d4 < 0)
{
continue;
}
if (d1 > 0)
{
f1.AddPoint(i, d1);
}
if (d2 > 0)
{
f2.AddPoint(i, d2);
}
if (d3 > 0)
{
f3.AddPoint(i, d3);
}
if (d4 > 0)
{
f4.AddPoint(i, d4);
}
}
}
public List<HullEdge> GetSharedEdges(HullFace other)
{
List<HullEdge> result = new List<HullEdge>();
if (ab.IsContainedIn(other))
result.Add(ab);
if (ca.IsContainedIn(other))
result.Add(ca);
if (bc.IsContainedIn(other))
result.Add(bc);
return result;
}
public bool IsContainedIn(HullFace other)
{
return Equivalent(other.ab) || Equivalent(other.ca) || Equivalent(other.bc);
}