public void AreaGrowByFace()
{
List <TriMesh.Face> selectedFaces = new List <TriMesh.Face>();
for (int i = 0; i < this.mesh.Faces.Count; i++)
{
if (this.mesh.Faces[i].Traits.SelectedFlag > 0)
{
selectedFaces.Add(this.mesh.Faces[i]);
}
}
for (int i = 0; i < selectedFaces.Count; i++)
{
foreach (TriMesh.Face face in selectedFaces[i].Faces)
{
if (face.Traits.SelectedFlag == 0)
{
double temp1 = 0, temp2 = 0, temp = 0, area = 0;
temp1 = TriMeshUtil.ComputeAreaFace(face);
temp2 = TriMeshUtil.ComputeAreaFace(selectedFaces[i]);
temp = Math.Abs(temp1 - temp2);
for (int j = 0; j < selectedFaces[i].FaceCount; j++)
{
area += TriMeshUtil.ComputeAreaFace(selectedFaces[i].GetFace(j));
}
area = area / selectedFaces[i].FaceCount;
if (temp < 0.916 * area)
{
face.Traits.SelectedFlag = selectedFaces[i].Traits.SelectedFlag;
}
}
}
}
}
//vertex area
public static double ComputeAreaOneRing(TriMesh.Vertex vertex)
{
double area = 0;
foreach (TriMesh.Face face in vertex.Faces)
{
area += TriMeshUtil.ComputeAreaFace(face);
}
return(area);
}
public SparseMatrixDouble BuildHodgeStar2Form(TriMesh mesh)
{
SparseMatrixDouble star2 = new SparseMatrixDouble(mesh.Faces.Count, mesh.Faces.Count);
foreach (TriMesh.Face face in mesh.Faces)
{
star2[face.Index, face.Index] = 1 / TriMeshUtil.ComputeAreaFace(face);
}
Star2 = star2;
return(star2);
}
public SparseMatrixComplex cBuildHodgeStar2Form(TriMesh mesh)
{
SparseMatrixComplex star2 = new SparseMatrixComplex(mesh.Faces.Count, mesh.Faces.Count);
foreach (TriMesh.Face face in mesh.Faces)
{
Complex value = new Complex(1 / TriMeshUtil.ComputeAreaFace(face), 0);
star2[face.Index, face.Index] = value;
}
return(star2);
}
//public static void PreserveVolume(TriMesh mesh)
//{
// double oldVolume = TriMeshUtil.ComputeVolume(Mesh);
// double newVolume = TriMeshUtil.ComputeVolume(Mesh);
// for (int i = 0; i < n; i++)
// {
// Mesh.Vertices[i].Traits.Position.x *= Math.Pow(oldVolume / newVolume, 1 / 3);
// Mesh.Vertices[i].Traits.Position.y *= Math.Pow(oldVolume / newVolume, 1 / 3);
// Mesh.Vertices[i].Traits.Position.z *= Math.Pow(oldVolume / newVolume, 1 / 3);
// }
//}
public static void PreModifiyGeometry(TriMesh mesh)
{
double ModifyVertexScale = 100;
int n = mesh.Vertices.Count;
for (int j = 0; j < 10; j++)
{
bool updated = false;
TriMeshUtil.SetUpNormalVertex(mesh);
for (int i = 0; i < n; i++)
{
// build matrix U
Matrix3D U = new Matrix3D();
Vector3D u1 = mesh.Vertices[i].Traits.Position;
foreach (TriMesh.Vertex neighbor in mesh.Vertices[i].Vertices)
{
Vector3D u21 = neighbor.Traits.Position - u1;
U += u21.OuterCross(u21);
}
// Test for degenerated
Matrix3D invU = U.InverseSVD();
if (Matrix3D.lastSVDIsFullRank == false)
{
Vector3D normal = mesh.Vertices[i].Traits.Normal;
double area = 0;
foreach (TriMesh.Face face in mesh.Vertices[i].Faces)
{
area += TriMeshUtil.ComputeAreaFace(face);
}
Vector3D newU1 = u1 + normal.Normalize() * Math.Sqrt(area / 3.0) / ModifyVertexScale;
mesh.Vertices[i].Traits.Position = newU1;
updated = true;
}
}
if (!updated)
{
break;
}
}
}
SparseMatrixQuaternion BuildEigenValueProblem(double[] rho)
{
int nV = mesh.Vertices.Count;
SparseMatrixQuaternion E = new SparseMatrixQuaternion(nV, nV);
int[] Indices = new int[3];
foreach (TriMesh.Face face in mesh.Faces)
{
double A = TriMeshUtil.ComputeAreaFace(face);
double a = -1 / (4 * A);
double b = rho[face.Index] / 6;
double c = A * rho[face.Index] * rho[face.Index] / 9;
Indices[0] = face.GetVertex(0).Index;
Indices[1] = face.GetVertex(1).Index;
Indices[2] = face.GetVertex(2).Index;
Quaternion[] e = new Quaternion[3];
for (int i = 0; i < 3; i++)
{
Vector3D eV = mesh.Vertices[Indices[(i + 2) % 3]].Traits.Position -
mesh.Vertices[Indices[(i + 1) % 3]].Traits.Position;
e[i] = new Quaternion(eV, 0);
}
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
Quaternion q = a * e[i] * e[j] + b * (e[j] - e[i]) + c;
E[Indices[i], Indices[j]] += q;
}
}
}
return(E);
}
public SparseMatrix BuildMatrixMass(TriMesh mesh)
{
int n = mesh.Vertices.Count;
SparseMatrix L = new SparseMatrix(n, n);
for (int i = 0; i < mesh.Edges.Count; i++)
{
double face0area = 0;
double face1area = 0;
if (mesh.Edges[i].Face0 != null)
{
face0area = TriMeshUtil.ComputeAreaFace(mesh.Edges[i].Face0);
}
if (mesh.Edges[i].Face1 != null)
{
face1area = TriMeshUtil.ComputeAreaFace(mesh.Edges[i].Face1);
}
L.AddValueTo(mesh.Edges[i].Vertex0.Index,
mesh.Edges[i].Vertex1.Index,
(face0area + face1area) / 12);
L.AddValueTo(mesh.Edges[i].Vertex1.Index,
mesh.Edges[i].Vertex0.Index,
(face0area + face1area) / 12);
}
for (int i = 0; i < n; i++)
{
double sum = 0;
foreach (SparseMatrix.Element e in L.Rows[i])
{
sum += e.value;
}
L.AddValueTo(i, i, sum);
}
L.SortElement();
return(L);
}
public static void RegionGrow(TriMesh mesh)
{
Vector3D[] normal = TriMeshUtil.ComputeNormalFace(mesh);
double[] area = TriMeshUtil.ComputeAreaFace(mesh);
SortedList <double, TriMesh.Face> sort = new SortedList <double, HalfEdgeMesh.Face>();
foreach (var center in mesh.Faces)
{
List <double> list = new List <double>();
double sum = 0;
foreach (var round in center.Faces)
{
double l = (normal[round.Index] - normal[center.Index]).Length();// * area[round.Index]);
sum += l;
list.Add(l);
}
sum /= list.Count;
double d = 0;
foreach (var item in list)
{
d += Math.Pow(item - sum, 2);
}
d /= list.Count;
if (sum < 1 && d < 0.1)
{
sort.Add(sum, center);
}
}
Stack <TriMesh.Face> stack = new Stack <HalfEdgeMesh.Face>();
Dictionary <int, Cluster> dict = new Dictionary <int, Cluster>();
double k = 1;
int flag = 0;
do
{
if (stack.Count == 0)
{
bool run = false;
if (flag > 100)
{
return;
}
for (int i = flag; i < sort.Count; i++)
{
TriMesh.Face next = sort.Values[i];
if (next.Traits.SelectedFlag == 0)
{
flag++;
next.Traits.SelectedFlag = (byte)flag;
stack.Push(next);
dict[flag] = new Cluster();
dict[flag].Add(normal[sort.Values[i].Index]);
run = true;
break;
}
}
if (!run)
{
return;
}
}
TriMesh.Face center = stack.Pop();
foreach (var round in center.Faces)
{
if (round.Traits.SelectedFlag == 0 &&
(normal[round.Index] - normal[center.Index]).Length() < k &&
(normal[round.Index] - dict[flag].Center).Length() < k)
{
dict[flag].Add(normal[round.Index]);
round.Traits.SelectedFlag = (byte)flag;
stack.Push(round);
}
}
} while (true);
}
private void InitVertexInfo()
{
this.dataGridViewVertex.Rows.Clear();
foreach (TriMesh.Vertex vertex in Mesh.Vertices)
{
this.dataGridViewVertex.Rows.Add(vertex.Index, vertex.Traits.Position.x, vertex.Traits.Position.y, vertex.Traits.Position.z);
}
foreach (TriMesh.Face face in Mesh.Faces)
{
this.dataGridViewFace.Rows.Add(face.Index, face.GetVertex(0).Index, face.GetVertex(1).Index, face.GetVertex(2).Index, TriMeshUtil.ComputeAreaFace(face));
}
foreach (TriMesh.Edge edge in Mesh.Edges)
{
string face0 = "null";
string face1 = "null";
if (edge.Face0 != null)
{
face0 = edge.Face0.Index.ToString();
}
if (edge.Face1 != null)
{
face1 = edge.Face1.Index.ToString();
}
this.dataGridViewEdge.Rows.Add(edge.Index,
edge.Vertex0.Index,
edge.Vertex1.Index, face0,
face1, TriMeshUtil.ComputeEdgeLength(edge),
TriMeshUtil.ComputeDihedralAngle(edge) / 3.14 * 180);
}
}
protected override double GetValue(HalfEdgeMesh.Face target)
{
return(TriMeshUtil.ComputeAreaFace(target));
}
public static void ComputeCornerArea(TriMesh mesh, out double[] CornerArea, out double[] PointArea)
{
CornerArea = new double[mesh.HalfEdges.Count];
PointArea = new double[mesh.Vertices.Count];
foreach (var face in mesh.Faces)
{
double area = TriMeshUtil.ComputeAreaFace(face);
TriMesh.HalfEdge[] hf = new HalfEdgeMesh.HalfEdge[]
{
face.HalfEdge,
face.HalfEdge.Next,
face.HalfEdge.Previous
};
int[] index = new int[3];
for (int i = 0; i < 3; i++)
{
index[i] = hf[i].Index;
}
Vector3D[] e = new Vector3D[3];
for (int i = 0; i < 3; i++)
{
e[i] = TriMeshUtil.GetHalfEdgeVector(hf[i].Previous);
}
double[] l2 = new double[3];
for (int i = 0; i < 3; i++)
{
l2[i] = e[i].LengthSquared;
}
double[] ew = new double[3];
for (int i = 0; i < 3; i++)
{
ew[i] = l2[i] * (l2[(i + 1) % 3] + l2[(i + 2) % 3] - l2[i]);
}
bool flag = false;
for (int i = 0; i < 3; i++)
{
if (ew[i] < 0d)
{
int a = (i + 1) % 3;
int b = (i + 2) % 3;
CornerArea[index[a]] = -0.25d * l2[b] * area / e[i].Dot(e[b]);
CornerArea[index[b]] = -0.25d * l2[a] * area / e[i].Dot(e[a]);
CornerArea[index[i]] = area - CornerArea[index[a]] - CornerArea[index[b]];
flag = true;
}
}
if (!flag)
{
double ewscale = 0.5d * area / (ew[0] + ew[1] + ew[2]);
for (int i = 0; i < 3; i++)
{
CornerArea[index[i]] = ewscale * (ew[(i + 1) % 3] + ew[(i + 2) % 3]);
}
}
for (int i = 0; i < 3; i++)
{
PointArea[hf[i].ToVertex.Index] += CornerArea[index[i]];
}
}
}