public static void TransformationRotation(List <TriMesh.Vertex> vertice, Vector3D rotation, bool local)
{
Vector3D center = Vector3D.Zero;
Matrix4D m = Matrix4D.Identity();
if (local)
{
center = TriMeshUtil.GetCenter(vertice);
Matrix4D moveC = ComputeMatrixMove(ref center);
center.Negate();
Matrix4D moveCReverse = ComputeMatrixMove(ref center);
Matrix4D r = ComputeMatrixRotation(rotation);
m = moveCReverse * r * moveC;
}
else
{
m = ComputeMatrixRotation(rotation);
}
TransformationVertex(vertice, m);
}
protected Vector3D GetPos1(TriMesh.HalfEdge hf)
{
Vector3D from = hf.FromVertex.Traits.Position;
Vector3D to = hf.ToVertex.Traits.Position;
Vector3D l = to - from;
Vector3D[] vi = this.GetV(hf);
Vector3D[] vj = this.GetV(hf.Opposite);
Vector3D c1 = Vector3D.Zero;
Vector3D c2 = Vector3D.Zero;
for (int i = 0; i < vi.Length - 1; i++)
{
c1 += (vi[i] - from).Cross(vi[i + 1] - from);
}
for (int i = 0; i < vj.Length - 1; i++)
{
c2 += (vj[i + 1] - to).Cross(vj[i] - to);
}
Matrix4D m = Matrix4D.ZeroMatrix;
m.Row1 = new Vector4D(c1 - c2, to.Dot(c2) - from.Dot(c1));
m.Row2 = new Vector4D(l.y, -l.x, 0d, to.y * l.x - to.x * l.y);
m.Row3 = new Vector4D(l.z, 0d, -l.x, to.z * l.x - to.x * l.z);
m.Row4 = new Vector4D(0d, 0d, 0d, 1d);
Vector3D pos = Vector3D.Zero;
double det = Util.Solve(ref m, ref pos);
if (det == 0)
{
pos = TriMeshUtil.GetMidPoint(hf.Edge);
}
else
{
double vo1 = c1.Dot(pos - from);
double vo2 = c2.Dot(pos - to);
}
return(pos);
}
public double[] SetColor(string item, TriMesh mesh, CriteriaInfo criteriaInfo)
{
TriMeshUtil.ClearMeshColor(mesh);
double[] value = null;
if (item == "DehidraAngleMin")
{
value = ColorEdgeByDihedralAngle(mesh, criteriaInfo.DehidraAngleMin, criteriaInfo.DehidraAngleMax);
}
if (item == "DehidraAngleMax")
{
value = ColorEdgeByDihedralAngle(mesh, criteriaInfo.DehidraAngleMin, criteriaInfo.DehidraAngleMax);
}
if (item == "GaussinMin")
{
value = ColorVertexByGaussin(mesh, criteriaInfo.GaussinMin, criteriaInfo.GaussinMax);
}
if (item == "GaussinMax")
{
value = ColorVertexByGaussin(mesh, criteriaInfo.GaussinMin, criteriaInfo.GaussinMax);
}
if (item == "MeanCurvatureMax")
{
value = ColorVertexByMeanCurvature(mesh, criteriaInfo.MeanCurvatureMin, criteriaInfo.MeanCurvatureMax);
}
if (item == "MeanCurvatureMin")
{
value = ColorVertexByMeanCurvature(mesh, criteriaInfo.MeanCurvatureMin, criteriaInfo.MeanCurvatureMax);
}
return(value);
}
public SparseMatrix BuildMatrixMeanCurvature(TriMesh mesh)
{
int n = mesh.Vertices.Count;
SparseMatrix L = BuildLaplaceMatrixCotBasic(mesh);
double[] voronoiArea = TriMeshUtil.ComputeAreaVoronoi(mesh);
for (int i = 0; i < n; i++)
{
double sum = 0;
foreach (SparseMatrix.Element e in L.Rows[i])
{
e.value = e.value / (voronoiArea[e.i] * 4);
}
foreach (SparseMatrix.Element e in L.Rows[i])
{
sum += e.value;
}
L.AddValueTo(i, i, -sum);
}
L.SortElement();
return(L);
}
public CurvaturePG07(TriMesh mesh)
{
this.mesh = mesh;
this.K = new Vector3D[this.mesh.Vertices.Count];
this.Mean = new double[this.mesh.Vertices.Count];
this.Normal = new Vector3D[this.mesh.Vertices.Count];
this.PrincipalCurv = new PrincipalCurvature[this.mesh.Vertices.Count];
foreach (var v in this.mesh.Vertices)
{
double mixedArea = TriMeshUtil.ComputeAreaMixed(v);
this.K[v.Index] = ComputeK(v, mixedArea);
this.Mean[v.Index] = ComputeMeanCurvature(this.K[v.Index]);
this.Normal[v.Index] = ComputeNormal(this.K[v.Index]);
}
foreach (var v in this.mesh.Vertices)
{
this.PrincipalCurv[v.Index] = this.ComputePrincipalCurvature(v);
}
}
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);
}
private void InitCurvatureInfoGrid()
{
this.dataGridViewCurvature.Rows.Clear();
double[] curvature = TriMeshUtil.ComputeGaussianCurvature(Mesh);
double[] meanCurv = TriMeshUtil.ComputeMeanCurvature(Mesh);
PrincipalCurvature[] basic = TriMeshUtil.ComputePricipalCurvature(Mesh);
PrincipalCurvature[] pg = TriMeshUtil.ComputePricipalCurvaturePG07(Mesh);
CurvatureLib.Init(Mesh);
PrincipalCurvature[] ccc = CurvatureLib.ComputeCurvature();
for (int i = 0; i < curvature.Length; i++)
{
this.dataGridViewCurvature.Rows.Add(i,
curvature[i],
meanCurv[i],
ccc[i].max,
ccc[i].min,
pg[i].max,
pg[i].min);
}
}
public void Cut(Plane plane)
{
this.plane = plane;
this.list = new List <Triangle>();
this.cutPoint = new Dictionary <int, CutPoint>();
foreach (var hf in this.mesh.HalfEdges)
{
this.CutHalfEdge(hf);
}
foreach (var face in this.mesh.Faces)
{
this.CutFace(face);
}
List <TriMesh.Edge> edges = new List <HalfEdgeMesh.Edge>();
foreach (var hf in this.mesh.HalfEdges)
{
if (this.cutPoint.ContainsKey(hf.Index))
{
edges.Add(hf.Edge);
}
}
foreach (var item in edges)
{
TriMeshModify.RemoveEdge(item);
}
foreach (var item in this.list)
{
this.mesh.Faces.AddTriangles(item.V1, item.V2, item.V3);
}
TriMeshUtil.FixIndex(mesh);
TriMeshUtil.SetUpNormalVertex(mesh);
}
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 void DrawFaceNormal(TriMesh mesh)
{
OpenGLManager.Instance.SetColor(GlobalSetting.DisplaySetting.NormalColor);
double avgLength = TriMeshUtil.ComputeEdgeAvgLength(mesh);
avgLength *= GlobalSetting.DisplaySetting.NormalLength;
foreach (TriMesh.Face item in mesh.Faces)
{
double x = (item.GetVertex(0).Traits.Position.x +
item.GetVertex(1).Traits.Position.x +
item.GetVertex(2).Traits.Position.x) / 3;
double y = (item.GetVertex(0).Traits.Position.y +
item.GetVertex(1).Traits.Position.y +
item.GetVertex(2).Traits.Position.y) / 3;
double z = (item.GetVertex(0).Traits.Position.z +
item.GetVertex(1).Traits.Position.z +
item.GetVertex(2).Traits.Position.z) / 3;
Vector3D normal = item.Traits.Normal.Normalize() * avgLength;
GL.Begin(BeginMode.Lines);
GL.Vertex3(x, y, z);
GL.Vertex3(x + normal.x, y + normal.y, z + normal.z);
GL.End();
}
}
public TriMesh AddSelectionEdge(TriMesh mesh, int index)
{
List <TriMesh> sel = new List <TriMesh>();
for (int i = 0; i < mesh.Edges.Count; i++)
{
if (mesh.Edges[i].Traits.SelectedFlag == index)
{
TriMesh selV = TriMeshIO.FromObjFile(ConfigShape.Instance.EdgeFile);
TriMeshUtil.ScaleToUnit(selV, 1);
TriMeshUtil.ScaleToUnit(selV, ConfigShape.Instance.Scale);
Vector3D direction = mesh.Edges[i].Vertex1.Traits.Position - mesh.Edges[i].Vertex0.Traits.Position;
Vector3D loc = (mesh.Edges[i].Vertex1.Traits.Position + mesh.Edges[i].Vertex0.Traits.Position) / 2;
Matrix4D scale = TriMeshUtil.ComputeMatrixScale(direction.Length() / ConfigShape.Instance.Scale, 1d, 1d);
// TriMeshUtil.TransformationRotation(selV, direction);
TriMeshUtil.TransformationScale(selV, scale);
TriMeshUtil.TransformRoatationV(selV, direction, Vector3D.UnitX);
//TriMeshUtil.TransformRotationX(selV, direction.x);
//TriMeshUtil.TransformRotationY(selV, direction.y);
//TriMeshUtil.TransformRotationZ(selV, direction.z);
TriMeshUtil.TransformationMove(selV, loc);
sel.Add(selV);
}
}
TriMesh result = TriMeshUtil.Combine(sel);
result.FileName = Path.GetFileNameWithoutExtension(mesh.FileName) + "-E-" + index.ToString();
TriMeshUtil.SetUpVertexNormal(result, EnumNormal.AreaWeight);
return(result);
}
public DenseMatrixDouble InitWithTrivalHolonmy(SparseMatrixDouble Laplace, TriMesh mesh)
{
DenseMatrixDouble b = new DenseMatrixDouble(mesh.Vertices.Count, 1);
double[] tempSingularities = new double[mesh.Vertices.Count];
for (int i = 0; i < tempSingularities.Length; i++)
{
tempSingularities[i] = 0;
}
foreach (KeyValuePair <TriMesh.Vertex, double> pair in Singularities)
{
int index = pair.Key.Index;
double value = pair.Value;
tempSingularities[index] = value;
}
double[] GuassianCurvs = TriMeshUtil.ComputeGaussianCurvatureIntegrated(mesh);
foreach (TriMesh.Vertex v in mesh.Vertices)
{
double value = 0;
if (!v.OnBoundary)
{
value -= GuassianCurvs[v.Index];
value += 2 * Math.PI * tempSingularities[v.Index];
}
b[v.Index, 0] = value;
}
DenseMatrixDouble u = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref Laplace, ref b);
return(u);
}
private ErrorPair GetErrorPair(TriMesh.Face face)
{
Matrix4D m1 = this.GetVolumeMatrix(face);
if (m1[1] != m1[4] || m1[2] != m1[8] || m1[6] != m1[9] ||
m1[3] != m1[12] || m1[7] != m1[13] || m1[11] != m1[14]
)
{
throw new Exception("Matrix m1 is not symmetric");
}
Matrix4D m2 = Matrix4D.ZeroMatrix;
for (int i = 0; i <= 11; i++)
{
m2[i] = m1[i];
}
m2[12] = 0;
m2[13] = 0;
m2[14] = 0;
m2[15] = 1;
Vector3D newPos = Vector3D.Zero;
double det = Util.Solve(ref m2, ref newPos);
if (det == 0)
{
newPos = TriMeshUtil.GetMidPoint(face);
}
double error = this.GetError(m1, newPos);
return(new ErrorPair()
{
Pos = newPos, Error = error
});
}
public static Dictionary <string, string> BuildMeshInfo(TriMesh mesh)
{
Dictionary <string, string> meshinfo = new Dictionary <string, string>();
meshinfo.Add("Verties", mesh.Vertices.Count.ToString());
meshinfo.Add("Edges", mesh.Edges.Count.ToString());
meshinfo.Add("Faces", mesh.Faces.Count.ToString());
meshinfo.Add("Elur Formula For Genus=0", "V-E+F = 2");
meshinfo.Add("General Elur Formula on Genus !=0", "V-E+F=2(C-G)-B, C is Component Number,G is Genus Number,B is boundary Number");
meshinfo.Add("Elur Characteristic is ", "2(C-G)-B or V-E+F");
meshinfo.Add("Elur Characteristic on Current Mesh",
"V-E+F = " +
mesh.Vertices.Count.ToString() + " - " +
mesh.Edges.Count.ToString() + " + " +
mesh.Faces.Count.ToString() + " = " +
CountEulerCharacteristic(mesh).ToString());
meshinfo.Add("Component", CountComponents(mesh, false).ToString());
meshinfo.Add("Boundary Number", TriMeshUtil.CountBoundary(mesh).ToString());
meshinfo.Add("Genus", "G=-((V-E+F)+B)/2+C");
meshinfo.Add("Genus on Current mesh", CountGenus(mesh).ToString());
meshinfo.Add("Total Gaussian Curvature is ", TriMeshUtil.ComputeTotalGaussianCurvarture(mesh).ToString());
meshinfo.Add("Gaussian-Bonnet Theroem", "2*PI*(V-E+F) = SUM(Gaussian Curvature)");
meshinfo.Add("Current Gaussian-Bonnet Theroem",
"2*PI*(V-E+F)=" +
"2 x 3.1415 x " + CountEulerCharacteristic(mesh).ToString() + " = " +
(Math.PI * 2 * CountEulerCharacteristic(mesh))
+ " ??= " + TriMeshUtil.ComputeTotalGaussianCurvarture(mesh)
);
meshinfo.Add("Average Area", TriMeshUtil.ComputeAreaAverage(mesh).ToString());
meshinfo.Add("Volume", TriMeshUtil.ComputeVolume(mesh).ToString());
meshinfo.Add("Total Area", TriMeshUtil.ComputeAreaTotal(mesh).ToString());
return(meshinfo);
}
public static void BoundaryExpand(TriMesh mesh)
{
double length = TriMeshUtil.ComputeEdgeAvgLength(mesh);
List <List <TriMesh.HalfEdge> > holes = TriMeshUtil.RetrieveBoundaryEdgeAll(mesh);
foreach (var hole in holes)
{
TriMesh.Vertex[] arr = new HalfEdgeMesh.Vertex[hole.Count];
for (int i = 0; i < hole.Count; i++)
{
Vector3D normal = Vector3D.UnitX;
if (hole[i].Opposite.Face != null)
{
normal = TriMeshUtil.ComputeNormalFace(hole[i].Opposite.Face);
}
Vector3D toPos = hole[i].ToVertex.Traits.Position;
Vector3D fromPos = hole[i].FromVertex.Traits.Position;
Vector3D hfDir = toPos - fromPos;
Vector3D hfMid = (toPos + fromPos) / 2;
Vector3D pos = hfMid + normal.Cross(hfDir).Normalize() * length;
arr[i] = mesh.Vertices.Add(new VertexTraits(pos));
}
for (int i = 0; i < hole.Count; i++)
{
int next = (i + 1) % hole.Count;
TriMesh.Face face = mesh.Faces.Add(arr[i],
hole[i].ToVertex,
hole[next].ToVertex);
face.Traits.SelectedFlag = 1;
face = mesh.Faces.Add(arr[i],
hole[next].ToVertex,
arr[next]);
face.Traits.SelectedFlag = 1;
}
}
}
public void DrawTreeCotree(List <TriMesh.Edge> treeMarks, List <TriMesh.Edge> cotreeMarks)
{
OpenGLManager.Instance.SetColor(System.Drawing.Color.Green);
//Draw Tree
foreach (TriMesh.Edge item in treeMarks)
{
GL.Begin(BeginMode.Lines);
Vector3D a = item.Vertex0.Traits.Position;
Vector3D b = item.Vertex1.Traits.Position;
GL.Vertex3(a.x, a.y, a.z);
GL.Vertex3(b.x, b.y, b.z);
GL.End();
}
OpenGLManager.Instance.SetColor(System.Drawing.Color.Red);
//Draw CoTree
foreach (TriMesh.Edge item in cotreeMarks)
{
Vector3D a = TriMeshUtil.GetMidPoint(item.Face0);
Vector3D b = TriMeshUtil.GetMidPoint(item.Face1);
Vector3D centerOfEdge = (item.Vertex0.Traits.Position + item.Vertex1.Traits.Position) / 2;
GL.Begin(BeginMode.Lines);
GL.Vertex3(a.x, a.y, a.z);
GL.Vertex3(centerOfEdge.x, centerOfEdge.y, centerOfEdge.z);
GL.End();
GL.Begin(BeginMode.Lines);
GL.Vertex3(centerOfEdge.x, centerOfEdge.y, centerOfEdge.z);
GL.Vertex3(b.x, b.y, b.z);
GL.End();
}
}
protected Vector3D[] ComputeVectorField(DenseMatrixDouble u, TriMesh mesh)
{
Vector3D[] vectors = new Vector3D[mesh.Faces.Count];
foreach (TriMesh.Face f in mesh.Faces)
{
if (f.OnBoundary)
{
continue;
}
TriMesh.HalfEdge hij = f.HalfEdge;
TriMesh.HalfEdge hjk = hij.Next;
TriMesh.HalfEdge hki = hjk.Next;
TriMesh.Vertex vi = hij.FromVertex;
TriMesh.Vertex vj = hjk.FromVertex;
TriMesh.Vertex vk = hki.FromVertex;
double ui = u[vi.Index, 0];
double uj = u[vj.Index, 0];
double uk = u[vk.Index, 0];
Vector3D eijL = RotatedEdge(hij);
Vector3D ejkL = RotatedEdge(hjk);
Vector3D ekiL = RotatedEdge(hki);
double area = TriMeshUtil.ComputeAreaFaceTwo(f);
Vector3D x = 0.5 * (ui * ejkL + uj * ekiL + uk * eijL) / area;
vectors[f.Index] = -x.Normalize();
}
return(vectors);
}
public void Run()
{
TriMeshUtil.TransformationRotation(GlobalData.Instance.TriMesh, new Vector3D(0, 0, 0.001d));
}
private void scaleToUnitToolStripMenuItem_Click(object sender, EventArgs e)
{
TriMeshUtil.ScaleToUnit(Mesh, 0.9);
OnChanged(EventArgs.Empty);
}
private void moveToCenterToolStripMenuItem_Click(object sender, EventArgs e)
{
TriMeshUtil.MoveToCenter(Mesh);
OnChanged(EventArgs.Empty);
}
private void reverseToolStripMenuItem_Click(object sender, EventArgs e)
{
TriMeshUtil.SelectedVertexReverse(Mesh);
TriMeshUtil.GroupVertice(Mesh);
OnChanged(EventArgs.Empty);
}
private void randomToolStripMenuItem_Click(object sender, EventArgs e)
{
TriMeshUtil.SelectedVertexRandom(Mesh, ConfigMeshOP.Instance.RandomSelect);
OnChanged(EventArgs.Empty);
}
protected double GetValue(TriMesh.Vertex v)
{
return(TriMeshUtil.ComputeGaussianCurvature(v));
}
public static void RepairComplexHole(TriMesh mesh)
{
List <TriMesh.Vertex> hole = new List <TriMesh.Vertex>();
TriMesh.Vertex[] faceVertices = new TriMesh.Vertex[3];
while (true)//此循环只限单洞修补
{
//计算边界边的平均值
#region 计算边界边的平均值
hole = TriMeshUtil.RetrieveBoundarySingle(mesh);
double aver_l = 0;
double[] edgeLength = new double[hole.Count];
for (int i = 0; i < hole.Count; i++)
{
if (i == hole.Count - 1)
{
edgeLength[i] = Math.Sqrt(Math.Pow(hole[i].Traits.Position.x - hole[0].Traits.Position.x, 2) + Math.Pow(hole[i].Traits.Position.y - hole[0].Traits.Position.y, 2) + Math.Pow(hole[i].Traits.Position.z - hole[0].Traits.Position.z, 2));
break;
}
edgeLength[i] = Math.Sqrt(Math.Pow(hole[i].Traits.Position.x - hole[i + 1].Traits.Position.x, 2) + Math.Pow(hole[i].Traits.Position.y - hole[i + 1].Traits.Position.y, 2) + Math.Pow(hole[i].Traits.Position.z - hole[i + 1].Traits.Position.z, 2));
}
for (int i = 0; i < hole.Count; i++)
{
aver_l += edgeLength[i];
}
aver_l = aver_l / hole.Count;
#endregion
hole = TriMeshUtil.RetrieveBoundarySingle(mesh);
//计算角度值
#region 计算角度值
double[] angle = new double[hole.Count];
double a = 0, b = 0, c = 0;
for (int i = 0; i < hole.Count; i++)
{
if (i == 0)
{
a = Math.Sqrt(Math.Pow(hole[hole.Count - 1].Traits.Position.x - hole[i + 1].Traits.Position.x, 2) + Math.Pow(hole[hole.Count - 1].Traits.Position.y - hole[i + 1].Traits.Position.y, 2) + Math.Pow(hole[hole.Count - 1].Traits.Position.z - hole[i + 1].Traits.Position.z, 2));
b = Math.Sqrt(Math.Pow(hole[i].Traits.Position.x - hole[i + 1].Traits.Position.x, 2) + Math.Pow(hole[i].Traits.Position.y - hole[i + 1].Traits.Position.y, 2) + Math.Pow(hole[i].Traits.Position.z - hole[i + 1].Traits.Position.z, 2));
c = Math.Sqrt(Math.Pow(hole[hole.Count - 1].Traits.Position.x - hole[i].Traits.Position.x, 2) + Math.Pow(hole[hole.Count - 1].Traits.Position.y - hole[i].Traits.Position.y, 2) + Math.Pow(hole[hole.Count - 1].Traits.Position.z - hole[i].Traits.Position.z, 2));
angle[i] = Math.Acos((b * b + c * c - a * a) / (2 * b * c));
}
else if (i == hole.Count - 1)
{
a = Math.Sqrt(Math.Pow(hole[i - 1].Traits.Position.x - hole[0].Traits.Position.x, 2) + Math.Pow(hole[i - 1].Traits.Position.y - hole[0].Traits.Position.y, 2) + Math.Pow(hole[i - 1].Traits.Position.z - hole[0].Traits.Position.z, 2));
b = Math.Sqrt(Math.Pow(hole[i].Traits.Position.x - hole[0].Traits.Position.x, 2) + Math.Pow(hole[i].Traits.Position.y - hole[0].Traits.Position.y, 2) + Math.Pow(hole[i].Traits.Position.z - hole[0].Traits.Position.z, 2));
c = Math.Sqrt(Math.Pow(hole[i - 1].Traits.Position.x - hole[i].Traits.Position.x, 2) + Math.Pow(hole[i - 1].Traits.Position.y - hole[i].Traits.Position.y, 2) + Math.Pow(hole[i - 1].Traits.Position.z - hole[i].Traits.Position.z, 2));
angle[i] = Math.Acos((b * b + c * c - a * a) / (2 * b * c));
}
else
{
a = Math.Sqrt(Math.Pow(hole[i - 1].Traits.Position.x - hole[i + 1].Traits.Position.x, 2) + Math.Pow(hole[i - 1].Traits.Position.y - hole[i + 1].Traits.Position.y, 2) + Math.Pow(hole[i - 1].Traits.Position.z - hole[i + 1].Traits.Position.z, 2));
b = Math.Sqrt(Math.Pow(hole[i].Traits.Position.x - hole[i + 1].Traits.Position.x, 2) + Math.Pow(hole[i].Traits.Position.y - hole[i + 1].Traits.Position.y, 2) + Math.Pow(hole[i].Traits.Position.z - hole[i + 1].Traits.Position.z, 2));
c = Math.Sqrt(Math.Pow(hole[i - 1].Traits.Position.x - hole[i].Traits.Position.x, 2) + Math.Pow(hole[i - 1].Traits.Position.y - hole[i].Traits.Position.y, 2) + Math.Pow(hole[i - 1].Traits.Position.z - hole[i].Traits.Position.z, 2));
angle[i] = Math.Acos((b * b + c * c - a * a) / (2 * b * c));
}
}
#endregion
//取得最小的角度
#region 取得最小的角度
int min = 0;
for (int i = 0; i < hole.Count - 1; i++)
{
if (angle[i] < angle[i + 1])
{
min = i;
}
else
{
min = i + 1;
}
}
#endregion
//求最小角度对应的边长
#region 求最小角度对应的边长
double temp = 0;
if (min == hole.Count - 1)
{
temp = Math.Sqrt(Math.Pow(hole[min - 1].Traits.Position.x - hole[0].Traits.Position.x, 2) + Math.Pow(hole[min - 1].Traits.Position.y - hole[0].Traits.Position.y, 2) + Math.Pow(hole[min - 1].Traits.Position.z - hole[0].Traits.Position.z, 2));
}
else if (min == 0)
{
temp = Math.Sqrt(Math.Pow(hole[hole.Count - 1].Traits.Position.x - hole[min + 1].Traits.Position.x, 2) + Math.Pow(hole[hole.Count - 1].Traits.Position.y - hole[min + 1].Traits.Position.y, 2) + Math.Pow(hole[hole.Count - 1].Traits.Position.z - hole[min + 1].Traits.Position.z, 2));
}
else
{
temp = Math.Sqrt(Math.Pow(hole[min - 1].Traits.Position.x - hole[min + 1].Traits.Position.x, 2) + Math.Pow(hole[min - 1].Traits.Position.y - hole[min + 1].Traits.Position.y, 2) + Math.Pow(hole[min - 1].Traits.Position.z - hole[min + 1].Traits.Position.z, 2));
}
#endregion
//判断最小角对应的边与平均边界边长，并进行修补
#region 判断最小角对应的边与平均边界边长，并进行修补
if (temp > aver_l)
{
if (min == hole.Count - 1)
{
faceVertices[0] = mesh.Vertices[hole[min].Index];
faceVertices[1] = mesh.Vertices[hole[0].Index];
faceVertices[2] = mesh.Vertices[hole[min - 1].Index];
mesh.Faces.AddTriangles(faceVertices);
}
else if (min == 0)
{
faceVertices[0] = mesh.Vertices[hole[min].Index];
faceVertices[1] = mesh.Vertices[hole[min + 1].Index];
faceVertices[2] = mesh.Vertices[hole[hole.Count - 1].Index];
mesh.Faces.AddTriangles(faceVertices);
}
else
{
faceVertices[0] = mesh.Vertices[hole[min].Index];
faceVertices[1] = mesh.Vertices[hole[min + 1].Index];
faceVertices[2] = mesh.Vertices[hole[min - 1].Index];
mesh.Faces.AddTriangles(faceVertices);
}
}
else
{
if (min == hole.Count - 1)
{
Vector3D midPosition;
midPosition = (hole[min - 1].Traits.Position + hole[0].Traits.Position) / 2;
mesh.Vertices.Add(new VertexTraits(midPosition.x, midPosition.y, midPosition.z));
faceVertices[0] = mesh.Vertices[hole[min].Index];
faceVertices[1] = mesh.Vertices[mesh.Vertices.Count - 1];
faceVertices[2] = mesh.Vertices[hole[min - 1].Index];
mesh.Faces.AddTriangles(faceVertices);
faceVertices[0] = mesh.Vertices[hole[min].Index];
faceVertices[1] = mesh.Vertices[hole[0].Index];
faceVertices[2] = mesh.Vertices[mesh.Vertices.Count - 1];
mesh.Faces.AddTriangles(faceVertices);
}
else if (min == 0)
{
Vector3D midPosition;
midPosition = (hole[hole.Count - 1].Traits.Position + hole[min + 1].Traits.Position) / 2;
mesh.Vertices.Add(new VertexTraits(midPosition.x, midPosition.y, midPosition.z));
faceVertices[0] = mesh.Vertices[hole[min].Index];
faceVertices[1] = mesh.Vertices[mesh.Vertices.Count - 1];
faceVertices[2] = mesh.Vertices[hole[hole.Count - 1].Index];
mesh.Faces.AddTriangles(faceVertices);
faceVertices[0] = mesh.Vertices[hole[min].Index];
faceVertices[1] = mesh.Vertices[hole[min + 1].Index];
faceVertices[2] = mesh.Vertices[mesh.Vertices.Count - 1];
mesh.Faces.AddTriangles(faceVertices);
}
else
{
Vector3D midPosition;
midPosition = (hole[min - 1].Traits.Position + hole[min + 1].Traits.Position) / 2;
mesh.Vertices.Add(new VertexTraits(midPosition.x, midPosition.y, midPosition.z));
faceVertices[0] = mesh.Vertices[hole[min].Index];
faceVertices[1] = mesh.Vertices[mesh.Vertices.Count - 1];
faceVertices[2] = mesh.Vertices[hole[min - 1].Index];
mesh.Faces.AddTriangles(faceVertices);
faceVertices[0] = mesh.Vertices[hole[min].Index];
faceVertices[1] = mesh.Vertices[hole[min + 1].Index];
faceVertices[2] = mesh.Vertices[mesh.Vertices.Count - 1];
mesh.Faces.AddTriangles(faceVertices);
}
}
#endregion
//更新边界点，并判断空洞是否完整
#region 更新边界点，并判断空洞是否完整
TriMeshUtil.FixIndex(mesh);
hole = TriMeshUtil.RetrieveBoundarySingle(mesh);
if (hole.Count < 3)
{
break;
}
#endregion
}
}
public static double ComputePerimeter(TriMesh.Face face)
{
Triple <Vector3D> t = TriMeshUtil.GetHalfEdgesVector(face);
return(t.T0.Length() + t.T1.Length() + t.T2.Length());
}
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);
}
}
private void faceBySplitLineToolStripMenuItem_Click(object sender, EventArgs e)
{
TriMeshUtil.ShowMeshPatchColor(Mesh);
OnChanged(EventArgs.Empty);
}
public static EdgeContext Merge(TriMesh.Edge edge)
{
Vector3D position = TriMeshUtil.GetMidPoint(edge);
return(Merge(edge, position));
}
public void Run()
{
Stopwatch clock = new Stopwatch();
clock.Start();
double step = 0.01;
DECMeshDouble decMesh = new DECMeshDouble(mesh);
SparseMatrixDouble laplace = decMesh.Laplace;
SparseMatrixDouble star0 = decMesh.HodgeStar0Form;
SparseMatrixDouble star1 = decMesh.HodgeStar1Form;
SparseMatrixDouble d0 = decMesh.ExteriorDerivative0Form;
SparseMatrixDouble L = d0.Transpose() * star1 * d0;
SparseMatrixDouble A = star0 + step * L;
A.WriteToFile("A.ma");
double[] xs = new double[mesh.Vertices.Count];
double[] ys = new double[mesh.Vertices.Count];
double[] zs = new double[mesh.Vertices.Count];
foreach (TriMesh.Vertex v in mesh.Vertices)
{
xs[v.Index] = v.Traits.Position.x;
ys[v.Index] = v.Traits.Position.y;
zs[v.Index] = v.Traits.Position.z;
}
double[] rhs1 = star0 * xs;
double[] rhs2 = star0 * ys;
double[] rhs3 = star0 * zs;
//SparseMatrix.WriteVectorToFile("xs.ve", rhs1);
//SparseMatrix.WriteVectorToFile("ys.ve", rhs2);
//SparseMatrix.WriteVectorToFile("zs.ve", rhs3);
DenseMatrixDouble rhsx = new DenseMatrixDouble(mesh.Vertices.Count, 1);
DenseMatrixDouble rhsy = new DenseMatrixDouble(mesh.Vertices.Count, 1);
DenseMatrixDouble rhsz = new DenseMatrixDouble(mesh.Vertices.Count, 1);
for (int i = 0; i < mesh.Vertices.Count; i++)
{
rhsx[i, 0] = rhs1[i];
rhsy[i, 0] = rhs2[i];
rhsz[i, 0] = rhs3[i];
}
DenseMatrixDouble newX = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref A, ref rhsx);
DenseMatrixDouble newY = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref A, ref rhsy);
DenseMatrixDouble newZ = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref A, ref rhsz);
foreach (TriMesh.Vertex v in mesh.Vertices)
{
v.Traits.Position.x = newX[v.Index, 0];
v.Traits.Position.y = newY[v.Index, 0];
v.Traits.Position.z = newZ[v.Index, 0];
}
TriMeshUtil.ScaleToUnit(mesh, 1.0f);
TriMeshUtil.MoveToCenter(mesh);
clock.Stop();
decimal micro = clock.Elapsed.Ticks / 10m;
Console.WriteLine("Total time cost:{0}", micro);
}