// Result must be as large as Mesh.MaxVertexID
public bool SolveMultipleRHS(Vector3d[] Result)
{
if (WeightsM == null)
{
Initialize(); // force initialize...
}
UpdateForSolve();
// use initial positions as initial solution.
double[][] B = BufferUtil.InitNxM(3, N, new double[][] { Bx, By, Bz });
double[][] X = BufferUtil.InitNxM(3, N, new double[][] { Px, Py, Pz });
Action <double[][], double[][]> CombinedMultiply = (Xt, Bt) =>
{
PackedM.Multiply_Parallel_3(Xt, Bt);
gParallel.ForEach(Interval1i.Range(3), (j) =>
{
BufferUtil.MultiplyAdd(Bt[j], WeightsM.D, Xt[j]);
});
};
var Solver = new SparseSymmetricCGMultipleRHS()
{
B = B,
X = X,
MultiplyF = CombinedMultiply,
PreconditionMultiplyF = null,
UseXAsInitialGuess = true
};
bool ok = Solver.Solve();
if (ok == false)
{
return(false);
}
for (int i = 0; i < N; ++i)
{
int vid = ToMeshV[i];
Result[vid] = new Vector3d(X[0][i], X[1][i], X[2][i]);
}
// apply post-fixed constraints
if (HavePostFixedConstraints)
{
foreach (var constraint in SoftConstraints)
{
if (constraint.Value.PostFix)
{
int vid = constraint.Key;
Result[vid] = constraint.Value.Position;
}
}
}
return(true);
}
//
// DMesh3 construction utilities
//
/// <summary>
/// ultimate generic mesh-builder, pass it arrays of floats/doubles, or lists
/// of Vector3d, or anything in-between. Will figure out how to interpret
///
/// This static function attempts to retain a manifold mesh, if you need finer
/// control use the concrete class.
///
/// Number of issues encountered adding verices or triangls are stored in the
/// mesh metadata. Metadata can be cleared once the returning object is evaluated.
/// </summary>
public static DMesh3 Build <VType, TType, NType>(IEnumerable <VType> Vertices,
IEnumerable <TType> Triangles,
IEnumerable <NType> Normals = null,
IEnumerable <int> TriGroups = null)
{
DMesh3 mesh = new DMesh3(Normals != null, false, false, TriGroups != null);
// build outcomes are stored in the metadata to avoid changes to the function signature
//
int iAppendTriangleIssues = 0;
Vector3d[] v = BufferUtil.ToVector3d(Vertices);
for (int i = 0; i < v.Length; ++i)
{
mesh.AppendVertex(v[i]);
}
if (Normals != null)
{
Vector3f[] n = BufferUtil.ToVector3f(Normals);
if (n.Length != v.Length)
{
throw new Exception("DMesh3Builder.Build: incorrect number of normals provided");
}
for (int i = 0; i < n.Length; ++i)
{
mesh.SetVertexNormal(i, n[i]);
}
}
Index3i[] t = BufferUtil.ToIndex3i(Triangles);
for (int i = 0; i < t.Length; ++i)
{
var last = mesh.AppendTriangle(t[i]);
if (last == DMesh3.InvalidID || last == DMesh3.NonManifoldID)
{
iAppendTriangleIssues++;
}
}
if (TriGroups != null)
{
List <int> groups = new List <int>(TriGroups);
if (groups.Count != t.Length)
{
throw new Exception("DMesh3Builder.Build: incorect number of triangle groups");
}
for (int i = 0; i < t.Length; ++i)
{
mesh.SetTriangleGroup(i, groups[i]);
}
}
mesh.AttachMetadata("AppendTriangleIssues", iAppendTriangleIssues);
return(mesh);
}
//
// DMesh3 construction utilities
//
/// <summary>
/// ultimate generic mesh-builder, pass it arrays of floats/doubles, or lists
/// of Vector3d, or anything in-between. Will figure out how to interpret
/// </summary>
public static DMesh3 Build <VType, TType, NType>(IEnumerable <VType> Vertices,
IEnumerable <TType> Triangles,
IEnumerable <NType> Normals = null,
IEnumerable <int> TriGroups = null)
{
var mesh = new DMesh3(Normals != null, false, false, TriGroups != null);
Vector3d[] v = BufferUtil.ToVector3d(Vertices);
for (int i = 0; i < v.Length; ++i)
{
mesh.AppendVertex(v[i]);
}
if (Normals != null)
{
Vector3f[] n = BufferUtil.ToVector3f(Normals);
if (n.Length != v.Length)
{
throw new Exception("DMesh3Builder.Build: incorrect number of normals provided");
}
for (int i = 0; i < n.Length; ++i)
{
mesh.SetVertexNormal(i, n[i]);
}
}
Index3i[] t = BufferUtil.ToIndex3i(Triangles);
for (int i = 0; i < t.Length; ++i)
{
mesh.AppendTriangle(t[i]);
}
if (TriGroups != null)
{
var groups = new List <int>(TriGroups);
if (groups.Count != t.Length)
{
throw new Exception("DMesh3Builder.Build: incorect number of triangle groups");
}
for (int i = 0; i < t.Length; ++i)
{
mesh.SetTriangleGroup(i, groups[i]);
}
}
return(mesh);
}
/// <summary>
/// Find the set of boundary EdgeLoops. Note that if we encounter topological
/// issues, we will throw MeshBoundaryLoopsException w/ more info (if possible)
/// </summary>
public bool Compute()
{
// This algorithm assumes that triangles are oriented consistently,
// so closed boundary-loop can be followed by walking edges in-order
Loops = new List <EdgeLoop>();
Spans = new List <EdgeSpan>();
// early-out if we don't actually have boundaries
if (Mesh.CachedIsClosed)
{
return(true);
}
int NE = Mesh.MaxEdgeID;
// Temporary memory used to indicate when we have "used" an edge.
BitArray used_edge = new BitArray(NE);
used_edge.SetAll(false);
// current loop is stored here, cleared after each loop extracted
List <int> loop_edges = new List <int>(); // [RMS] not sure we need this...
List <int> loop_verts = new List <int>();
List <int> bowties = new List <int>();
// Temp buffer for reading back all boundary edges of a vertex.
// probably always small but in pathological cases it could be large...
int[] all_e = new int[16];
// [TODO] might make sense to precompute some things here, like num_be for each bdry vtx?
// process all edges of mesh
for (int eid = 0; eid < NE; ++eid)
{
if (!Mesh.IsEdge(eid))
{
continue;
}
if (used_edge[eid] == true)
{
continue;
}
if (Mesh.IsBoundaryEdge(eid) == false)
{
continue;
}
if (EdgeFilterF != null && EdgeFilterF(eid) == false)
{
used_edge[eid] = true;
continue;
}
// ok this is start of a boundary chain
int eStart = eid;
used_edge[eStart] = true;
loop_edges.Add(eStart);
int eCur = eid;
// follow the chain in order of oriented edges
bool bClosed = false;
bool bIsOpenSpan = false;
while (!bClosed)
{
Index2i ev = Mesh.GetOrientedBoundaryEdgeV(eCur);
int cure_a = ev.a, cure_b = ev.b;
if (bIsOpenSpan)
{
cure_a = ev.b; cure_b = ev.a;
}
else
{
loop_verts.Add(cure_a);
}
int e0 = -1, e1 = 1;
int bdry_nbrs = Mesh.VtxBoundaryEdges(cure_b, ref e0, ref e1);
// have to filter this list, if we are filtering. this is ugly.
if (EdgeFilterF != null)
{
if (bdry_nbrs > 2)
{
if (bdry_nbrs >= all_e.Length)
{
all_e = new int[bdry_nbrs];
}
// we may repreat this below...irritating...
int num_be = Mesh.VtxAllBoundaryEdges(cure_b, all_e);
num_be = BufferUtil.CountValid(all_e, EdgeFilterF, num_be);
}
else
{
if (EdgeFilterF(e0) == false)
{
bdry_nbrs--;
}
if (EdgeFilterF(e1) == false)
{
bdry_nbrs--;
}
}
}
if (bdry_nbrs < 2) // hit an 'endpoint' vertex (should only happen when Filter is on...)
{
if (SpanBehavior == SpanBehaviors.ThrowException)
{
throw new MeshBoundaryLoopsException("MeshBoundaryLoops.Compute: found open span at vertex " + cure_b)
{
UnclosedLoop = true
}
}
;
if (bIsOpenSpan)
{
bClosed = true;
continue;
}
else
{
bIsOpenSpan = true; // begin open span
eCur = loop_edges[0]; // restart at other end of loop
loop_edges.Reverse(); // do this so we can push to front
continue;
}
}
int eNext = -1;
if (bdry_nbrs > 2)
{
// found "bowtie" vertex...things just got complicated!
if (cure_b == loop_verts[0])
{
// The "end" of the current edge is the same as the start vertex.
// This means we can close the loop here. Might as well!
eNext = -2; // sentinel value used below
}
else
{
// try to find an unused outgoing edge that is oriented properly.
// This could create sub-loops, we will handle those later
if (bdry_nbrs >= all_e.Length)
{
all_e = new int[2 * bdry_nbrs];
}
int num_be = Mesh.VtxAllBoundaryEdges(cure_b, all_e);
Debug.Assert(num_be == bdry_nbrs);
if (EdgeFilterF != null)
{
num_be = BufferUtil.FilterInPlace(all_e, EdgeFilterF, num_be);
}
// Try to pick the best "turn left" vertex.
eNext = find_left_turn_edge(eCur, cure_b, all_e, num_be, used_edge);
if (eNext == -1)
{
if (FailureBehavior == FailureBehaviors.ThrowException || SpanBehavior == SpanBehaviors.ThrowException)
{
throw new MeshBoundaryLoopsException("MeshBoundaryLoops.Compute: cannot find valid outgoing edge at bowtie vertex " + cure_b)
{
BowtieFailure = true
}
}
;
// ok, we are stuck. all we can do now is terminate this loop and keep it as a span
if (bIsOpenSpan)
{
bClosed = true;
}
else
{
bIsOpenSpan = true;
bClosed = true;
}
continue;
}
}
if (bowties.Contains(cure_b) == false)
{
bowties.Add(cure_b);
}
}
else
{
// walk forward to next available edge
Debug.Assert(e0 == eCur || e1 == eCur);
eNext = (e0 == eCur) ? e1 : e0;
}
if (eNext == -2)
{
// found a bowtie vert that is the same as start-of-loop, so we
// are just closing it off explicitly
bClosed = true;
}
else if (eNext == eStart)
{
// found edge at start of loop, so loop is done.
bClosed = true;
}
else if (used_edge[eNext] != false)
{
// disaster case - the next edge is already used, but it is not the start of our loop
// All we can do is convert to open span and terminate
if (FailureBehavior == FailureBehaviors.ThrowException || SpanBehavior == SpanBehaviors.ThrowException)
{
throw new MeshBoundaryLoopsException("MeshBoundaryLoops.Compute: encountered repeated edge " + eNext)
{
RepeatedEdge = true
}
}
;
bIsOpenSpan = true;
bClosed = true;
}
else
{
// push onto accumulated list
Debug.Assert(used_edge[eNext] == false);
loop_edges.Add(eNext);
used_edge[eNext] = true;
eCur = eNext;
}
}
if (bIsOpenSpan)
{
SawOpenSpans = true;
if (SpanBehavior == SpanBehaviors.Compute)
{
loop_edges.Reverse(); // orient properly
EdgeSpan span = EdgeSpan.FromEdges(Mesh, loop_edges);
Spans.Add(span);
}
}
else if (bowties.Count > 0)
{
// if we saw a bowtie vertex, we might need to break up this loop,
// so call extract_subloops
Subloops subloops = extract_subloops(loop_verts, loop_edges, bowties);
foreach (var loop in subloops.Loops)
{
Loops.Add(loop);
}
if (subloops.Spans.Count > 0)
{
FellBackToSpansOnFailure = true;
foreach (var span in subloops.Spans)
{
Spans.Add(span);
}
}
}
else
{
// clean simple loop, convert to EdgeLoop instance
EdgeLoop loop = new EdgeLoop(Mesh);
loop.Vertices = loop_verts.ToArray();
loop.Edges = loop_edges.ToArray();
Loops.Add(loop);
}
// reset these lists
loop_edges.Clear();
loop_verts.Clear();
bowties.Clear();
}
return(true);
}
// [TODO] cache this in a dictionary? we will not need very many, but we will
// need each multiple times!
Vector3d get_vtx_normal(int vid)
{
Vector3d n = Vector3d.Zero;
foreach (int ti in Mesh.VtxTrianglesItr(vid))
{
n += Mesh.GetTriNormal(ti);
}
n.Normalize();
return(n);
}
// ok, bdry_edges[0...bdry_edges_count] contains the boundary edges coming out of bowtie_v.
// We want to pick the best one to continue the loop that came in to bowtie_v on incoming_e.
// If the loops are all sane, then we will get the smallest loops by "turning left" at bowtie_v.
// So, we compute the tangent plane at bowtie_v, and then the signed angle for each
// viable edge in this plane.
//
// [TODO] handle degenerate edges. what do we do then? Currently will only chose
// degenerate edge if there are no other options (I think...)
int find_left_turn_edge(int incoming_e, int bowtie_v, int[] bdry_edges, int bdry_edges_count, BitArray used_edges)
{
// compute normal and edge [a,bowtie]
Vector3d n = get_vtx_normal(bowtie_v);
int other_v = Mesh.edge_other_v(incoming_e, bowtie_v);
Vector3d ab = Mesh.GetVertex(bowtie_v) - Mesh.GetVertex(other_v);
// our winner
int best_e = -1;
double best_angle = double.MaxValue;
for (int i = 0; i < bdry_edges_count; ++i)
{
int bdry_eid = bdry_edges[i];
if (used_edges[bdry_eid] == true)
{
continue; // this edge is already used
}
Index2i bdry_ev = Mesh.GetOrientedBoundaryEdgeV(bdry_eid);
if (bdry_ev.a != bowtie_v)
{
continue; // have to be able to chain to end of current edge, orientation-wise
}
// compute projected angle
Vector3d bc = Mesh.GetVertex(bdry_ev.b) - Mesh.GetVertex(bowtie_v);
float fAngleS = MathUtil.PlaneAngleSignedD((Vector3f)ab, (Vector3f)bc, (Vector3f)n);
// turn left!
if (best_angle == double.MaxValue || fAngleS < best_angle)
{
best_angle = fAngleS;
best_e = bdry_eid;
}
}
// [RMS] w/ bowtie vertices and open spans, this does happen
//Debug.Assert(best_e != -1);
return(best_e);
}
/// <summary>
/// Preconditioned variant
/// Similar to non-preconditioned version, this can suffer if one solution converges
/// much slower than others, as we can't skip matrix multiplies in that case.
/// </summary>
public bool SolvePreconditioned()
{
Iterations = 0;
if (B == null || MultiplyF == null || PreconditionMultiplyF == null)
{
throw new Exception("SparseSymmetricCGMultipleRHS.SolvePreconditioned(): Must set B and MultiplyF and PreconditionMultiplyF!");
}
int NRHS = B.Length;
if (NRHS == 0)
{
throw new Exception("SparseSymmetricCGMultipleRHS.SolvePreconditioned(): Need at least one RHS vector in B");
}
int n = B[0].Length;
R = BufferUtil.AllocNxM(NRHS, n);
P = BufferUtil.AllocNxM(NRHS, n);
AP = BufferUtil.AllocNxM(NRHS, n);
Z = BufferUtil.AllocNxM(NRHS, n);
if (X == null || UseXAsInitialGuess == false)
{
if (X == null)
{
X = BufferUtil.AllocNxM(NRHS, n);
}
for (int j = 0; j < NRHS; ++j)
{
Array.Clear(X[j], 0, n);
Array.Copy(B[j], R[j], n);
}
}
else
{
// hopefully is X is a decent initialization...
InitializeR(R);
}
// [RMS] for convergence test?
double[] norm = new double[NRHS];
for (int j = 0; j < NRHS; ++j)
{
norm[j] = BufferUtil.Dot(B[j], B[j]);
}
double[] root1 = new double[NRHS];
for (int j = 0; j < NRHS; ++j)
{
root1[j] = Math.Sqrt(norm[j]);
}
// r_0 = b - A*x_0
MultiplyF(X, R);
for (int j = 0; j < NRHS; ++j)
{
for (int i = 0; i < n; ++i)
{
R[j][i] = B[j][i] - R[j][i];
}
}
// z0 = M_inverse * r_0
PreconditionMultiplyF(R, Z);
// p0 = z0
for (int j = 0; j < NRHS; ++j)
{
Array.Copy(Z[j], P[j], n);
}
// compute initial R*Z
double[] RdotZ_k = new double[NRHS];
for (int j = 0; j < NRHS; ++j)
{
RdotZ_k[j] = BufferUtil.Dot(R[j], Z[j]);
}
double[] alpha_k = new double[NRHS];
double[] beta_k = new double[NRHS];
bool[] converged = new bool[NRHS];
var rhs = Interval1i.Range(NRHS);
int iter = 0;
while (iter++ < MaxIterations)
{
// convergence test
bool done = true;
for (int j = 0; j < NRHS; ++j)
{
if (converged[j] == false)
{
double root0 = Math.Sqrt(RdotZ_k[j]);
if (root0 <= ConvergeTolerance * root1[j])
{
converged[j] = true;
}
}
if (converged[j] == false)
{
done = false;
}
}
if (done)
{
break;
}
MultiplyF(P, AP);
gParallel.ForEach(rhs, (j) =>
{
if (converged[j] == false)
{
alpha_k[j] = RdotZ_k[j] / BufferUtil.Dot(P[j], AP[j]);
}
});
// x_k+1 = x_k + alpha_k * p_k
gParallel.ForEach(rhs, (j) =>
{
if (converged[j] == false)
{
BufferUtil.MultiplyAdd(X[j], alpha_k[j], P[j]);
}
});
// r_k+1 = r_k - alpha_k * A * p_k
gParallel.ForEach(rhs, (j) =>
{
if (converged[j] == false)
{
BufferUtil.MultiplyAdd(R[j], -alpha_k[j], AP[j]);
}
});
// z_k+1 = M_inverse * r_k+1
PreconditionMultiplyF(R, Z);
// beta_k = (z_k+1 * r_k+1) / (z_k * r_k)
gParallel.ForEach(rhs, (j) =>
{
if (converged[j] == false)
{
beta_k[j] = BufferUtil.Dot(Z[j], R[j]) / RdotZ_k[j];
}
});
// can do these in parallel but improvement is minimal
// p_k+1 = z_k+1 + beta_k * p_k
gParallel.ForEach(rhs, (j) =>
{
if (converged[j] == false)
{
for (int i = 0; i < n; ++i)
{
P[j][i] = Z[j][i] + beta_k[j] * P[j][i];
}
}
});
gParallel.ForEach(rhs, (j) =>
{
if (converged[j] == false)
{
RdotZ_k[j] = BufferUtil.Dot(R[j], Z[j]);
}
});
}
//System.Console.WriteLine("{0} iterations", iter);
Iterations = iter;
return(iter < MaxIterations);
}
public bool Solve()
{
Iterations = 0;
int size = B.Length;
// Based on the algorithm in "Matrix Computations" by Golum and Van Loan.
R = new double[size];
P = new double[size];
AP = new double[size];
if (X == null || UseXAsInitialGuess == false)
{
if (X == null)
{
X = new double[size];
}
Array.Clear(X, 0, X.Length);
Array.Copy(B, R, B.Length);
}
else
{
// hopefully is X is a decent initialization...
InitializeR(R);
}
// [RMS] these were inside loop but they are constant!
double norm = BufferUtil.Dot(B, B);
double root1 = Math.Sqrt(norm);
// The first iteration.
double rho0 = BufferUtil.Dot(R, R);
// [RMS] If we were initialized w/ constraints already satisfied,
// then we are done! (happens for example in mesh deformations)
if (rho0 < MathUtil.ZeroTolerance * root1)
{
return(true);
}
Array.Copy(R, P, R.Length);
MultiplyF(P, AP);
double alpha = rho0 / BufferUtil.Dot(P, AP);
BufferUtil.MultiplyAdd(X, alpha, P);
BufferUtil.MultiplyAdd(R, -alpha, AP);
double rho1 = BufferUtil.Dot(R, R);
// The remaining iterations.
int iter;
for (iter = 1; iter < MaxIterations; ++iter)
{
double root0 = Math.Sqrt(rho1);
if (root0 <= MathUtil.ZeroTolerance * root1)
{
break;
}
double beta = rho1 / rho0;
UpdateP(P, beta, R);
MultiplyF(P, AP);
alpha = rho1 / BufferUtil.Dot(P, AP);
// can compute these two steps simultaneously
double RdotR = 0;
gParallel.Evaluate(
() => { BufferUtil.MultiplyAdd(X, alpha, P); },
() => { RdotR = BufferUtil.MultiplyAdd_GetSqrSum(R, -alpha, AP); }
);
rho0 = rho1;
rho1 = RdotR; // BufferUtil.Dot(R, R);
}
//System.Console.WriteLine("{0} iterations", iter);
Iterations = iter;
return(iter < MaxIterations);
}
/// <summary>
/// standard CG solve
/// </summary>
public bool Solve()
{
Iterations = 0;
if (B == null || MultiplyF == null)
{
throw new Exception("SparseSymmetricCGMultipleRHS.Solve(): Must set B and MultiplyF!");
}
int NRHS = B.Length;
if (NRHS == 0)
{
throw new Exception("SparseSymmetricCGMultipleRHS.Solve(): Need at least one RHS vector in B");
}
int size = B[0].Length;
// Based on the algorithm in "Matrix Computations" by Golum and Van Loan.
R = BufferUtil.AllocNxM(NRHS, size);
P = BufferUtil.AllocNxM(NRHS, size);
W = BufferUtil.AllocNxM(NRHS, size);
if (X == null || UseXAsInitialGuess == false)
{
if (X == null)
{
X = BufferUtil.AllocNxM(NRHS, size);
}
for (int j = 0; j < NRHS; ++j)
{
Array.Clear(X[j], 0, size);
Array.Copy(B[j], R[j], size);
}
}
else
{
// hopefully is X is a decent initialization...
InitializeR(R);
}
// [RMS] these were inside loop but they are constant!
double[] norm = new double[NRHS];
for (int j = 0; j < NRHS; ++j)
{
norm[j] = BufferUtil.Dot(B[j], B[j]);
}
double[] root1 = new double[NRHS];
for (int j = 0; j < NRHS; ++j)
{
root1[j] = Math.Sqrt(norm[j]);
}
// The first iteration.
double[] rho0 = new double[NRHS];
for (int j = 0; j < NRHS; ++j)
{
rho0[j] = BufferUtil.Dot(R[j], R[j]);
}
// [RMS] If we were initialized w/ constraints already satisfied,
// then we are done! (happens for example in mesh deformations)
bool[] converged = new bool[NRHS];
int nconverged = 0;
for (int j = 0; j < NRHS; ++j)
{
converged[j] = rho0[j] < (ConvergeTolerance * root1[j]);
if (converged[j])
{
nconverged++;
}
}
if (nconverged == NRHS)
{
return(true);
}
for (int j = 0; j < NRHS; ++j)
{
Array.Copy(R[j], P[j], size);
}
MultiplyF(P, W);
double[] alpha = new double[NRHS];
for (int j = 0; j < NRHS; ++j)
{
alpha[j] = rho0[j] / BufferUtil.Dot(P[j], W[j]);
}
for (int j = 0; j < NRHS; ++j)
{
BufferUtil.MultiplyAdd(X[j], alpha[j], P[j]);
}
for (int j = 0; j < NRHS; ++j)
{
BufferUtil.MultiplyAdd(R[j], -alpha[j], W[j]);
}
double[] rho1 = new double[NRHS];
for (int j = 0; j < NRHS; ++j)
{
rho1[j] = BufferUtil.Dot(R[j], R[j]);
}
double[] beta = new double[NRHS];
var rhs = Interval1i.Range(NRHS);
// The remaining iterations.
int iter;
for (iter = 1; iter < MaxIterations; ++iter)
{
bool done = true;
for (int j = 0; j < NRHS; ++j)
{
if (converged[j] == false)
{
double root0 = Math.Sqrt(rho1[j]);
if (root0 <= ConvergeTolerance * root1[j])
{
converged[j] = true;
}
}
if (converged[j] == false)
{
done = false;
}
}
if (done)
{
break;
}
for (int j = 0; j < NRHS; ++j)
{
beta[j] = rho1[j] / rho0[j];
}
UpdateP(P, beta, R, converged);
MultiplyF(P, W);
gParallel.ForEach(rhs, (j) =>
{
if (converged[j] == false)
{
alpha[j] = rho1[j] / BufferUtil.Dot(P[j], W[j]);
}
});
// can do all these in parallel, but improvement is minimal
gParallel.ForEach(rhs, (j) =>
{
if (converged[j] == false)
{
BufferUtil.MultiplyAdd(X[j], alpha[j], P[j]);
}
});
gParallel.ForEach(rhs, (j) =>
{
if (converged[j] == false)
{
rho0[j] = rho1[j];
rho1[j] = BufferUtil.MultiplyAdd_GetSqrSum(R[j], -alpha[j], W[j]);
}
});
}
//System.Console.WriteLine("{0} iterations", iter);
Iterations = iter;
return(iter < MaxIterations);
}
public bool SolvePreconditioned()
{
Iterations = 0;
int n = B.Length;
R = new double[n];
P = new double[n];
AP = new double[n];
Z = new double[n];
if (X == null || UseXAsInitialGuess == false)
{
if (X == null)
{
X = new double[n];
}
Array.Clear(X, 0, X.Length);
Array.Copy(B, R, B.Length);
}
else
{
// hopefully is X is a decent initialization...
InitializeR(R);
}
// [RMS] for convergence test?
double norm = BufferUtil.Dot(B, B);
double root1 = Math.Sqrt(norm);
// r_0 = b - A*x_0
MultiplyF(X, R);
for (int i = 0; i < n; ++i)
{
R[i] = B[i] - R[i];
}
// z0 = M_inverse * r_0
PreconditionMultiplyF(R, Z);
// p0 = z0
Array.Copy(Z, P, n);
double RdotZ_k = BufferUtil.Dot(R, Z);
int iter = 0;
while (iter++ < MaxIterations)
{
// convergence test
double root0 = Math.Sqrt(RdotZ_k);
if (root0 <= MathUtil.ZeroTolerance * root1)
{
break;
}
MultiplyF(P, AP);
double alpha_k = RdotZ_k / BufferUtil.Dot(P, AP);
gParallel.Evaluate(
// x_k+1 = x_k + alpha_k * p_k
() => { BufferUtil.MultiplyAdd(X, alpha_k, P); },
// r_k+1 = r_k - alpha_k * A * p_k
() => { BufferUtil.MultiplyAdd(R, -alpha_k, AP); }
);
// z_k+1 = M_inverse * r_k+1
PreconditionMultiplyF(R, Z);
// beta_k = (z_k+1 * r_k+1) / (z_k * r_k)
double beta_k = BufferUtil.Dot(Z, R) / RdotZ_k;
gParallel.Evaluate(
// p_k+1 = z_k+1 + beta_k * p_k
() =>
{
for (int i = 0; i < n; ++i)
{
P[i] = Z[i] + beta_k * P[i];
}
},
() => { RdotZ_k = BufferUtil.Dot(R, Z); }
);
}
//System.Console.WriteLine("{0} iterations", iter);
Iterations = iter;
return(iter < MaxIterations);
}
/// <summary>
/// Find the set of boundary EdgeLoops. Note that if we encounter topological
/// issues, we will throw MeshBoundaryLoopsException w/ more info (if possible)
/// </summary>
public bool Compute()
{
// This algorithm assumes that triangles are oriented consistently,
// so closed boundary-loop can be followed by walking edges in-order
Loops = new List <EdgeLoop>();
Spans = new List <EdgeSpan>();
int NE = Mesh.MaxEdgeID;
// Temporary memory used to indicate when we have "used" an edge.
BitArray used_edge = new BitArray(NE);
used_edge.SetAll(false);
// current loop is stored here, cleared after each loop extracted
List <int> loop_edges = new List <int>(); // [RMS] not sure we need this...
List <int> loop_verts = new List <int>();
List <int> bowties = new List <int>();
// Temp buffer for reading back all boundary edges of a vertex.
// probably always small but in pathological cases it could be large...
int[] all_e = new int[16];
// [TODO] might make sense to precompute some things here, like num_be for each bdry vtx?
// process all edges of mesh
for (int eid = 0; eid < NE; ++eid)
{
if (!Mesh.IsEdge(eid))
{
continue;
}
if (used_edge[eid] == true)
{
continue;
}
if (Mesh.IsBoundaryEdge(eid) == false)
{
continue;
}
if (EdgeFilterF != null && EdgeFilterF(eid) == false)
{
used_edge[eid] = true;
continue;
}
// ok this is start of a boundary chain
int eStart = eid;
used_edge[eStart] = true;
loop_edges.Add(eStart);
int eCur = eid;
// follow the chain in order of oriented edges
bool bClosed = false;
bool bIsOpenSpan = false;
while (!bClosed)
{
Index2i ev = Mesh.GetOrientedBoundaryEdgeV(eCur);
int cure_a = ev.a, cure_b = ev.b;
if (bIsOpenSpan)
{
cure_a = ev.b; cure_b = ev.a;
}
else
{
loop_verts.Add(cure_a);
}
int e0 = -1, e1 = 1;
int bdry_nbrs = Mesh.VtxBoundaryEdges(cure_b, ref e0, ref e1);
// have to filter this list, if we are filtering. this is ugly.
if (EdgeFilterF != null)
{
if (bdry_nbrs > 2)
{
if (bdry_nbrs >= all_e.Length)
{
all_e = new int[bdry_nbrs];
}
// we may repreat this below...irritating...
int num_be = Mesh.VtxAllBoundaryEdges(cure_b, all_e);
num_be = BufferUtil.CountValid(all_e, EdgeFilterF, num_be);
}
else
{
if (EdgeFilterF(e0) == false)
{
bdry_nbrs--;
}
if (EdgeFilterF(e1) == false)
{
bdry_nbrs--;
}
}
}
if (bdry_nbrs < 2) // hit an 'endpoint' vertex (should only happen when Filter is on...)
{
if (SpanBehavior == SpanBehaviors.ThrowException)
{
throw new MeshBoundaryLoopsException("MeshBoundaryLoops.Compute: found open span at vertex " + cure_b)
{
UnclosedLoop = true
}
}
;
if (bIsOpenSpan)
{
bClosed = true;
continue;
}
else
{
bIsOpenSpan = true; // begin open span
eCur = loop_edges[0]; // restart at other end of loop
loop_edges.Reverse(); // do this so we can push to front
continue;
}
}
int eNext = -1;
if (bdry_nbrs > 2)
{
// found "bowtie" vertex...things just got complicated!
if (cure_b == loop_verts[0])
{
// The "end" of the current edge is the same as the start vertex.
// This means we can close the loop here. Might as well!
eNext = -2; // sentinel value used below
}
else
{
// try to find an unused outgoing edge that is oriented properly.
// This could create sub-loops, we will handle those later
if (bdry_nbrs >= all_e.Length)
{
all_e = new int[2 * bdry_nbrs];
}
int num_be = Mesh.VtxAllBoundaryEdges(cure_b, all_e);
Debug.Assert(num_be == bdry_nbrs);
if (EdgeFilterF != null)
{
num_be = BufferUtil.FilterInPlace(all_e, EdgeFilterF, num_be);
}
// Try to pick the best "turn left" vertex.
eNext = find_left_turn_edge(eCur, cure_b, all_e, num_be, used_edge);
if (eNext == -1)
{
if (FailureBehavior == FailureBehaviors.ThrowException || SpanBehavior == SpanBehaviors.ThrowException)
{
throw new MeshBoundaryLoopsException("MeshBoundaryLoops.Compute: cannot find valid outgoing edge at bowtie vertex " + cure_b)
{
BowtieFailure = true
}
}
;
// ok, we are stuck. all we can do now is terminate this loop and keep it as a span
if (bIsOpenSpan)
{
bClosed = true;
}
else
{
bIsOpenSpan = true;
bClosed = true;
}
continue;
}
}
if (bowties.Contains(cure_b) == false)
{
bowties.Add(cure_b);
}
}
else
{
// walk forward to next available edge
Debug.Assert(e0 == eCur || e1 == eCur);
eNext = (e0 == eCur) ? e1 : e0;
}
if (eNext == -2)
{
// found a bowtie vert that is the same as start-of-loop, so we
// are just closing it off explicitly
bClosed = true;
}
else if (eNext == eStart)
{
// found edge at start of loop, so loop is done.
bClosed = true;
}
else if (used_edge[eNext] != false)
{
// disaster case - the next edge is already used, but it is not the start of our loop
// All we can do is convert to open span and terminate
if (FailureBehavior == FailureBehaviors.ThrowException || SpanBehavior == SpanBehaviors.ThrowException)
{
throw new MeshBoundaryLoopsException("MeshBoundaryLoops.Compute: encountered repeated edge " + eNext)
{
RepeatedEdge = true
}
}
;
bIsOpenSpan = true;
bClosed = true;
}
else
{
// push onto accumulated list
Debug.Assert(used_edge[eNext] == false);
loop_edges.Add(eNext);
used_edge[eNext] = true;
eCur = eNext;
}
}
if (bIsOpenSpan)
{
SawOpenSpans = true;
if (SpanBehavior == SpanBehaviors.Compute)
{
loop_edges.Reverse(); // orient properly
EdgeSpan span = EdgeSpan.FromEdges(Mesh, loop_edges);
Spans.Add(span);
}
}
else if (bowties.Count > 0)
{
// if we saw a bowtie vertex, we might need to break up this loop,
// so call extract_subloops
List <EdgeLoop> subloops = extract_subloops(loop_verts, loop_edges, bowties);
for (int i = 0; i < subloops.Count; ++i)
{
Loops.Add(subloops[i]);
}
}
else
{
// clean simple loop, convert to EdgeLoop instance
EdgeLoop loop = new EdgeLoop(Mesh);
loop.Vertices = loop_verts.ToArray();
loop.Edges = loop_edges.ToArray();
Loops.Add(loop);
}
// reset these lists
loop_edges.Clear();
loop_verts.Clear();
bowties.Clear();
}
return(true);
}
// [TODO] cache this in a dictionary? we will not need very many, but we will
// need each multiple times!
Vector3d get_vtx_normal(int vid)
{
Vector3d n = Vector3d.Zero;
foreach (int ti in Mesh.VtxTrianglesItr(vid))
{
n += Mesh.GetTriNormal(ti);
}
n.Normalize();
return(n);
}
// ok, bdry_edges[0...bdry_edges_count] contains the boundary edges coming out of bowtie_v.
// We want to pick the best one to continue the loop that came in to bowtie_v on incoming_e.
// If the loops are all sane, then we will get the smallest loops by "turning left" at bowtie_v.
// So, we compute the tangent plane at bowtie_v, and then the signed angle for each
// viable edge in this plane.
//
// [TODO] handle degenerate edges. what do we do then? Currently will only chose
// degenerate edge if there are no other options (I think...)
int find_left_turn_edge(int incoming_e, int bowtie_v, int[] bdry_edges, int bdry_edges_count, BitArray used_edges)
{
// compute normal and edge [a,bowtie]
Vector3d n = get_vtx_normal(bowtie_v);
int other_v = Mesh.edge_other_v(incoming_e, bowtie_v);
Vector3d ab = Mesh.GetVertex(bowtie_v) - Mesh.GetVertex(other_v);
// our winner
int best_e = -1;
double best_angle = double.MaxValue;
for (int i = 0; i < bdry_edges_count; ++i)
{
int bdry_eid = bdry_edges[i];
if (used_edges[bdry_eid] == true)
{
continue; // this edge is already used
}
Index2i bdry_ev = Mesh.GetOrientedBoundaryEdgeV(bdry_eid);
if (bdry_ev.a != bowtie_v)
{
continue; // have to be able to chain to end of current edge, orientation-wise
}
// compute projected angle
Vector3d bc = Mesh.GetVertex(bdry_ev.b) - Mesh.GetVertex(bowtie_v);
float fAngleS = MathUtil.PlaneAngleSignedD((Vector3f)ab, (Vector3f)bc, (Vector3f)n);
// turn left!
if (best_angle == double.MaxValue || fAngleS < best_angle)
{
best_angle = fAngleS;
best_e = bdry_eid;
}
}
// [RMS] w/ bowtie vertices and open spans, this does happen
//Debug.Assert(best_e != -1);
return(best_e);
}
// This is called when loopV contains one or more "bowtie" vertices.
// These vertices *might* be duplicated in loopV (but not necessarily)
// If they are, we have to break loopV into subloops that don't contain duplicates.
//
// The list bowties contains all the possible duplicates
// (all v in bowties occur in loopV at least once)
//
// Currently loopE is not used, and the returned EdgeLoop objects do not have their Edges
// arrays initialized. Perhaps to improve in future.
List <EdgeLoop> extract_subloops(List <int> loopV, List <int> loopE, List <int> bowties)
{
List <EdgeLoop> subs = new List <EdgeLoop>();
// figure out which bowties we saw are actually duplicated in loopV
List <int> dupes = new List <int>();
foreach (int bv in bowties)
{
if (count_in_list(loopV, bv) > 1)
{
dupes.Add(bv);
}
}
// we might not actually have any duplicates, if we got luck. Early out in that case
if (dupes.Count == 0)
{
subs.Add(new EdgeLoop(Mesh)
{
Vertices = loopV.ToArray(), Edges = loopE.ToArray(), BowtieVertices = bowties.ToArray()
});
return(subs);
}
// This loop extracts subloops until we have dealt with all the
// duplicate vertices in loopV
while (dupes.Count > 0)
{
// Find shortest "simple" loop, ie a loop from a bowtie to itself that
// does not contain any other bowties. This is an independent loop.
// We're doing a lot of extra work here if we only have one element in dupes...
int bi = 0, bv = 0;
int start_i = -1, end_i = -1;
int bv_shortest = -1; int shortest = int.MaxValue;
for ( ; bi < dupes.Count; ++bi)
{
bv = dupes[bi];
if (is_simple_bowtie_loop(loopV, dupes, bv, out start_i, out end_i))
{
int len = count_span(loopV, start_i, end_i);
if (len < shortest)
{
bv_shortest = bv;
shortest = len;
}
}
}
if (bv_shortest == -1)
{
throw new MeshBoundaryLoopsException("MeshBoundaryLoops.Compute: Cannot find a valid simple loop");
}
if (bv != bv_shortest)
{
bv = bv_shortest;
// running again just to get start_i and end_i...
is_simple_bowtie_loop(loopV, dupes, bv, out start_i, out end_i);
}
Debug.Assert(loopV[start_i] == bv && loopV[end_i] == bv);
EdgeLoop loop = new EdgeLoop(Mesh);
loop.Vertices = extract_span(loopV, start_i, end_i, true);
loop.Edges = EdgeLoop.VertexLoopToEdgeLoop(Mesh, loop.Vertices);
loop.BowtieVertices = bowties.ToArray();
subs.Add(loop);
// If there are no more duplicates of this bowtie, we can treat
// it like a regular vertex now
if (count_in_list(loopV, bv) < 2)
{
dupes.Remove(bv);
}
}
// Should have one loop left that contains duplicates.
// Extract this as a separate loop
int nLeft = 0;
for (int i = 0; i < loopV.Count; ++i)
{
if (loopV[i] != -1)
{
nLeft++;
}
}
if (nLeft > 0)
{
EdgeLoop loop = new EdgeLoop(Mesh);
loop.Vertices = new int[nLeft];
int vi = 0;
for (int i = 0; i < loopV.Count; ++i)
{
if (loopV[i] != -1)
{
loop.Vertices[vi++] = loopV[i];
}
}
loop.Edges = EdgeLoop.VertexLoopToEdgeLoop(Mesh, loop.Vertices);
loop.BowtieVertices = bowties.ToArray();
subs.Add(loop);
}
return(subs);
}
/*
* In all the functions below, the list loopV is assumed to possibly
* contain "removed" vertices indicated by -1. These are ignored.
*/
// Check if the loop from bowtieV to bowtieV inside loopV contains any other bowtie verts.
// Also returns start and end indices in loopV of "clean" loop
// Note that start may be < end, if the "clean" loop wraps around the end
bool is_simple_bowtie_loop(List <int> loopV, List <int> bowties, int bowtieV, out int start_i, out int end_i)
{
// find two indices of bowtie vert
start_i = find_index(loopV, 0, bowtieV);
end_i = find_index(loopV, start_i + 1, bowtieV);
if (is_simple_path(loopV, bowties, bowtieV, start_i, end_i))
{
return(true);
}
else if (is_simple_path(loopV, bowties, bowtieV, end_i, start_i))
{
int tmp = start_i; start_i = end_i; end_i = tmp;
return(true);
}
else
{
return(false); // not a simple bowtie loop!
}
}
// check if forward path from loopV[i1] to loopV[i2] contains any bowtie verts other than bowtieV
bool is_simple_path(List <int> loopV, List <int> bowties, int bowtieV, int i1, int i2)
{
int N = loopV.Count;
for (int i = i1; i != i2; i = (i + 1) % N)
{
int vi = loopV[i];
if (vi == -1)
{
continue; // skip removed vertices
}
if (vi != bowtieV && bowties.Contains(vi))
{
return(false);
}
}
return(true);
}
// Read out the span from loop[i0] to loop [i1-1] into an array.
// If bMarkInvalid, then these values are set to -1 in loop
int[] extract_span(List <int> loop, int i0, int i1, bool bMarkInvalid)
{
int num = count_span(loop, i0, i1);
int[] a = new int[num];
int ai = 0;
int N = loop.Count;
for (int i = i0; i != i1; i = (i + 1) % N)
{
if (loop[i] != -1)
{
a[ai++] = loop[i];
if (bMarkInvalid)
{
loop[i] = -1;
}
}
}
return(a);
}
// count number of valid vertices in l between loop[i0] and loop[i1-1]
int count_span(List <int> l, int i0, int i1)
{
int c = 0;
int N = l.Count;
for (int i = i0; i != i1; i = (i + 1) % N)
{
if (l[i] != -1)
{
c++;
}
}
return(c);
}
// find the index of item in loop, starting at start index
int find_index(List <int> loop, int start, int item)
{
for (int i = start; i < loop.Count; ++i)
{
if (loop[i] == item)
{
return(i);
}
}
return(-1);
}
// count number of times item appears in loop
int count_in_list(List <int> loop, int item)
{
int c = 0;
for (int i = 0; i < loop.Count; ++i)
{
if (loop[i] == item)
{
c++;
}
}
return(c);
}
}
}
/// <summary>
/// Find the set of boundary EdgeLoops. Note that if we encounter topological
/// issues, we will throw MeshBoundaryLoopsException w/ more info (if possible)
/// </summary>
public bool Compute()
{
// This algorithm assumes that triangles are oriented consistently,
// so closed boundary-loop can be followed by walking edges in-order
Loops = new List <EdgeLoop>();
Spans = new List <EdgeSpan>();
// early-out if we don't actually have boundaries
if (Mesh.CachedIsClosed)
{
return(true);
}
int NE = Mesh.MaxEdgeID;
// Temporary memory used to indicate when we have "used" an edge.
var used_edge = new BitArray(NE);
used_edge.SetAll(false);
// current loop is stored here, cleared after each loop extracted
var loop_edges = new List <int>(); // [RMS] not sure we need this...
var loop_verts = new List <int>();
var bowties = new List <int>();
// Temp buffer for reading back all boundary edges of a vertex.
// probably always small but in pathological cases it could be large...
int[] all_e = new int[16];
// [TODO] might make sense to precompute some things here, like num_be for each bdry vtx?
// process all edges of mesh
for (int eid = 0; eid < NE; ++eid)
{
if (!Mesh.IsEdge(eid))
{
continue;
}
if (used_edge[eid] == true)
{
continue;
}
if (Mesh.IsBoundaryEdge(eid) == false)
{
continue;
}
if (EdgeFilterF != null && EdgeFilterF(eid) == false)
{
used_edge[eid] = true;
continue;
}
// ok this is start of a boundary chain
int eStart = eid;
used_edge[eStart] = true;
loop_edges.Add(eStart);
int eCur = eid;
// follow the chain in order of oriented edges
bool bClosed = false;
bool bIsOpenSpan = false;
while (!bClosed)
{
Index2i ev = Mesh.GetOrientedBoundaryEdgeV(eCur);
int cure_a = ev.a, cure_b = ev.b;
if (bIsOpenSpan)
{
cure_a = ev.b; cure_b = ev.a;
}
else
{
loop_verts.Add(cure_a);
}
int e0 = -1, e1 = 1;
int bdry_nbrs = Mesh.VtxBoundaryEdges(cure_b, ref e0, ref e1);
// have to filter this list, if we are filtering. this is ugly.
if (EdgeFilterF != null)
{
if (bdry_nbrs > 2)
{
if (bdry_nbrs >= all_e.Length)
{
all_e = new int[bdry_nbrs];
}
// we may repreat this below...irritating...
int num_be = Mesh.VtxAllBoundaryEdges(cure_b, all_e);
num_be = BufferUtil.CountValid(all_e, EdgeFilterF, num_be);
}
else
{
if (EdgeFilterF(e0) == false)
{
bdry_nbrs--;
}
if (EdgeFilterF(e1) == false)
{
bdry_nbrs--;
}
}
}
if (bdry_nbrs < 2)
{ // hit an 'endpoint' vertex (should only happen when Filter is on...)
if (SpanBehavior == SpanBehaviors.ThrowException)
{
throw new MeshBoundaryLoopsException("MeshBoundaryLoops.Compute: found open span at vertex " + cure_b)
{
UnclosedLoop = true
};
}
if (bIsOpenSpan)
{
bClosed = true;
continue;
}
else
{
bIsOpenSpan = true; // begin open span
eCur = loop_edges[0]; // restart at other end of loop
loop_edges.Reverse(); // do this so we can push to front
continue;
}
}
int eNext = -1;
if (bdry_nbrs > 2)
{
// found "bowtie" vertex...things just got complicated!
if (cure_b == loop_verts[0])
{
// The "end" of the current edge is the same as the start vertex.
// This means we can close the loop here. Might as well!
eNext = -2; // sentinel value used below
}
else
{
// try to find an unused outgoing edge that is oriented properly.
// This could create sub-loops, we will handle those later
if (bdry_nbrs >= all_e.Length)
{
all_e = new int[2 * bdry_nbrs];
}
int num_be = Mesh.VtxAllBoundaryEdges(cure_b, all_e);
Debug.Assert(num_be == bdry_nbrs);
if (EdgeFilterF != null)
{
num_be = BufferUtil.FilterInPlace(all_e, EdgeFilterF, num_be);
}
// Try to pick the best "turn left" vertex.
eNext = find_left_turn_edge(eCur, cure_b, all_e, num_be, used_edge);
if (eNext == -1)
{
if (FailureBehavior == FailureBehaviors.ThrowException || SpanBehavior == SpanBehaviors.ThrowException)
{
throw new MeshBoundaryLoopsException("MeshBoundaryLoops.Compute: cannot find valid outgoing edge at bowtie vertex " + cure_b)
{
BowtieFailure = true
};
}
// ok, we are stuck. all we can do now is terminate this loop and keep it as a span
if (bIsOpenSpan)
{
bClosed = true;
}
else
{
bIsOpenSpan = true;
bClosed = true;
}
continue;
}
}
if (bowties.Contains(cure_b) == false)
{
bowties.Add(cure_b);
}
}
else
{
// walk forward to next available edge
Debug.Assert(e0 == eCur || e1 == eCur);
eNext = (e0 == eCur) ? e1 : e0;
}
if (eNext == -2)
{
// found a bowtie vert that is the same as start-of-loop, so we
// are just closing it off explicitly
bClosed = true;
}
else if (eNext == eStart)
{
// found edge at start of loop, so loop is done.
bClosed = true;
}
else if (used_edge[eNext] != false)
{
// disaster case - the next edge is already used, but it is not the start of our loop
// All we can do is convert to open span and terminate
if (FailureBehavior == FailureBehaviors.ThrowException || SpanBehavior == SpanBehaviors.ThrowException)
{
throw new MeshBoundaryLoopsException("MeshBoundaryLoops.Compute: encountered repeated edge " + eNext)
{
RepeatedEdge = true
};
}
bIsOpenSpan = true;
bClosed = true;
}
else
{
// push onto accumulated list
Debug.Assert(used_edge[eNext] == false);
loop_edges.Add(eNext);
used_edge[eNext] = true;
eCur = eNext;
}
}
if (bIsOpenSpan)
{
SawOpenSpans = true;
if (SpanBehavior == SpanBehaviors.Compute)
{
loop_edges.Reverse(); // orient properly
var span = EdgeSpan.FromEdges(Mesh, loop_edges);
Spans.Add(span);
}
}
else if (bowties.Count > 0)
{
// if we saw a bowtie vertex, we might need to break up this loop,
// so call extract_subloops
Subloops subloops = extract_subloops(loop_verts, loop_edges, bowties);
foreach (var loop in subloops.Loops)
{
Loops.Add(loop);
}
if (subloops.Spans.Count > 0)
{
FellBackToSpansOnFailure = true;
foreach (var span in subloops.Spans)
{
Spans.Add(span);
}
}
}
else
{
// clean simple loop, convert to EdgeLoop instance
var loop = new EdgeLoop(Mesh);
loop.Vertices = loop_verts.ToArray();
loop.Edges = loop_edges.ToArray();
Loops.Add(loop);
}
// reset these lists
loop_edges.Clear();
loop_verts.Clear();
bowties.Clear();
}
return(true);
}
/// <summary>
/// Similar to the static <see cref="Build()"/> method below, but uses the
/// <see cref="NonManifoldTriBehavior"/> and <see cref="AddTriangleFailBehaviors"/> properties
/// to affect the meshing process and avoids exceptions, preferring feedback in the mesh metadata.
/// </summary>
public DMesh3 AppendMesh <VType, TType, NType>(IEnumerable <VType> Vertices,
IEnumerable <TType> Triangles,
IEnumerable <NType> Normals = null,
IEnumerable <int> TriGroups = null)
{
// build outcomes are stored in the metadata to keep the function signature like the static method Build
//
int iAppendTriangleIssues = 0;
bool addNormals = Normals != null;
string NormalsMetadata = "None";
bool addTriGroups = TriGroups != null;
string TriGroupsMetadata = "None";
// data preparation
Vector3d[] v = BufferUtil.ToVector3d(Vertices);
Vector3f[] n = null;
if (addNormals)
{
n = BufferUtil.ToVector3f(Normals);
if (n.Length != v.Length)
{
NormalsMetadata = "Error: incorrect number of normals provided, ignored.";
addNormals = false;
}
}
Index3i[] t = BufferUtil.ToIndex3i(Triangles);
List <int> groups = null;
if (addTriGroups)
{
groups = new List <int>(TriGroups);
if (groups.Count != t.Length)
{
TriGroupsMetadata = "Error: incorrect number of groups provided, ignored.";
addTriGroups = false;
}
}
DMesh3 mesh = new DMesh3(addNormals, false, false, addTriGroups);
AppendNewMesh(mesh);
// vertices
for (int i = 0; i < v.Length; ++i)
{
mesh.AppendVertex(v[i]);
}
// normals
if (addNormals)
{
for (int i = 0; i < n.Length; ++i)
{
mesh.SetVertexNormal(i, n[i]);
}
NormalsMetadata = "Ok";
}
// triangles
for (int i = 0; i < t.Length; ++i)
{
var last = AppendTriangle(t[i]);
if (last == DMesh3.InvalidID || last == DMesh3.NonManifoldID)
{
iAppendTriangleIssues++;
}
}
// groups
if (addTriGroups)
{
for (int i = 0; i < t.Length; ++i)
{
mesh.SetTriangleGroup(i, groups[i]);
}
TriGroupsMetadata = "Ok";
}
// adding the metadata
//
mesh.AttachMetadata("AppendTriangleIssues", iAppendTriangleIssues);
mesh.AttachMetadata("Normals", NormalsMetadata);
mesh.AttachMetadata("TriGroups", TriGroupsMetadata);
return(mesh);
}
public bool Solve()
{
int size = B.Length;
// Based on the algorithm in "Matrix Computations" by Golum and Van Loan.
R = new double[size];
P = new double[size];
W = new double[size];
if (X == null || UseXAsInitialGuess == false)
{
if (X == null)
{
X = new double[size];
}
Array.Clear(X, 0, X.Length);
Array.Copy(B, R, B.Length);
}
else
{
// hopefully is X is a decent initialization...
InitializeR(R);
}
// The first iteration.
double rho0 = BufferUtil.Dot(R, R);
Array.Copy(R, P, R.Length);
MultiplyF(P, W);
double alpha = rho0 / BufferUtil.Dot(P, W);
BufferUtil.MultiplyAdd(X, alpha, P);
BufferUtil.MultiplyAdd(R, -alpha, W);
double rho1 = BufferUtil.Dot(R, R);
// [RMS] these were inside loop but they are constant!
double norm = BufferUtil.Dot(B, B);
double root1 = Math.Sqrt(norm);
// The remaining iterations.
int iter;
for (iter = 1; iter < MaxIterations; ++iter)
{
double root0 = Math.Sqrt(rho1);
if (root0 <= MathUtil.ZeroTolerance * root1)
{
break;
}
double beta = rho1 / rho0;
UpdateP(P, beta, R);
MultiplyF(P, W);
alpha = rho1 / BufferUtil.Dot(P, W);
BufferUtil.MultiplyAdd(X, alpha, P);
BufferUtil.MultiplyAdd(R, -alpha, W);
rho0 = rho1;
rho1 = BufferUtil.Dot(R, R);
}
System.Console.WriteLine("{0} iterations", iter);
return(iter < MaxIterations);
}
