internal MeshGeometry3D AutoSnake(MeshGeometry3D mesh, ref MeshBuilder newmbP)
{
//Dictionary<Int32, SmileEdge> neighbours = SmileVisual3D.findNeighbours(mesh);
Point3DCollection positions = mesh.Positions;
Int32Collection triangleIndices = mesh.TriangleIndices;
Mesh3D m3d = new Mesh3D(positions, triangleIndices);
Vector3DCollection t = new Vector3DCollection(positions.Count);
Vector3DCollection b = new Vector3DCollection(positions.Count);
Vector3DCollection n = new Vector3DCollection(positions.Count);
double eThreshold = -0.5;
double nThreshold = 0.8;
double minEnergy = 10;
double alpha = 1;
double betha = 1;
double ballon = 1;
double lambda = 1;
Vector3DCollection e = new Vector3DCollection(positions.Count);
Vector3DCollection eInt = new Vector3DCollection(positions.Count);
Vector3DCollection eExt = new Vector3DCollection(positions.Count);
Vector3DCollection delta = new Vector3DCollection(positions.Count);
Vector3DCollection f = new Vector3DCollection(positions.Count);
Vector3DCollection tETF = new Vector3DCollection(positions.Count);
//Vector3DCollection k = new Vector3DCollection();
//DoubleCollection kH = new DoubleCollection();
Dictionary <int, Double> kH = new Dictionary <int, double>();
MeshBuilder newmbD = new MeshBuilder(false, false);
for (int i = 0; i < triangleIndices.Count; i += 3)
{
for (int a = 0; a < 3; a++)
{
int vi = triangleIndices[i + a];
if (!kH.ContainsKey(vi))
{
double kHi = _MeanCurvature(m3d, vi);
kH.Add(vi, kHi);
}
//Console.WriteLine("start mean");
//kH.Add(kHi);
//Console.WriteLine("end mean");
if (a == 2)
{
int vi1 = triangleIndices[i + a - 1];
int vi2 = triangleIndices[i + a - 2];
double kH3 = 0;
kH.TryGetValue(vi, out kH3);
double kH2 = 0;
kH.TryGetValue(vi1, out kH2);
double kH1 = 0;
kH.TryGetValue(vi2, out kH1);
if ((kH3 < eThreshold || kH2 < eThreshold || kH1 < eThreshold))
{
newmbD.Positions.Add(positions[vi]);
newmbD.Positions.Add(positions[vi1]);
newmbD.Positions.Add(positions[vi2]);
newmbD.TriangleIndices.Add(i + a);
newmbD.TriangleIndices.Add(i + a - 1);
newmbD.TriangleIndices.Add(i + a - 2);
}
if ((kH3 > nThreshold || kH2 > nThreshold || kH1 > nThreshold))
{
newmbP.Positions.Add(positions[vi]);
newmbP.Positions.Add(positions[vi1]);
newmbP.Positions.Add(positions[vi2]);
newmbP.TriangleIndices.Add(i + a);
newmbP.TriangleIndices.Add(i + a - 1);
newmbP.TriangleIndices.Add(i + a - 2);
}
}
int[] nbrs = m3d.GetNeighbourVertices(vi);
Vector3DCollection N = new Vector3DCollection(positions.Count);
Point3D pi = positions[vi];
int i0 = triangleIndices[i + a];
if (i + a - 1 >= 0)
{
i0 = triangleIndices[i + a - 1];
}
Point3D pi0 = positions[i0];
int i1 = vi;
if (i + a + i < triangleIndices.Count)
{
i1 = triangleIndices[i + a + 1];
}
Point3D pi1 = positions[i1];
t.Insert(vi, (pi1 - pi0) / (Point3D.Subtract(pi1, pi0).Length));
//t[i] = (pi1 - pi0) / Math.Sqrt((Point3D.Subtract(pi1, pi0).Length));
n.Insert(vi, SmileVisual3D.CalculateNormal(pi0, pi, pi1));
b.Insert(vi, Vector3D.CrossProduct(t[vi], n[vi]));
Vector3D eIntV = new Vector3D(); //eInt[vi];
Vector3D eExtV = new Vector3D(); //eExt[vi];
Vector3D eV = new Vector3D(); //e[vi];
Vector3D sumDeltaNbrs = new Vector3D();
Vector3D sumFNbrs = new Vector3D();
int maxNbrs = (nbrs.Length > 2 ? 2 : nbrs.Length);
for (int j = 0; j < maxNbrs; j++)
{
Point3D nbj = positions[nbrs[j]];
N.Add(nbj.ToVector3D());
}
double determinantVi = determinant(N);
double kv = 0;
kH.TryGetValue(vi, out kv);
double jminEnergy = minEnergy;
Point3D tempNbj = pi;
for (int j = 0; j < maxNbrs; j++)
{
Point3D nbj = positions[nbrs[j]];
double ku = 0;
kH.TryGetValue(nbrs[j], out ku);
sumDeltaNbrs += Vector3D.Multiply((kv - ku), Vector3D.Divide(Point3D.Subtract(nbj, pi), (Point3D.Subtract(nbj, pi).Length)));
delta.Insert(vi, (1 / determinantVi) * sumDeltaNbrs);
f.Insert(vi, Vector3D.Multiply((1 - lambda), Vector3D.Multiply((1 / determinantVi), new Vector3D())) + Vector3D.Multiply(lambda, delta[vi]));
double eIntj = alpha * (Point3D.Subtract(pi0, nbj).Length) + betha * (Point3D.Subtract(pi0, Point3D.Add(pi1, (Vector3D)nbj)).Length); //TODO: crosscheck
double eFaej = ballon * (-(f[vi].Length) - Vector3D.DotProduct((f[vi] / f[vi].Length), (Point3D.Subtract(nbj, pi) / Point3D.Subtract(nbj, pi).Length))); //TODO: crosscheck
double ePressj = ballon * Vector3D.DotProduct(b[vi], (Point3D.Subtract(pi0, nbj) / Point3D.Subtract(pi0, nbj).Length));
double eExtj = eFaej + ePressj;
double ej = eIntj + eExtj;
if (j == 0)
{
eIntV.X = eIntj;
eExtV.X = eExtj;
eV.X = ej;
}
if (j == 1)
{
eIntV.Y = eIntj;
eExtV.Y = eExtj;
eV.Y = ej;
}
if (j == 2)
{
eIntV.Z = eIntj;
eExtV.Z = eExtj;
eV.Z = ej;
}
if (ej < jminEnergy)
{
jminEnergy = ej;
tempNbj = nbj;
//TODO: snake movement
//AddSnakeElement(nbj);
}
}
AddSnakeElement(tempNbj);
eInt.Insert(vi, eIntV);
eExt.Insert(vi, eExtV);
e.Insert(vi, eV);
//delta.Insert(vi, (1 / determinant(N[vi])) * sumDeltaNbrs); //TODO:implemenet
//f.Insert(vi, n[vi]);// (1 - lambda) * (1 / (Math.Abs(nbrs.Count))) + lambda *delta[i]; //TODO:implemenet
tETF.Insert(vi, Vector3D.CrossProduct(delta[vi], n[vi]));
}
}
return(newmbD.ToMesh());
/*
* for (int i = 0; i < positions.Count; i++)
* {
* Int32Collection nbrs = neighbours[i].neighbours;
*
* Point3D pi = positions[i];
* int i0 = i;
* if (i - 1 >= 0) i0 = i - 1;
* Point3D pi0 = positions[i0];
* int i1 = i;
* if (i + i < triangleIndices.Count) i = i + 1;
* Point3D pi1 = positions[i1];
*
* t[i] = (pi1 - pi0) / (Point3D.Subtract(pi1, pi0).Length);
* //t[i] = (pi1 - pi0) / Math.Sqrt((Point3D.Subtract(pi1, pi0).Length));
* n[i] = SmileVisual3D.CalculateNormal(pi0, pi, pi1);
* b[i] = Vector3D.CrossProduct(t[i], n[i]);
*
*
* Vector3D eIntV = eInt[i];
* Vector3D eExtV = eExt[i];
* Vector3D eV = e[i];
* int maxNbrs = (nbrs.Count > 2 ? 2 : nbrs.Count);
* for (int j = 0; j < maxNbrs; j++)
* {
* Point3D nbj = positions[nbrs[j]];
* double eIntj = alpha * (Point3D.Subtract(pi0, nbj).Length) + betha * (Point3D.Subtract(pi0, Point3D.Add(pi1, (Vector3D)nbj)).Length); //TODO: crosscheck
*
*
* delta[i] = n[i];// 1 / determinant(N[i]); //TODO:implemenet
* f[i] = n[i];// (1 - lambda) * (1 / (Math.Abs(nbrs.Count))) + lambda *delta[i]; //TODO:implemenet
*
*
* double eFaej = ballon * (-(f[i].Length) - Vector3D.DotProduct((f[i] / f[i].Length), (Point3D.Subtract(nbj, pi) / Point3D.Subtract(nbj, pi).Length))); //TODO: crosscheck
* double ePressj = ballon * Vector3D.DotProduct(b[i], (Point3D.Subtract(pi0, nbj) / Point3D.Subtract(pi0, nbj).Length));
* double eExtj = eFaej + ePressj;
* double ej = eIntj + eExtj;
*
* if (j == 0)
* {
* eIntV.X = eIntj;
* eExtV.X = eExtj;
* eV.X = ej;
* }
* if (j == 1)
* {
* eIntV.Y = eIntj;
* eExtV.Y = eExtj;
* eV.Y = ej;
* }
* if (j == 2)
* {
* eIntV.Z = eIntj;
* eExtV.Z = eExtj;
* eV.Z = ej;
* }
*
* if (ej < minEnergy)
* {
* minEnergy = ej;
* //TODO: snake movement
* AddSnakeElement(nbj);
* }
*
* eInt[i] = eIntV;
* eExt[i] = eExtV;
* e[i] = eV;
* }
*
* tETF[i] = Vector3D.CrossProduct(delta[i], n[i]);
*
* }
* */
}
//ref: Snake-Based Segmentation of Teeth from Virtual Dental Casts
//pLane located manually, set of verteks D and P from manual cutting plane
//the plan is: teeth and gum separated then teeth segmented using snake below
public static void snake(MeshGeometry3D mesh)
{
Dictionary <Int32, SmileEdge> neighbours = SmileVisual3D.findNeighbours(mesh);
Point3DCollection pos = mesh.Positions;
Int32Collection ind = mesh.TriangleIndices;
Vector3DCollection t = new Vector3DCollection();
Vector3DCollection b = new Vector3DCollection();
Vector3DCollection n = new Vector3DCollection();
double eThreshold = -0.3;
double nThreshold = 0.8;
double minEnergy = 10;
double alpha = 1;
double betha = 1;
double ballon = 1;
double lambda = 1;
Vector3DCollection e = new Vector3DCollection();
Vector3DCollection eInt = new Vector3DCollection();
Vector3DCollection eExt = new Vector3DCollection();
Vector3DCollection delta = new Vector3DCollection();
List <Vector3DCollection> N = new List <Vector3DCollection>();
Vector3DCollection f = new Vector3DCollection();
Vector3DCollection tETF = new Vector3DCollection();
Vector3DCollection k = new Vector3DCollection();
Vector3DCollection kH = new Vector3DCollection();
Vector3DCollection kMin = new Vector3DCollection();
Vector3DCollection kMax = new Vector3DCollection();
for (int i = 0; i < ind.Count; i++)
{
Point3D pi = pos[i];
//kij = 2ni ยท (pi - pj)/|pi- pj |2
kH[i] = (kMin[i] + kMax[i]) / 2;
}
for (int i = 0; i < ind.Count; i++)
{
Int32Collection nbrs = neighbours[i].neighbours;
Point3D pi = pos[i];
int i0 = i;
if (i - 1 >= 0)
{
i0 = i - 1;
}
Point3D pi0 = pos[i0];
int i1 = i;
if (i + i < ind.Count)
{
i = i + 1;
}
Point3D pi1 = pos[i1];
t[i] = (pi1 - pi0) / (Point3D.Subtract(pi1, pi0).Length);
//t[i] = (pi1 - pi0) / Math.Sqrt((Point3D.Subtract(pi1, pi0).Length));
n[i] = SmileVisual3D.CalculateNormal(pi0, pi, pi1);
b[i] = Vector3D.CrossProduct(t[i], n[i]);
Vector3D eIntV = eInt[i];
Vector3D eExtV = eExt[i];
Vector3D eV = e[i];
int maxNbrs = (nbrs.Count > 2 ? 2 : nbrs.Count);
for (int j = 0; j < maxNbrs; j++)
{
Point3D nbj = pos[nbrs[j]];
double eIntj = alpha * (Point3D.Subtract(pi0, nbj).Length) + betha * (Point3D.Subtract(pi0, Point3D.Add(pi1, (Vector3D)nbj)).Length); //TODO: crosscheck
delta[i] = n[i]; // 1 / determinant(N[i]); //TODO:implemenet
f[i] = n[i]; // (1 - lambda) * (1 / (Math.Abs(nbrs.Count))) + lambda *delta[i]; //TODO:implemenet
double eFaej = ballon * (-(f[i].Length) - Vector3D.DotProduct((f[i] / f[i].Length), (Point3D.Subtract(nbj, pi) / Point3D.Subtract(nbj, pi).Length))); //TODO: crosscheck
double ePressj = ballon * Vector3D.DotProduct(b[i], (Point3D.Subtract(pi0, nbj) / Point3D.Subtract(pi0, nbj).Length));
double eExtj = eFaej + ePressj;
double ej = eIntj + eExtj;
if (j == 0)
{
eIntV.X = eIntj;
eExtV.X = eExtj;
eV.X = ej;
}
if (j == 1)
{
eIntV.Y = eIntj;
eExtV.Y = eExtj;
eV.Y = ej;
}
if (j == 2)
{
eIntV.Z = eIntj;
eExtV.Z = eExtj;
eV.Z = ej;
}
if (ej < minEnergy)
{
minEnergy = ej;
//TODO: snake movement
AddSnakeElement(nbj);
}
eInt[i] = eIntV;
eExt[i] = eExtV;
e[i] = eV;
}
tETF[i] = Vector3D.CrossProduct(delta[i], n[i]);
}
}