/// <summary>
/// processing z-slabs of cells in parallel
/// </summary>
void generate_parallel()
{
hash_lock = new SpinLock();
mesh_lock = new SpinLock();
bParallel = true;
// [TODO] maybe shouldn't alway use Z axis here?
gParallel.ForEach(Interval1i.Range(CellDimensions.z), (zi) => {
GridCell cell = new GridCell();
Vector3d[] vertlist = new Vector3d[12];
for (int yi = 0; yi < CellDimensions.y; ++yi)
{
// compute full cell at x=0, then slide along x row, which saves half of value computes
Vector3i idx = new Vector3i(0, yi, zi);
initialize_cell(cell, ref idx);
polygonize_cell(cell, vertlist);
for (int xi = 1; xi < CellDimensions.x; ++xi)
{
shift_cell_x(cell, xi);
polygonize_cell(cell, vertlist);
}
}
});
bParallel = false;
}
/// <summary>
/// Process indices [iStart,iEnd] *inclusive* by passing sub-intervals [start,end] to blockF.
/// Blocksize is automatically determind unless you specify one.
/// Iterate over [start,end] *inclusive* in each block
/// </summary>
public static void BlockStartEnd(int iStart, int iEnd, Action <int, int> blockF, int iBlockSize = -1, bool bDisableParallel = false)
{
if (iBlockSize == -1)
{
iBlockSize = 100; // seems to work
}
int N = (iEnd - iStart + 1);
int num_blocks = N / iBlockSize;
// process main blocks in parallel
if (bDisableParallel)
{
ForEach_Sequential(Interval1i.Range(num_blocks), (bi) => {
int k = iStart + iBlockSize * bi;
blockF(k, k + iBlockSize - 1);
});
}
else
{
ForEach(Interval1i.Range(num_blocks), (bi) => {
int k = iStart + iBlockSize * bi;
blockF(k, k + iBlockSize - 1);
});
}
// process leftover elements
int remaining = N - (num_blocks * iBlockSize);
if (remaining > 0)
{
int k = iStart + num_blocks * iBlockSize;
blockF(k, k + remaining - 1);
}
}
/// <summary>
/// Construct packed versions of input matrices, and then use sparse row/column dot
/// to compute elements of output matrix. This is faster. But still relatively expensive.
/// </summary>
void multiply_fast(SymmetricSparseMatrix M2in, ref SymmetricSparseMatrix Rin, bool bParallel)
{
int N = Rows;
if (M2in.Rows != N)
{
throw new Exception("SymmetricSparseMatrix.Multiply: matrices have incompatible dimensions");
}
if (Rin == null)
{
Rin = new SymmetricSparseMatrix();
}
SymmetricSparseMatrix R = Rin; // require alias for use in lambda below
PackedSparseMatrix M = new PackedSparseMatrix(this);
M.Sort();
PackedSparseMatrix M2 = new PackedSparseMatrix(M2in, true);
M2.Sort();
// Parallel variant is vastly faster, uses spinlock to control access to R
if (bParallel)
{
// goddamn SpinLock is in .Net 4
//SpinLock spin = new SpinLock();
gParallel.ForEach(Interval1i.Range(N), (r1i) => {
for (int c2i = r1i; c2i < N; c2i++)
{
double v = M.DotRowColumn(r1i, c2i, M2);
if (Math.Abs(v) > MathUtil.ZeroTolerance)
{
//bool taken = false;
//spin.Enter(ref taken);
//Debug.Assert(taken);
//R[r1i, c2i] = v;
//spin.Exit();
lock (R) {
R[r1i, c2i] = v;
}
}
}
});
}
else
{
for (int r1i = 0; r1i < N; r1i++)
{
for (int c2i = r1i; c2i < N; c2i++)
{
double v = M.DotRowColumn(r1i, c2i, M2);
if (Math.Abs(v) > MathUtil.ZeroTolerance)
{
R[r1i, c2i] = v;
}
}
}
}
}
// 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);
}
/// <summary>
/// Evaluate input actions in parallel
/// </summary>
public static void Evaluate(params Action[] funcs)
{
int N = funcs.Length;
gParallel.ForEach(Interval1i.Range(N), (i) => {
funcs[i]();
});
}
public void Sort()
{
gParallel.ForEach(Interval1i.Range(Rows.Length), (i) => {
Array.Sort(Rows[i], (x, y) => { return(x.j.CompareTo(y.j)); });
});
//for ( int i = 0; i < Rows.Length; ++i )
// Array.Sort(Rows[i], (x, y) => { return x.j.CompareTo(y.j); } );
Sorted = true;
}
public void Multiply(DenseMatrix M2, ref DenseMatrix R, bool bParallel = true)
{
int rows1 = N, cols1 = M;
int rows2 = M2.N, cols2 = M2.M;
if (cols1 != rows2)
{
throw new Exception("DenseMatrix.Multiply: matrices have incompatible dimensions");
}
if (R == null)
{
R = new DenseMatrix(Rows, M2.Columns);
}
if (R.Rows != rows1 || R.Columns != cols2)
{
throw new Exception("DenseMatrix.Multiply: Result matrix has incorrect dimensions");
}
if (bParallel)
{
DenseMatrix Rt = R;
gParallel.ForEach(Interval1i.Range(0, rows1), (r1i) =>
{
int ii = r1i * M;
for (int c2i = 0; c2i < cols2; c2i++)
{
double v = 0;
for (int k = 0; k < cols1; ++k)
{
v += d[ii + k] * M2.d[k * M + c2i];
}
Rt[ii + c2i] = v;
}
});
}
else
{
for (int r1i = 0; r1i < rows1; r1i++)
{
int ii = r1i * M;
for (int c2i = 0; c2i < cols2; c2i++)
{
double v = 0;
for (int k = 0; k < cols1; ++k)
{
v += d[ii + k] * M2.d[k * M + c2i];
}
R[ii + c2i] = v;
}
}
}
}
// returns this*this (requires less memory)
public SymmetricSparseMatrix Square(bool bParallel = true)
{
var R = new SymmetricSparseMatrix();
var M = new PackedSparseMatrix(this);
M.Sort();
// Parallel variant is vastly faster, uses spinlock to control access to R
if (bParallel)
{
// goddamn SpinLock is in .Net 4
//SpinLock spin = new SpinLock();
gParallel.ForEach(Interval1i.Range(N), (r1i) =>
{
for (int c2i = r1i; c2i < N; c2i++)
{
double v = M.DotRowColumn(r1i, c2i, M);
if (Math.Abs(v) > MathUtil.ZeroTolerance)
{
//bool taken = false;
//spin.Enter(ref taken);
//Debug.Assert(taken);
//R[r1i, c2i] = v;
//spin.Exit();
lock (R)
{
R[r1i, c2i] = v;
}
}
}
});
}
else
{
for (int r1i = 0; r1i < N; r1i++)
{
for (int c2i = r1i; c2i < N; c2i++)
{
double v = M.DotRowColumn(r1i, c2i, M);
if (Math.Abs(v) > MathUtil.ZeroTolerance)
{
R[r1i, c2i] = v;
}
}
}
}
return(R);
}
public int Dist(Interval1i o)
{
if (b < o.a)
{
return(o.a - b);
}
else if (a > o.b)
{
return(a - o.b);
}
else
{
return(0);
}
}
void UpdateP(double[][] P, double[] beta, double[][] R, bool[] converged)
{
Interval1i rhs = Interval1i.Range(P.Length);
gParallel.ForEach(rhs, (j) => {
if (converged[j] == false)
{
int n = P[j].Length;
for (int i = 0; i < n; ++i)
{
P[j][i] = R[j][i] + beta[j] * P[j][i];
}
}
});
}
public int SquaredDist(Interval1i o)
{
if (b < o.a)
{
return((o.a - b) * (o.a - b));
}
else if (a > o.b)
{
return((a - o.b) * (a - o.b));
}
else
{
return(0);
}
}
// for each From[i], find closest point on TargetSurface
void update_to()
{
double max_dist = double.MaxValue;
bool bNormals = (UseNormals && Source.HasVertexNormals);
var range = Interval1i.Range(From.Length);
gParallel.ForEach(range, (vi) =>
{
int tid = TargetSurface.FindNearestTriangle(From[vi], max_dist);
if (tid == DMesh3.InvalidID)
{
Weights[vi] = 0;
return;
}
DistPoint3Triangle3 d = MeshQueries.TriangleDistance(TargetSurface.Mesh, tid, From[vi]);
if (d.DistanceSquared > MaxAllowableDistance * MaxAllowableDistance)
{
Weights[vi] = 0;
return;
}
To[vi] = d.TriangleClosest;
Weights[vi] = 1.0f;
if (bNormals)
{
Vector3d fromN = Rotation * Source.GetVertexNormal(vi);
Vector3d toN = TargetSurface.Mesh.GetTriNormal(tid);
double fDot = fromN.Dot(toN);
Debug.Assert(MathUtil.IsFinite(fDot));
if (fDot < 0)
{
Weights[vi] = 0;
}
else
{
Weights[vi] += Math.Sqrt(fDot);
}
}
});
}
/// <summary>
/// Calculate the two most extreme vertices along an axis, with optional transform
/// </summary>
public static Interval1i ExtremeVertices(DMesh3 mesh, Vector3d axis, Func <Vector3d, Vector3d> TransformF = null)
{
Interval1d extent = Interval1d.Empty;
Interval1i extreme = new Interval1i(DMesh3.InvalidID, DMesh3.InvalidID);
if (TransformF == null)
{
foreach (int vid in mesh.VertexIndices())
{
double t = mesh.GetVertex(vid).Dot(ref axis);
if (t < extent.a)
{
extent.a = t;
extreme.a = vid;
}
else if (t > extent.b)
{
extent.b = t;
extreme.b = vid;
}
}
}
else
{
foreach (int vid in mesh.VertexIndices())
{
double t = TransformF(mesh.GetVertex(vid)).Dot(ref axis);
if (t < extent.a)
{
extent.a = t;
extreme.a = vid;
}
else if (t > extent.b)
{
extent.b = t;
extreme.b = vid;
}
}
}
return(extreme);
}
/// <summary>
/// For row r, find interval that nonzeros lie in
/// </summary>
public Interval1i NonZerosRange(int r)
{
nonzero[] Row = Rows[r];
if (Row.Length == 0)
{
return(Interval1i.Empty);
}
if (Sorted == false)
{
Interval1i range = Interval1i.Empty;
for (int i = 0; i < Row.Length; ++i)
{
range.Contain(Row[i].j);
}
return(range);
}
else
{
return(new Interval1i(Row[0].j, Row[Row.Length - 1].j));
}
}
// TODO: parallel version, cache tri normals
void Compute_FaceAvg_AreaWeighted()
{
int NV = Mesh.MaxVertexID;
if (NV != Normals.size)
{
Normals.resize(NV);
}
for (int i = 0; i < NV; ++i)
{
Normals[i] = Vector3d.Zero;
}
int NT = Mesh.MaxTriangleID;
for (int ti = 0; ti < NT; ++ti)
{
if (Mesh.IsTriangle(ti) == false)
{
continue;
}
Index3i tri = Mesh.GetTriangle(ti);
Vector3d va = Mesh.GetVertex(tri.a);
Vector3d vb = Mesh.GetVertex(tri.b);
Vector3d vc = Mesh.GetVertex(tri.c);
Vector3d N = MathUtil.Normal(va, vb, vc);
double a = MathUtil.Area(va, vb, vc);
Normals[tri.a] += a * N;
Normals[tri.b] += a * N;
Normals[tri.c] += a * N;
}
gParallel.ForEach(Interval1i.Range(NV), (vi) => {
if (Normals[vi].LengthSquared > MathUtil.ZeroTolerancef)
{
Normals[vi] = Normals[vi].Normalized;
}
});
}
public virtual bool Smooth()
{
int NV = Loop.Vertices.Length;
double a = MathUtil.Clamp(Alpha, 0, 1);
double num_rounds = MathUtil.Clamp(Rounds, 0, 10000);
for (int round = 0; round < num_rounds; ++round)
{
// compute
gParallel.ForEach(Interval1i.Range(NV), (i) =>
{
int vid = Loop.Vertices[(i + 1) % NV];
Vector3d prev = Mesh.GetVertex(Loop.Vertices[i]);
Vector3d cur = Mesh.GetVertex(vid);
Vector3d next = Mesh.GetVertex(Loop.Vertices[(i + 2) % NV]);
Vector3d centroid = (prev + next) * 0.5;
SmoothedPostions[i] = (1 - a) * cur + (a) * centroid;
});
// bake
gParallel.ForEach(Interval1i.Range(NV), (i) =>
{
int vid = Loop.Vertices[(i + 1) % NV];
Vector3d pos = SmoothedPostions[i];
if (ProjectF != null)
{
pos = ProjectF(pos, vid);
}
Mesh.SetVertex(vid, pos);
});
}
return(true);
}
// TODO: parallel version, cache tri normals
void Compute_FaceAvg_AreaWeighted()
{
int NV = Mesh.MaxVertexID;
if (NV != Normals.size)
{
Normals.resize(NV);
}
for (int i = 0; i < NV; ++i)
{
Normals[i] = Vector3d.Zero;
}
SpinLock Normals_lock = new SpinLock();
gParallel.ForEach(Mesh.TriangleIndices(), (ti) => {
Index3i tri = Mesh.GetTriangle(ti);
Vector3d va = Mesh.GetVertex(tri.a);
Vector3d vb = Mesh.GetVertex(tri.b);
Vector3d vc = Mesh.GetVertex(tri.c);
Vector3d N = MathUtil.Normal(ref va, ref vb, ref vc);
double a = MathUtil.Area(ref va, ref vb, ref vc);
bool taken = false;
Normals_lock.Enter(ref taken);
Normals[tri.a] += a * N;
Normals[tri.b] += a * N;
Normals[tri.c] += a * N;
Normals_lock.Exit();
});
gParallel.ForEach(Interval1i.Range(NV), (vi) => {
if (Normals[vi].LengthSquared > MathUtil.ZeroTolerancef)
{
Normals[vi] = Normals[vi].Normalized;
}
});
}
// Result must be as large as Mesh.MaxVertexID
public bool SolveMultipleCG(Vector3d[] Result)
{
if (WeightsM == null)
{
Initialize(); // force initialize...
}
UpdateForSolve();
// use initial positions as initial solution.
Array.Copy(Px, Sx, N);
Array.Copy(Py, Sy, N);
Array.Copy(Pz, Sz, N);
Action <double[], double[]> CombinedMultiply = (X, B) => {
//PackedM.Multiply(X, B);
PackedM.Multiply_Parallel(X, B);
for (int i = 0; i < N; ++i)
{
B[i] += WeightsM[i, i] * X[i];
}
};
List <SparseSymmetricCG> Solvers = new List <SparseSymmetricCG>();
if (SolveX)
{
Solvers.Add(new SparseSymmetricCG()
{
B = Bx, X = Sx,
MultiplyF = CombinedMultiply, PreconditionMultiplyF = Preconditioner.Multiply,
UseXAsInitialGuess = true
});
}
if (SolveY)
{
Solvers.Add(new SparseSymmetricCG()
{
B = By, X = Sy,
MultiplyF = CombinedMultiply, PreconditionMultiplyF = Preconditioner.Multiply,
UseXAsInitialGuess = true
});
}
if (SolveZ)
{
Solvers.Add(new SparseSymmetricCG()
{
B = Bz, X = Sz,
MultiplyF = CombinedMultiply, PreconditionMultiplyF = Preconditioner.Multiply,
UseXAsInitialGuess = true
});
}
bool[] ok = new bool[Solvers.Count];
gParallel.ForEach(Interval1i.Range(Solvers.Count), (i) => {
ok[i] = Solvers[i].Solve();
// preconditioned solve is slower =\
//ok[i] = solvers[i].SolvePreconditioned();
});
ConvergeFailed = false;
foreach (bool b in ok)
{
if (b == false)
{
ConvergeFailed = true;
}
}
for (int i = 0; i < N; ++i)
{
int vid = ToCurveV[i];
Result[vid] = new Vector3d(Sx[i], Sy[i], Sz[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);
}
public virtual bool Apply()
{
HashSet <int> OnCurveVerts = new HashSet <int>(); // original vertices that were epsilon-coincident w/ curve vertices
insert_corners(OnCurveVerts);
// [RMS] not using this?
//HashSet<int> corner_v = new HashSet<int>(CurveVertices);
// not sure we need to track all of these
HashSet <int> ZeroEdges = new HashSet <int>();
HashSet <int> ZeroVertices = new HashSet <int>();
OnCutEdges = new HashSet <int>();
HashSet <int> NewEdges = new HashSet <int>();
HashSet <int> NewCutVertices = new HashSet <int>();
sbyte[] signs = new sbyte[2 * Mesh.MaxVertexID + 2 * Curve.VertexCount];
HashSet <int> segTriangles = new HashSet <int>();
HashSet <int> segVertices = new HashSet <int>();
HashSet <int> segEdges = new HashSet <int>();
// loop over segments, insert each one in sequence
int N = (IsLoop) ? Curve.VertexCount : Curve.VertexCount - 1;
for (int si = 0; si < N; ++si)
{
int i0 = si;
int i1 = (si + 1) % Curve.VertexCount;
Segment2d seg = new Segment2d(Curve[i0], Curve[i1]);
int i0_vid = CurveVertices[i0];
int i1_vid = CurveVertices[i1];
// If these vertices are already connected by an edge, we can just continue.
int existing_edge = Mesh.FindEdge(i0_vid, i1_vid);
if (existing_edge != DMesh3.InvalidID)
{
add_cut_edge(existing_edge);
continue;
}
if (triSpatial != null)
{
segTriangles.Clear(); segVertices.Clear(); segEdges.Clear();
AxisAlignedBox2d segBounds = new AxisAlignedBox2d(seg.P0); segBounds.Contain(seg.P1);
segBounds.Expand(MathUtil.ZeroTolerancef * 10);
triSpatial.FindTrianglesInRange(segBounds, segTriangles);
IndexUtil.TrianglesToVertices(Mesh, segTriangles, segVertices);
IndexUtil.TrianglesToEdges(Mesh, segTriangles, segEdges);
}
int MaxVID = Mesh.MaxVertexID;
IEnumerable <int> vertices = Interval1i.Range(MaxVID);
if (triSpatial != null)
{
vertices = segVertices;
}
// compute edge-crossing signs
// [TODO] could walk along mesh from a to b, rather than computing for entire mesh?
if (signs.Length < MaxVID)
{
signs = new sbyte[2 * MaxVID];
}
gParallel.ForEach(vertices, (vid) => {
if (Mesh.IsVertex(vid))
{
if (vid == i0_vid || vid == i1_vid)
{
signs[vid] = 0;
}
else
{
Vector2d v2 = PointF(vid);
// tolerance defines band in which we will consider values to be zero
signs[vid] = (sbyte)seg.WhichSide(v2, SpatialEpsilon);
}
}
else
{
signs[vid] = sbyte.MaxValue;
}
});
// have to skip processing of new edges. If edge id
// is > max at start, is new. Otherwise if in NewEdges list, also new.
// (need both in case we re-use an old edge index)
int MaxEID = Mesh.MaxEdgeID;
NewEdges.Clear();
NewCutVertices.Clear();
NewCutVertices.Add(i0_vid);
NewCutVertices.Add(i1_vid);
// cut existing edges with segment
IEnumerable <int> edges = Interval1i.Range(MaxEID);
if (triSpatial != null)
{
edges = segEdges;
}
foreach (int eid in edges)
{
if (Mesh.IsEdge(eid) == false)
{
continue;
}
if (eid >= MaxEID || NewEdges.Contains(eid))
{
continue;
}
// cannot cut boundary edges?
if (Mesh.IsBoundaryEdge(eid))
{
continue;
}
Index2i ev = Mesh.GetEdgeV(eid);
int eva_sign = signs[ev.a];
int evb_sign = signs[ev.b];
// [RMS] should we be using larger epsilon here? If we don't track OnCurveVerts explicitly, we
// need to at least use same epsilon we passed to insert_corner_from_bary...do we still also
// need that to catch the edges we split in the poke?
bool eva_in_segment = false;
if (eva_sign == 0)
{
eva_in_segment = OnCurveVerts.Contains(ev.a) || Math.Abs(seg.Project(PointF(ev.a))) < (seg.Extent + SpatialEpsilon);
}
bool evb_in_segment = false;
if (evb_sign == 0)
{
evb_in_segment = OnCurveVerts.Contains(ev.b) || Math.Abs(seg.Project(PointF(ev.b))) < (seg.Extent + SpatialEpsilon);
}
// If one or both vertices are on-segment, we have special case.
// If just one vertex is on the segment, we can skip this edge.
// If both vertices are on segment, then we can just re-use this edge.
if (eva_in_segment || evb_in_segment)
{
if (eva_in_segment && evb_in_segment)
{
ZeroEdges.Add(eid);
add_cut_edge(eid);
NewCutVertices.Add(ev.a); NewCutVertices.Add(ev.b);
}
else
{
int zvid = eva_in_segment ? ev.a : ev.b;
ZeroVertices.Add(zvid);
NewCutVertices.Add(zvid);
}
continue;
}
// no crossing
if (eva_sign * evb_sign > 0)
{
continue;
}
// compute segment/segment intersection
Vector2d va = PointF(ev.a);
Vector2d vb = PointF(ev.b);
Segment2d edge_seg = new Segment2d(va, vb);
IntrSegment2Segment2 intr = new IntrSegment2Segment2(seg, edge_seg);
intr.Compute();
if (intr.Type == IntersectionType.Segment)
{
// [RMS] we should have already caught this above, so if it happens here it is probably spurious?
// we should have caught this case above, but numerics are different so it might occur again
ZeroEdges.Add(eid);
NewCutVertices.Add(ev.a); NewCutVertices.Add(ev.b);
add_cut_edge(eid);
continue;
}
else if (intr.Type != IntersectionType.Point)
{
continue; // no intersection
}
Vector2d x = intr.Point0;
double t = Math.Sqrt(x.DistanceSquared(va) / va.DistanceSquared(vb));
// this case happens if we aren't "on-segment" but after we do the test the intersection pt
// is within epsilon of one end of the edge. This is a spurious t-intersection and we
// can ignore it. Some other edge should exist that picks up this vertex as part of it.
// [TODO] what about if this edge is degenerate?
bool x_in_segment = Math.Abs(edge_seg.Project(x)) < (edge_seg.Extent - SpatialEpsilon);
if (!x_in_segment)
{
continue;
}
Index2i et = Mesh.GetEdgeT(eid);
spatial_remove_triangles(et.a, et.b);
// split edge at this segment
DMesh3.EdgeSplitInfo splitInfo;
MeshResult result = Mesh.SplitEdge(eid, out splitInfo, t);
if (result != MeshResult.Ok)
{
throw new Exception("MeshInsertUVSegment.Apply: SplitEdge failed - " + result.ToString());
//return false;
}
// move split point to intersection position
SetPointF(splitInfo.vNew, x);
NewCutVertices.Add(splitInfo.vNew);
NewEdges.Add(splitInfo.eNewBN);
NewEdges.Add(splitInfo.eNewCN);
spatial_add_triangles(et.a, et.b);
spatial_add_triangles(splitInfo.eNewT2, splitInfo.eNewT3);
// some splits - but not all - result in new 'other' edges that are on
// the polypath. We want to keep track of these edges so we can extract loop later.
Index2i ecn = Mesh.GetEdgeV(splitInfo.eNewCN);
if (NewCutVertices.Contains(ecn.a) && NewCutVertices.Contains(ecn.b))
{
add_cut_edge(splitInfo.eNewCN);
}
// since we don't handle bdry edges this should never be false, but maybe we will handle bdry later...
if (splitInfo.eNewDN != DMesh3.InvalidID)
{
NewEdges.Add(splitInfo.eNewDN);
Index2i edn = Mesh.GetEdgeV(splitInfo.eNewDN);
if (NewCutVertices.Contains(edn.a) && NewCutVertices.Contains(edn.b))
{
add_cut_edge(splitInfo.eNewDN);
}
}
}
}
// extract the cut paths
if (EnableCutSpansAndLoops)
{
find_cut_paths(OnCutEdges);
}
return(true);
} // Apply()
/// <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 void FindConnectedT()
{
Components = new List <Component>();
int NT = Mesh.MaxTriangleID;
// [TODO] could use Euler formula to determine if mesh is closed genus-0...
Func <int, bool> filter_func = (i) => { return(Mesh.IsTriangle(i)); };
if (FilterF != null)
{
filter_func = (i) => { return(Mesh.IsTriangle(i) && FilterF(i)); }
}
;
// initial active set contains all valid triangles
byte[] active = new byte[Mesh.MaxTriangleID];
Interval1i activeRange = Interval1i.Empty;
if (FilterSet != null)
{
for (int i = 0; i < NT; ++i)
{
active[i] = 255;
}
foreach (int tid in FilterSet)
{
bool bValid = filter_func(tid);
if (bValid)
{
active[tid] = 0;
activeRange.Contain(tid);
}
}
}
else
{
for (int i = 0; i < NT; ++i)
{
bool bValid = filter_func(i);
if (bValid)
{
active[i] = 0;
activeRange.Contain(i);
}
else
{
active[i] = 255;
}
}
}
// temporary buffers
List <int> queue = new List <int>(NT / 10);
List <int> cur_comp = new List <int>(NT / 10);
// keep finding valid seed triangles and growing connected components
// until we are done
IEnumerable <int> range = (FilterSet != null) ? FilterSet : activeRange;
foreach (int i in range)
{
//for ( int i = 0; i < NT; ++i ) {
if (active[i] == 255)
{
continue;
}
int seed_t = i;
if (SeedFilterF != null && SeedFilterF(seed_t) == false)
{
continue;
}
queue.Add(seed_t);
active[seed_t] = 1; // in queue
while (queue.Count > 0)
{
int cur_t = queue[queue.Count - 1];
queue.RemoveAt(queue.Count - 1);
active[cur_t] = 2; // tri has been processed
cur_comp.Add(cur_t);
Index3i nbrs = Mesh.GetTriNeighbourTris(cur_t);
for (int j = 0; j < 3; ++j)
{
int nbr_t = nbrs[j];
if (nbr_t != DMesh3.InvalidID && active[nbr_t] == 0)
{
queue.Add(nbr_t);
active[nbr_t] = 1; // in queue
}
}
}
Component comp = new Component()
{
Indices = cur_comp.ToArray()
};
Components.Add(comp);
// remove tris in this component from active set
for (int j = 0; j < comp.Indices.Length; ++j)
{
active[comp.Indices[j]] = 255;
}
cur_comp.Clear();
queue.Clear();
}
}
/// <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 void Set(Interval1i o)
{
a = o.a; b = o.b;
}
public Interval1i(Interval1i copy)
{
a = copy.a; b = copy.b;
}
public virtual bool Apply()
{
insert_corners();
// [RMS] not using this?
//HashSet<int> corner_v = new HashSet<int>(CurveVertices);
// not sure we need to track all of these
HashSet <int> ZeroEdges = new HashSet <int>();
HashSet <int> ZeroVertices = new HashSet <int>();
OnCutEdges = new HashSet <int>();
// loop over segments, insert each one in sequence
int N = (IsLoop) ? Curve.VertexCount : Curve.VertexCount - 1;
for (int si = 0; si < N; ++si)
{
int i0 = si;
int i1 = (si + 1) % Curve.VertexCount;
Segment2d seg = new Segment2d(Curve[i0], Curve[i1]);
int i0_vid = CurveVertices[i0];
int i1_vid = CurveVertices[i1];
// If these vertices are already connected by an edge, we can just continue.
int existing_edge = Mesh.FindEdge(i0_vid, i1_vid);
if (existing_edge != DMesh3.InvalidID)
{
OnCutEdges.Add(existing_edge);
continue;
}
// compute edge-crossing signs
// [TODO] could walk along mesh from a to b, rather than computing for entire mesh?
int MaxVID = Mesh.MaxVertexID;
int[] signs = new int[MaxVID];
gParallel.ForEach(Interval1i.Range(MaxVID), (vid) => {
if (Mesh.IsVertex(vid))
{
if (vid == i0_vid || vid == i1_vid)
{
signs[vid] = 0;
}
else
{
Vector2d v2 = PointF(vid);
// tolerance defines band in which we will consider values to be zero
signs[vid] = seg.WhichSide(v2, MathUtil.ZeroTolerance);
}
}
else
{
signs[vid] = int.MaxValue;
}
});
// have to skip processing of new edges. If edge id
// is > max at start, is new. Otherwise if in NewEdges list, also new.
// (need both in case we re-use an old edge index)
int MaxEID = Mesh.MaxEdgeID;
HashSet <int> NewEdges = new HashSet <int>();
HashSet <int> NewCutVertices = new HashSet <int>();
NewCutVertices.Add(i0_vid);
NewCutVertices.Add(i1_vid);
// cut existing edges with segment
for (int eid = 0; eid < MaxEID; ++eid)
{
if (Mesh.IsEdge(eid) == false)
{
continue;
}
if (eid >= MaxEID || NewEdges.Contains(eid))
{
continue;
}
// cannot cut boundary edges?
if (Mesh.IsBoundaryEdge(eid))
{
continue;
}
Index2i ev = Mesh.GetEdgeV(eid);
int eva_sign = signs[ev.a];
int evb_sign = signs[ev.b];
bool eva_in_segment = false;
if (eva_sign == 0)
{
eva_in_segment = Math.Abs(seg.Project(PointF(ev.a))) < (seg.Extent + MathUtil.ZeroTolerance);
}
bool evb_in_segment = false;
if (evb_sign == 0)
{
evb_in_segment = Math.Abs(seg.Project(PointF(ev.b))) < (seg.Extent + MathUtil.ZeroTolerance);
}
// If one or both vertices are on-segment, we have special case.
// If just one vertex is on the segment, we can skip this edge.
// If both vertices are on segment, then we can just re-use this edge.
if (eva_in_segment || evb_in_segment)
{
if (eva_in_segment && evb_in_segment)
{
ZeroEdges.Add(eid);
OnCutEdges.Add(eid);
}
else
{
ZeroVertices.Add(eva_in_segment ? ev.a : ev.b);
}
continue;
}
// no crossing
if (eva_sign * evb_sign > 0)
{
continue;
}
// compute segment/segment intersection
Vector2d va = PointF(ev.a);
Vector2d vb = PointF(ev.b);
Segment2d edge_seg = new Segment2d(va, vb);
IntrSegment2Segment2 intr = new IntrSegment2Segment2(seg, edge_seg);
intr.Compute();
if (intr.Type == IntersectionType.Segment)
{
// [RMS] we should have already caught this above, so if it happens here it is probably spurious?
// we should have caught this case above, but numerics are different so it might occur again
ZeroEdges.Add(eid);
OnCutEdges.Add(eid);
continue;
}
else if (intr.Type != IntersectionType.Point)
{
continue; // no intersection
}
Vector2d x = intr.Point0;
// this case happens if we aren't "on-segment" but after we do the test the intersection pt
// is within epsilon of one end of the edge. This is a spurious t-intersection and we
// can ignore it. Some other edge should exist that picks up this vertex as part of it.
// [TODO] what about if this edge is degenerate?
bool x_in_segment = Math.Abs(edge_seg.Project(x)) < (edge_seg.Extent - MathUtil.ZeroTolerance);
if (!x_in_segment)
{
continue;
}
// split edge at this segment
DMesh3.EdgeSplitInfo splitInfo;
MeshResult result = Mesh.SplitEdge(eid, out splitInfo);
if (result != MeshResult.Ok)
{
throw new Exception("MeshInsertUVSegment.Cut: failed in SplitEdge");
//return false;
}
// move split point to intersection position
SetPointF(splitInfo.vNew, x);
NewCutVertices.Add(splitInfo.vNew);
NewEdges.Add(splitInfo.eNewBN);
NewEdges.Add(splitInfo.eNewCN);
// some splits - but not all - result in new 'other' edges that are on
// the polypath. We want to keep track of these edges so we can extract loop later.
Index2i ecn = Mesh.GetEdgeV(splitInfo.eNewCN);
if (NewCutVertices.Contains(ecn.a) && NewCutVertices.Contains(ecn.b))
{
OnCutEdges.Add(splitInfo.eNewCN);
}
// since we don't handle bdry edges this should never be false, but maybe we will handle bdry later...
if (splitInfo.eNewDN != DMesh3.InvalidID)
{
NewEdges.Add(splitInfo.eNewDN);
Index2i edn = Mesh.GetEdgeV(splitInfo.eNewDN);
if (NewCutVertices.Contains(edn.a) && NewCutVertices.Contains(edn.b))
{
OnCutEdges.Add(splitInfo.eNewDN);
}
}
}
}
//MeshEditor editor = new MeshEditor(Mesh);
//foreach (int eid in OnCutEdges)
// editor.AppendBox(new Frame3f(Mesh.GetEdgePoint(eid, 0.5)), 0.1f);
//Util.WriteDebugMesh(Mesh, string.Format("C:\\git\\geometry3SharpDemos\\geometry3Test\\test_output\\after_inserted.obj"));
// extract the cut paths
if (EnableCutSpansAndLoops)
{
find_cut_paths(OnCutEdges);
}
return(true);
} // Apply()
public virtual bool Cut()
{
double invalidDist = double.MinValue;
MeshEdgeSelection CutEdgeSet = null;
MeshVertexSelection CutVertexSet = null;
if (CutFaceSet != null)
{
CutEdgeSet = new MeshEdgeSelection(Mesh, CutFaceSet);
CutVertexSet = new MeshVertexSelection(Mesh, CutEdgeSet);
}
// compute signs
int MaxVID = Mesh.MaxVertexID;
double[] signs = new double[MaxVID];
gParallel.ForEach(Interval1i.Range(MaxVID), (vid) => {
if (Mesh.IsVertex(vid))
{
Vector3d v = Mesh.GetVertex(vid);
signs[vid] = (v - PlaneOrigin).Dot(PlaneNormal);
}
else
{
signs[vid] = invalidDist;
}
});
HashSet <int> ZeroEdges = new HashSet <int>();
HashSet <int> ZeroVertices = new HashSet <int>();
HashSet <int> OnCutEdges = new HashSet <int>();
// have to skip processing of new edges. If edge id
// is > max at start, is new. Otherwise if in NewEdges list, also new.
int MaxEID = Mesh.MaxEdgeID;
HashSet <int> NewEdges = new HashSet <int>();
IEnumerable <int> edgeItr = Interval1i.Range(MaxEID);
if (CutEdgeSet != null)
{
edgeItr = CutEdgeSet;
}
// cut existing edges with plane, using edge split
foreach (int eid in edgeItr)
{
if (Mesh.IsEdge(eid) == false)
{
continue;
}
if (eid >= MaxEID || NewEdges.Contains(eid))
{
continue;
}
Index2i ev = Mesh.GetEdgeV(eid);
double f0 = signs[ev.a];
double f1 = signs[ev.b];
// If both signs are 0, this edge is on-contour
// If one sign is 0, that vertex is on-contour
int n0 = (Math.Abs(f0) < MathUtil.Epsilon) ? 1 : 0;
int n1 = (Math.Abs(f1) < MathUtil.Epsilon) ? 1 : 0;
if (n0 + n1 > 0)
{
if (n0 + n1 == 2)
{
ZeroEdges.Add(eid);
}
else
{
ZeroVertices.Add((n0 == 1) ? ev[0] : ev[1]);
}
continue;
}
// no crossing
if (f0 * f1 > 0)
{
continue;
}
DMesh3.EdgeSplitInfo splitInfo;
MeshResult result = Mesh.SplitEdge(eid, out splitInfo);
if (result != MeshResult.Ok)
{
throw new Exception("MeshPlaneCut.Cut: failed in SplitEdge");
//return false;
}
// SplitEdge just bisects edge - use plane intersection instead
double t = f0 / (f0 - f1);
Vector3d newPos = (1 - t) * Mesh.GetVertex(ev.a) + (t) * Mesh.GetVertex(ev.b);
Mesh.SetVertex(splitInfo.vNew, newPos);
NewEdges.Add(splitInfo.eNewBN);
NewEdges.Add(splitInfo.eNewCN); OnCutEdges.Add(splitInfo.eNewCN);
if (splitInfo.eNewDN != DMesh3.InvalidID)
{
NewEdges.Add(splitInfo.eNewDN);
OnCutEdges.Add(splitInfo.eNewDN);
}
}
// remove one-rings of all positive-side vertices.
IEnumerable <int> vertexSet = Interval1i.Range(MaxVID);
if (CutVertexSet != null)
{
vertexSet = CutVertexSet;
}
foreach (int vid in vertexSet)
{
if (signs[vid] > 0 && Mesh.IsVertex(vid))
{
Mesh.RemoveVertex(vid, true, false);
}
}
// ok now we extract boundary loops, but restricted
// to either the zero-edges we found, or the edges we created! bang!!
Func <int, bool> CutEdgeFilterF = (eid) => {
if (OnCutEdges.Contains(eid) || ZeroEdges.Contains(eid))
{
return(true);
}
return(false);
};
try {
MeshBoundaryLoops loops = new MeshBoundaryLoops(Mesh, false);
loops.EdgeFilterF = CutEdgeFilterF;
loops.Compute();
CutLoops = loops.Loops;
CutSpans = loops.Spans;
CutLoopsFailed = false;
FoundOpenSpans = CutSpans.Count > 0;
} catch {
CutLoops = new List <EdgeLoop>();
CutLoopsFailed = true;
}
return(true);
} // Cut()
public bool Overlaps(Interval1i o)
{
return(!(o.a > b || o.b < a));
}
public IntSequence(int iStart, int iEnd)
{
range = new Interval1i(iStart, iEnd);
}
public IntSequence(Interval1i ival)
{
range = ival;
}
