public Vector3D ComputeFaceNormals(TriMesh.Face f)
{
Vector3D p0 = f.GetVertex(0).Traits.Position;
Vector3D p1 = f.GetVertex(1).Traits.Position;
Vector3D p2 = f.GetVertex(2).Traits.Position;
return((p1 - p0).Cross(p2 - p0).Normalize());
}
public Vector3D[] ComputeVectorField(double initAngle)
{
Vector3D[] vectorFields = new Vector3D[mesh.Faces.Count];
bool[] visitedFlags = new bool[mesh.Faces.Count];
for (int i = 0; i < visitedFlags.Length; i++)
{
visitedFlags[i] = false;
}
//Find a initial root to expend
TriMesh.Face rootFace = mesh.Faces[0];
var v1 = rootFace.GetVertex(0);
var v3 = rootFace.GetVertex(2);
var v2 = rootFace.GetVertex(1);
Vector3D w0 = (rootFace.GetVertex(2).Traits.Position - rootFace.GetVertex(0).Traits.Position).Normalize();
//Init transpot
Vector3D av = v1.Traits.Position;
Vector3D bv = v2.Traits.Position;
Vector3D cv = v3.Traits.Position;
Matrix3D Ei = Orthogonalize(bv - av, cv - av);
Vector3D w0i = (Ei * Matrix3D.Rotate(initAngle) * Ei.Inverse() * w0);
vectorFields[rootFace.Index] = w0i;
visitedFlags[rootFace.Index] = true;
//Recurse all faces
Queue <TriMesh.Face> queue = new Queue <HalfEdgeMesh.Face>();
queue.Enqueue(rootFace);
int ii = 0;
while (queue.Count > 0)
{
TriMesh.Face currentFace = queue.Dequeue();
Vector3D wI = vectorFields[currentFace.Index];
foreach (TriMesh.Face neighbor in currentFace.Faces)
{
if (visitedFlags[neighbor.Index] == false)
{
Vector3D wj = Transport2(wI, currentFace, neighbor);
vectorFields[neighbor.Index] = wj;
queue.Enqueue(neighbor);
visitedFlags[neighbor.Index] = true;
}
}
ii++;
}
return(vectorFields);
}
//face area
public static double ComputeAreaFaceTwo(TriMesh.Face face)
{
Vector3D v1 = new Vector3D(face.GetVertex(0).Traits.Position.x,
face.GetVertex(0).Traits.Position.y,
face.GetVertex(0).Traits.Position.z);
Vector3D v2 = new Vector3D(face.GetVertex(1).Traits.Position.x,
face.GetVertex(1).Traits.Position.y,
face.GetVertex(1).Traits.Position.z);
Vector3D v3 = new Vector3D(face.GetVertex(2).Traits.Position.x,
face.GetVertex(2).Traits.Position.y,
face.GetVertex(2).Traits.Position.z);
double a = Math.Sqrt((v1.x - v2.x) * (v1.x - v2.x)
+ (v1.y - v2.y) * (v1.y - v2.y)
+ (v1.z - v2.z) * (v1.z - v2.z));
double b = Math.Sqrt((v3.x - v2.x) * (v3.x - v2.x)
+ (v3.y - v2.y) * (v3.y - v2.y)
+ (v3.z - v2.z) * (v3.z - v2.z));
double c = Math.Sqrt((v1.x - v3.x) * (v1.x - v3.x)
+ (v1.y - v3.y) * (v1.y - v3.y)
+ (v1.z - v3.z) * (v1.z - v3.z));
double p = (a + b + c) / 2;
double area = Math.Sqrt(p * (p - a) * (p - b) * (p - c));
return(area);
}
public static double ComputeInradius(TriMesh.Face face)
{
Vector3D a = face.GetVertex(0).Traits.Position;
Vector3D b = face.GetVertex(1).Traits.Position;
Vector3D c = face.GetVertex(2).Traits.Position;
double u = (a - b).Length();
double v = (b - c).Length();
double w = (c - a).Length();
return(0.5 * Math.Sqrt(((u + v - w) * (w + u - v) * (v + w - u)) / (u + v + w)));
}
public static List <double> ComputeAngle(TriMesh.Face face)
{
List <double> angles = new List <double>();
double angle1 = ComputeAngle(face.GetVertex(0).HalfEdge);
double angle2 = ComputeAngle(face.GetVertex(1).HalfEdge);
double angle3 = ComputeAngle(face.GetVertex(2).HalfEdge);
angles.Add(angle1);
angles.Add(angle2);
angles.Add(angle3);
return(angles);
}
//public void ComputeFrameAngles(double initialAngle)
//{
// TreeNode<TriMesh.Face> Root = transportTree.Root;
// Queue<TreeNode<HalfEdgeMesh.Face>> queue = new Queue<TreeNode<HalfEdgeMesh.Face>>();
// queue.Enqueue(transportTree.Root);
// bool[] processedFlag = new bool[Mesh.Faces.Count];
// while (queue.Count != 0)
// {
// TreeNode<HalfEdgeMesh.Face> currentFaceNode = queue.Dequeue();
// TriMesh.HalfEdge startHf = currentFaceNode.Attribute.HalfEdge;
// TriMesh.HalfEdge currentHf = startHf;
// do
// {
// TriMesh.Face neighborFace = currentHf.Opposite.Face;
// TransportData td = transDatas[currentHf.Index];
// td.alphaJ = td.alphaI + td.delta - td.sign * td.omega;
// currentHf = currentHf.Next;
// } while (currentHf != startHf);
// }
//}
//public void UpdateAngles(int initAngle)
//{
// TriMesh.Face faceTransport = Mesh.Faces[3];
// FaceAngle[faceTransport.Index] = initAngle;
// Queue<TriMesh.Face> queue = new Queue<TriMesh.Face>();
// queue.Enqueue(faceTransport);
// bool[] processedFlag = new bool[Mesh.Faces.Count];
// while (queue.Count != 0)
// {
// TriMesh.Face currentFace = queue.Dequeue();
// TriMesh.HalfEdge startHf = currentFace.HalfEdge;
// TriMesh.HalfEdge currentHf = startHf;
// double currentDelta = Deltas[currentFace.Index];
// do
// {
// TriMesh.Face neighborFace = currentHf.Opposite.Face;
// if (processedFlag[neighborFace.Index] == false &&
// neighborFace != faceTransport &&
// !neighborFace.OnBoundary
// )
// {
// processedFlag[neighborFace.Index] = true;
// queue.Enqueue(neighborFace);
// double delta = ComputeParallTransport(currentDelta, currentHf);
// Deltas[neighborFace.Index] = delta;
// double omega = EdgeTheta[currentHf.Edge.Index];
// double sign = currentHf.FromVertex.Index > currentHf.ToVertex.Index ? -1 : 1;
// FaceAngle[neighborFace.Index] = FaceAngle[currentFace.Index] + delta - sign * omega;
// }
// currentHf = currentHf.Next;
// } while (currentHf != startHf);
// }
//}
//public void AppendDirectionalConstraints(TriMesh mesh, List<List<TriMesh.HalfEdge>> cycles)
//{
// transDatas = new TransportData[mesh.HalfEdges.Count];
// TriMesh.Face faceTransport = mesh.Faces[3];
// transportTree = new DynamicTree<HalfEdgeMesh.Face>();
// transportTree.Root = new TreeNode<HalfEdgeMesh.Face>(faceTransport);
// Queue<TreeNode<HalfEdgeMesh.Face>> queue = new Queue<TreeNode<HalfEdgeMesh.Face>>();
// queue.Enqueue(transportTree.Root);
// bool[] processedFlag = new bool[mesh.Faces.Count];
// while (queue.Count != 0)
// {
// TreeNode<HalfEdgeMesh.Face> currentFaceNode = queue.Dequeue();
// TriMesh.HalfEdge startHf = currentFaceNode.Attribute.HalfEdge;
// TriMesh.HalfEdge currentHf = startHf;
// do
// {
// TriMesh.Face neighborFace = currentHf.Opposite.Face;
// if (processedFlag[neighborFace.Index] == false &&
// neighborFace != faceTransport &&
// !neighborFace.OnBoundary
// )
// {
// TreeNode<HalfEdgeMesh.Face> neighNode = new TreeNode<HalfEdgeMesh.Face>(neighborFace);
// processedFlag[neighborFace.Index] = true;
// currentFaceNode.AddChild(neighNode);
// queue.Enqueue(neighNode);
// TransportData td = new TransportData();
// td.delta = ComputeParallTransport(0, currentHf);
// td.sign = currentHf.FromVertex.Index > currentHf.ToVertex.Index ? 1 : -1;
// td.omega = EdgeTheta[currentHf.Edge.Index];
// td.alphaI = FaceAngle[currentHf.Face.Index];
// td.alphaJ = FaceAngle[currentHf.Opposite.Face.Index];
// transDatas[currentHf.Index] = td;
// Deltas[currentHf.Face.Index] = td.delta;
// }
// currentHf = currentHf.Next;
// } while (currentHf != startHf);
// }
//}
public Vector3D[] ComputeVectorField(double initAngle)
{
Vector3D[] vectorFields = new Vector3D[Mesh.Faces.Count];
bool[] visitedFlags = new bool[Mesh.Faces.Count];
for (int i = 0; i < visitedFlags.Length; i++)
{
visitedFlags[i] = false;
}
//Find a initial root to expend
TriMesh.Face rootFace = Mesh.Faces[0];
var v1 = rootFace.GetVertex(0);
var v3 = rootFace.GetVertex(2);
var v2 = rootFace.GetVertex(1);
Vector3D w0 = (rootFace.GetVertex(2).Traits.Position - rootFace.GetVertex(0).Traits.Position).Normalize();
//Init transpot
Vector3D av = v1.Traits.Position;
Vector3D bv = v2.Traits.Position;
Vector3D cv = v3.Traits.Position;
Matrix3D Ei = Orthogonalize(bv - av, cv - av);
Vector3D w0i = (Ei * Matrix3D.Rotate(initAngle) * Ei.Inverse() * w0);
vectorFields[rootFace.Index] = w0i;
visitedFlags[rootFace.Index] = true;
//Recurse all faces
Queue <TriMesh.Face> queue = new Queue <HalfEdgeMesh.Face>();
queue.Enqueue(rootFace);
int ii = 0;
while (queue.Count > 0)
{
TriMesh.Face currentFace = queue.Dequeue();
Vector3D wI = vectorFields[currentFace.Index];
TriMesh.HalfEdge cuHe = currentFace.HalfEdge;
do
{
TriMesh.Face neighbor = cuHe.Opposite.Face;
if (neighbor == null)
{
cuHe = cuHe.Next;
continue;
}
if (visitedFlags[neighbor.Index] == false)
{
double angle = EdgeTheta[cuHe.Edge.Index];
int i = cuHe.FromVertex.Index;
int j = cuHe.ToVertex.Index;
if (i > j)
{
angle = -angle;
}
Vector3D wj = Transport(wI, currentFace, neighbor, angle);
vectorFields[neighbor.Index] = wj;
queue.Enqueue(neighbor);
visitedFlags[neighbor.Index] = true;
}
cuHe = cuHe.Next;
} while (cuHe != currentFace.HalfEdge);
ii++;
}
return(vectorFields);
}