public void GetValleyFacePairBasicInfo(CMesh cm)
{
Mesh m = cm.mesh;
List <Tuple <double, double> > face_heignt_pairs = new List <Tuple <double, double> >();
List <double> edge_length_between_face_pairs = new List <double>();
m.FaceNormals.ComputeFaceNormals();
MeshVertexList vert = m.Vertices;
for (int e_ind = 0; e_ind < cm.valley_edges.Count; e_ind++)
{
// Register indices
IndexPair edge_ind = cm.valley_edges[e_ind];
int u = edge_ind.I;
int v = edge_ind.J;
IndexPair face_ind = cm.valley_face_pairs[e_ind];
int P = face_ind.I;
int Q = face_ind.J;
MeshFace face_P = m.Faces[P];
MeshFace face_Q = m.Faces[Q];
int p = 0;
int q = 0;
for (int i = 0; i < 3; i++)
{
if (!edge_ind.Contains(face_P[i]))
{
p = face_P[i];
}
if (!edge_ind.Contains(face_Q[i]))
{
q = face_Q[i];
}
}
/// Compute h_P & cot_Pu
Vector3d vec_up = vert[p] - vert[u];
Vector3d vec_uv = vert[v] - vert[u];
double sin_Pu = (Vector3d.CrossProduct(vec_up, vec_uv) / (vec_up.Length * vec_uv.Length)).Length;
double len_up = (vec_up - vec_uv).Length;
double h_P = len_up * sin_Pu;
/// Compute h_Q & cot_Qu
Vector3d vec_uq = vert[q] - vert[u];
double sin_Qu = (Vector3d.CrossProduct(vec_uq, vec_uv) / (vec_uq.Length * vec_uv.Length)).Length;
double len_uq = (vec_uq - vec_uv).Length;
double h_Q = len_uq * sin_Qu;
// Compute len_uv
double len_uv = vec_uv.Length;
// Set Tuple<h_P, h_Q>
Tuple <double, double> face_height_pair = new Tuple <double, double>(h_P, h_Q);
face_heignt_pairs.Add(face_height_pair);
edge_length_between_face_pairs.Add(len_uv);
}
cm.valley_face_height_pairs = face_heignt_pairs;
cm.length_of_valley_diagonal_edges = edge_length_between_face_pairs;
}
public override CRS Jacobian(CMesh cm)
{
// 等長拘束をかける辺の数取得
int n = equal_fold_angle_edge_id.Count;
List <double> var = new List <double>();
List <int> rind = new List <int>();
List <int> cind = new List <int>();
List <Point3d> verts = new List <Point3d>(cm.mesh.Vertices.ToPoint3dArray());
Mesh m = cm.mesh;
m.FaceNormals.ComputeFaceNormals();
// メッシュの TopologyEdges 取得
MeshTopologyEdgeList topo_edges = m.TopologyEdges;
for (int i = 0; i < n; i++)
{
// Register indices
int edge_index = equal_fold_angle_edge_id[i];
IndexPair edge_ind = topo_edges.GetTopologyVertices(edge_index);
int u = edge_ind.I;
int v = edge_ind.J;
IndexPair face_ind = cm.face_pairs[edge_index];
int P = face_ind[0];
int Q = face_ind[1];
MeshFace face_P = m.Faces[P];
MeshFace face_Q = m.Faces[Q];
int p = 0;
int q = 0;
for (int j = 0; j < 3; j++)
{
if (!edge_ind.Contains(face_P[j]))
{
p = face_P[j];
}
if (!edge_ind.Contains(face_Q[j]))
{
q = face_Q[j];
}
}
/// Compute normals
Vector3d normal_P = m.FaceNormals[P];
Vector3d normal_Q = m.FaceNormals[Q];
/// Compute h_P & cot_Pu
Vector3d vec_up = verts[p] - verts[u];
Vector3d vec_uv = verts[v] - verts[u];
double sin_Pu = (Vector3d.CrossProduct(vec_up, vec_uv) / (vec_up.Length * vec_uv.Length)).Length;
double cos_Pu = (vec_up * vec_uv) / (vec_up.Length * vec_uv.Length);
double cot_Pu = cos_Pu / sin_Pu;
double len_up = vec_up.Length;
double h_P = len_up * sin_Pu;
/// Compute cot_Pv
Vector3d vec_vp = verts[p] - verts[v];
Vector3d vec_vu = verts[u] - verts[v];
double sin_Pv = (Vector3d.CrossProduct(vec_vp, vec_vu) / (vec_vp.Length * vec_vu.Length)).Length;
double cos_Pv = (vec_vp * vec_vu) / (vec_vp.Length * vec_vu.Length);
double cot_Pv = cos_Pv / sin_Pv;
/// Compute h_Q & cot_Qu
Vector3d vec_uq = verts[q] - verts[u];
double sin_Qu = (Vector3d.CrossProduct(vec_uq, vec_uv) / (vec_uq.Length * vec_uv.Length)).Length;
double cos_Qu = (vec_uq * vec_uv) / (vec_uq.Length * vec_uv.Length);
double cot_Qu = cos_Qu / sin_Qu;
double len_uq = vec_uq.Length;
double h_Q = len_uq * sin_Qu;
/// Compute cot_Qv
Vector3d vec_vq = verts[q] - verts[v];
double sin_Qv = (Vector3d.CrossProduct(vec_vq, vec_vu) / (vec_vq.Length * vec_vu.Length)).Length;
double cos_Qv = vec_vq * vec_vu / (vec_vq.Length * vec_vu.Length);
double cot_Qv = cos_Qv / sin_Qv;
List <double> normal_P_list = new List <double>();
List <double> normal_Q_list = new List <double>();
normal_P_list.Add(normal_P.X);
normal_P_list.Add(normal_P.Y);
normal_P_list.Add(normal_P.Z);
normal_Q_list.Add(normal_Q.X);
normal_Q_list.Add(normal_Q.Y);
normal_Q_list.Add(normal_Q.Z);
/// Compute coefficients
double co_pv = (-1 * cot_Pv) / (cot_Pu + cot_Pv);
double co_qv = (-1 * cot_Qv) / (cot_Qu + cot_Qv);
double co_pu = (-1 * cot_Pu) / (cot_Pu + cot_Pv);
double co_qu = (-1 * cot_Qu) / (cot_Qu + cot_Qv);
/// Compute Jacobian
for (int v_ind = 0; v_ind < verts.Count; v_ind++)
{
if (v_ind == p)
{
for (int x = 0; x < 3; x++)
{
var.Add((normal_P_list[x] / (h_P)));
cind.Add(3 * v_ind + x);
rind.Add(i);
}
}
if (v_ind == q)
{
for (int x = 0; x < 3; x++)
{
var.Add((normal_Q_list[x] / (h_Q)));
cind.Add(3 * v_ind + x);
rind.Add(i);
}
}
if (v_ind == u)
{
for (int x = 0; x < 3; x++)
{
var.Add(((co_pv * (normal_P_list[x] / h_P) + co_qv * (normal_Q_list[x] / h_Q))));
cind.Add(3 * v_ind + x);
rind.Add(i);
}
}
if (v_ind == v)
{
for (int x = 0; x < 3; x++)
{
var.Add(((co_pu * (normal_P_list[x] / h_P) + co_qu * (normal_Q_list[x] / h_Q))));
cind.Add(3 * v_ind + x);
rind.Add(i);
}
}
}
}
CRS Jaco = new CRS(var, rind, cind, n, verts.Count * 3);
return(Jaco);
}
public override Vec Error(CMesh cm)
{
Mesh m = cm.mesh;
List <Point3d> verts = new List <Point3d>(m.Vertices.ToPoint3dArray());
List <double> foldang = new List <double>();
// 等長拘束をかける辺の数取得
int n = equal_fold_angle_edge_id.Count;
// メッシュの TopologyEdges 取得
MeshTopologyEdgeList topo_edges = m.TopologyEdges;
// 法線方向計算
m.FaceNormals.ComputeFaceNormals();
for (int i = 0; i < n; i++)
{
double foldang_i = 0;
/// Register indices
int edge_index = equal_fold_angle_edge_id[i];
IndexPair edge_ind = topo_edges.GetTopologyVertices(edge_index);
int u = edge_ind.I;
int v = edge_ind.J;
IndexPair face_ind = cm.face_pairs[edge_index];
int P = face_ind[0];
int Q = face_ind[1];
MeshFace face_P = m.Faces[P];
MeshFace face_Q = m.Faces[Q];
int p = 0;
int q = 0;
for (int j = 0; j < 3; j++)
{
if (!edge_ind.Contains(face_P[j]))
{
p = face_P[j];
}
if (!edge_ind.Contains(face_Q[j]))
{
q = face_Q[j];
}
}
/// Compute normals
Vector3d normal_P = m.FaceNormals[P];
Vector3d normal_Q = m.FaceNormals[Q];
/// cos(foldang_e) = n_i * n_j
double cos_foldang_e = normal_P * normal_Q;
/// sin(foldang_e) = n_i × n_j
Vector3d vec_e = verts[u] - verts[v];
vec_e.Unitize();
double sin_foldang_e = Vector3d.CrossProduct(normal_P, normal_Q) * vec_e;
if (sin_foldang_e >= 0)
{
if (cos_foldang_e >= 1.0)
{
foldang_i = 0;
}
else if (cos_foldang_e <= -1.0)
{
foldang_i = Math.PI;
}
else
{
foldang_i = Math.Acos(cos_foldang_e);
}
}
else
{
if (cos_foldang_e >= 1.0)
{
foldang_i = 0;
}
else if (cos_foldang_e <= -1.0)
{
foldang_i = -Math.PI;
}
else
{
foldang_i = -Math.Acos(cos_foldang_e);
}
}
if (is_set_angle)
{
foldang_i -= fold_angle;
}
foldang.Add(foldang_i);
}
Vec ans = new Vec(foldang);
return(ans);
}