private void Form1_Load(object sender, EventArgs e)
{
Mesh M = new Mesh();
FiniteSolverMethod Method = FiniteSolverMethod.EnergyModel;
//Interop with catia to retrive exported stlPath
string StlPath = CAT.SaveSurfaceAndFixedPoints(ref M.FixedPoints, ref M.oVecPlane);
//Parse stlFile to Vertice and triangle matrix
STLReader.STLRead(StlPath, ref M);
if (M.Vertices.Count == 0 || M.TrianglesVertices.Count == 0) {
MessageBox.Show("Não foi encontrada nenhuma informação na superficie exportada. Tente outra vez.");
Environment.Exit(0);
}
//Detection of the most apropriated verticePoints
M.ComputeFixedPoints();
//Calculation of Plane of flattening
M.ComputePlaneofFlattening();
//Solve using the edge to edge interpretation of the article
Vector<double> X = EdgeToEdgeSolver.Solve(M);
//Print Result of triangles in CATIA;
CAT.PrintTriangles(X, M);
Vector<double> Y = Vector<double>.Build.Dense(X.Count);
if (Method== FiniteSolverMethod.NewtonRaphson) {
//Try to calculate de displacement vector based on finite-element analysis using NewtonRapson Method
//ATENTION - IS NOT COMPLETE/WITH ERRORS!
Y =NewtonRaphsonFiniteSolver.solve(X, M);
} else if (Method == FiniteSolverMethod.EnergyModel) {
//Try to calculate de displacement vector based on energy analysis
//ATENTION - IS NOT COMPLETE/WITH ERRORS!
Y = EnergyModelFiniteSolver.solve(X, M);
}
CAT.PrintTriangles(Y, M);
Application.Exit();
}
internal void PrintTriangles(Vector<double> X2, Mesh M)
{
PrintTriangles(X2, M.TrianglesVertices, M.oRoot, M.vDir1, M.vDir2, M.OneIndFix, M.OnePointFix);
}
public static Vector<double> solve(
List<double[]> Vertices,
List<int[]> TrianglesVertices,
List<double[]> FacetNormals,
Vector<double> X, Point3D oRoot,
UnitVector3D vDir1,
UnitVector3D vDir2, Mesh M)
{
//Method from article -Wang,Smith. Surface flattening based on energy model. Computer-Aided Design (2002) 823-833
//PseudoCode
//Input: P - Set of nodes, in the initial position and N is the number of nodes
//Output: the final positions of P with E(o) minimized
// FOR i = 1 TO n
// mi = p / 3 Sum(Ak), where Ak is the area
// WHILE (Relative Area difference Es > Permissible accuracy or Relative edge length difference Ec > Permissible accuracy)
// AND Variation of E(o) > Permissible percentage €
// AND the number of iterations < Permissible number N
// FOR i = 1 TO n
// Compute Tensile force of Node Pi: Fi = Sum(C * (Dist(PiPj) - Dist(QiQj)))nij where(P - 2D - Q - 3D nij - Vector Pi to Pj)
// Compute new position of Pi qi = qi + dtqi. + dt ^ 2 / 2 qi..where qi.= qi.+ dtqi..and qi..= Fi / mi
// Compute Penalty force and aplly to Fpi
// Compute new position of Pi qi = qi + dtqi. + dt ^ 2 / 2 qi..where qi.= qi.+ dtqi..and qi..= Fpi / mi
// Compute new Es= Sum(TotalAreaNow - TotalAreaBefore) / TotalAreaNow
// Compute new Ec= Sum(TotalLenghtNow - TotalLenghtBefore) / TotalLenghtNow
// Compute new E(o)Sum(E(pi)) where E(pi) = 0.5 * Sum(C * (Dist(PiPj) - Dist(QiQj))) ^ 2
double[] Mass = new double [Vertices.Count];
int[] MassCounter = new int[Vertices.Count];
double Permissible = 0.00000001;
Vector<double> Fi = Vector<double>.Build.Dense(2);
List<Vector<double>> dqi = new List<Vector<double>>();
List<Vector<double>> qi = new List<Vector<double>>();
double LastEc = 0, Ec = 0;
double LastEs = 0, Es = 0;
double LastEo = 0, Eo = 0;
double C = 0.5;
double ro = 1;
double t = 0.01;
int N = 100;
int Iteration = 0;
double Total = 0;
double LastTotal = 0;
foreach (int[] tri in TrianglesVertices) {
double A = getArea(Vertices[tri[0]], Vertices[tri[1]], Vertices[tri[2]]);
double P = getPerimeter(Vertices[tri[0]], Vertices[tri[1]], Vertices[tri[2]]);
Mass[tri[0]] += ((double)1 / (double)3) * A * ro;
Mass[tri[1]] += ((double)1 / (double)3) * A * ro;
Mass[tri[2]] += ((double)1 / (double)3) * A * ro;
MassCounter[tri[0]] += 1;
MassCounter[tri[1]] += 1;
MassCounter[tri[2]] += 1;
LastEc += A;
LastEs += P;
}
for (int i = 0; i < Vertices.Count; i++) {
Mass[i] = Mass[i] / MassCounter[i];
qi.Add(Vector<double>.Build.DenseOfArray(new double[] { X[i * 2], X[i * 2 + 1], 0 }));
dqi.Add(Vector<double>.Build.DenseOfArray(new double[] { 0, 0, 0 }));
}
do {
Iteration += 1;
LastEo = Eo;
Eo = 0;
Total = 0;
for (int i = 0; i < Vertices.Count; i++) {
Point3D Pi = new Point3D(qi[i][0], qi[i][1], qi[i][2]);
Point3D Qi = new Point3D(Vertices[i][0], Vertices[i][1], Vertices[i][2]);
Fi = Vector<double>.Build.Dense(3);
for (int j = i+1; j < Vertices.Count; j++) {
if (i == j) continue;
Point3D Pj = new Point3D(qi[j][0], qi[j][1], qi[j][2]);
Point3D Qj = new Point3D(Vertices[j][0], Vertices[j][1], Vertices[j][2]);
UnitVector3D nij = new UnitVector3D((Pi.ToVector()- Pj.ToVector()).ToArray());
Fi += C * ((Pi.DistanceTo(Pj) - Qi.DistanceTo(Qj)) * nij).ToVector();
Eo += Math.Pow(C * ((Pi.DistanceTo(Pj) - Qi.DistanceTo(Qj))), 2);
}
Vector<double> ddqi = Fi / Mass[i];
Console.WriteLine(Fi);
dqi[i] += t * ddqi;
qi[i] += dqi[i] * t + 0.5 * Math.Pow(t, 2) * ddqi;
Total += Math.Abs(qi[i][0] - X[i * 2]);
Total += Math.Abs(qi[i][1] - X[i * 2] + 1);
}
Console.WriteLine(Total- LastTotal);
LastTotal = Total;
LastEc = Ec;
Ec = 0;
LastEs = Es;
Es = 0;
foreach (int[] tri in TrianglesVertices) {
double A = getArea(Vertices[tri[0]], Vertices[tri[1]], Vertices[tri[2]]);
double P = getPerimeter(Vertices[tri[0]], Vertices[tri[1]], Vertices[tri[2]]);
Ec += A;
Es += P;
}
if (((Ec - LastEc) / Ec < Permissible || (Es - LastEs) / Es < Permissible)
&& (Eo - LastEo) / Eo < Permissible
&& Iteration > N) break;
} while (true);
Vector<double> XResult = Vector<double>.Build.DenseOfArray(X.ToArray());
for (int i = 0; i < Vertices.Count; i++) {
//Console.WriteLine(qi[i][0] - X[i * 2]);
Total += Math.Abs(qi[i][0] - X[i * 2]);
XResult[i * 2] = qi[i][0];
//Console.WriteLine(qi[i][1] - X[i * 2+1]);
Total += Math.Abs(qi[i][1] - X[i * 2]+1);
XResult[i * 2+1] = qi[i][1];
}
Console.WriteLine(Total);
return XResult;
}
internal static Vector<double> solve(Vector<double> X, Mesh M)
{
return solve(M.Vertices, M.TrianglesVertices, M.FacetNormals, X, M.oRoot, M.vDir1, M.vDir2,M);
}
internal static void STLRead(string stlPath, ref Mesh M)
{
STLRead(stlPath, ref M.Vertices, ref M.TrianglesVertices, ref M.TrianglesEdges, ref M.Edges, ref M.FacetNormals);
}
internal static Vector<double> Solve(Mesh M)
{
return Solve(M.Vertices, M.TrianglesEdges, M.Edges, M.IndiceOfFixedPoints, M.oRoot, M.vDir1, M.vDir2);
}