internal void CloseSMatrixSet()
{
if (Pole.Length == 4)
{
PGeom.CloseMatrixSet(SMatrices);
}
}
private void CreateTwistMaps()
{
PermByMatr perm = new PermByMatr(Axes.Length, Faces.Length);
foreach (PBaseAxis Ax in BaseAxes)
{
foreach (PBaseTwist tw in Ax.Twists)
{
double[,] matr = PGeom.ApplyTwist(tw.Dir, PGeom.MatrixIdentity(Dim));
int[][] R = ConvertStickersFromLayers(Ax, matr, perm);
int[][] R1 = new int[Ax.NLayers][];
for (int i = 0; i < Ax.NLayers; i++)
{
if (R[i] != null)
{
R1[i] = new int[R[i].Length];
for (int j = 0; j < R[i].Length; j++)
{
int h = Array.BinarySearch <int>(Ax.Layers[i], R[i][j]);
if (h < 0)
{
throw new Exception("Can't find sticker image in twist");
}
R[i][j] = h; R1[i][h] = j;
}
}
}
tw.Map = R; tw.InvMap = R1;
}
}
}
internal double[,] GetBestMatrix(int f0, double[] p0, int f1, double[] p1)
{
// move from (f0,p0) to (f1,p1); point p is on the cell surface.
PFace F0 = Faces[f0], F1 = Faces[f1];
if (F0.Base.Id != F1.Base.Id)
{
return(null);
}
double[] q0 = PGeom.ApplyInvMatrix(F0.Matrix, p0);
double[] q1 = PGeom.ApplyInvMatrix(F1.Matrix, p1);
double dbest = double.MaxValue;
double[,] mr = null;
foreach (double[,] m in F0.Base.SMatrices)
{
double[] qq = PGeom.ApplyMatrix(m, q0);
double v = PGeom.Dist2(qq, q1);
if (v < dbest)
{
dbest = v; mr = m;
}
}
return(PGeom.MatrixMulInv2(F0.Matrix, PGeom.MatrixMul(mr, F1.Matrix)));
}
internal PFace(PBaseFace bas)
{
Base = bas;
Pole = bas.Pole;
int dim = Pole.Length;
Matrix = PGeom.MatrixIdentity(dim);
RefAxis = 0;
}
internal int FindTwist(double[] p, double[,] matr, out bool qrev)
{
double[] q = PGeom.ApplyMatrixToTwist(matr, p);
qrev = false;
for (int i = 0; i < Twists.Length; i++)
{
if (PGeom.TwistsEqual(q, Twists[i], out qrev))
{
return(i);
}
}
throw new Exception("Can't fing twist");
}
internal PAxis(PAxis src, double [] tw)
{
Base = src.Base;
Dir = PGeom.ApplyTwist(tw, src.Dir);
Matrix = PGeom.ApplyTwist(tw, src.Matrix);
int ntw = src.Twists.Length;
Twists = new double[ntw][];
for (int i = 0; i < ntw; i++)
{
Twists[i] = PGeom.ApplyTwist(tw, src.Twists[i]);
}
}
internal void AddSMatrix(double[,] mf, double[,] p)
{
// Pole*mf=Pole*p => Pole*(mf*p')=Pole
double[,] mr = PGeom.MatrixMulInv(mf, p);
foreach (double[,] m in SMatrices)
{
if (PGeom.MatrixEqual(m, mr))
{
return;
}
}
SMatrices.Add(mr);
}
internal PAxis(PBaseAxis bas)
{
Base = bas;
Dir = bas.Dir;
int dim = Dir.Length;
Matrix = PGeom.MatrixIdentity(dim);
int ntw = bas.Twists.Length;
Twists = new double[ntw][];
for (int i = 0; i < ntw; i++)
{
Twists[i] = bas.Twists[i].Dir;
}
}
private void ExpandFaces()
{
PFace[] CFaces = new PFace[MaxNVert];
int NRefl = Group.Length;
int p, q = BaseFaces.Length;
for (int i = 0; i < q; i++)
{
BaseFaces[i].Id = i;
CFaces[i] = new PFace(BaseFaces[i]);
}
for (p = 0; p < q; p++)
{
foreach (double [] G in Group)
{
double[] v = PGeom.ApplyTwist(G, CFaces[p].Pole);
int j;
for (j = 0; j < q; j++)
{
if (PGeom.VertEqual(v, CFaces[j].Pole))
{
double[,] mf = PGeom.ApplyTwist(G, CFaces[p].Matrix);
CFaces[p].Base.AddSMatrix(mf, CFaces[j].Matrix);
break;
}
}
if (j == q)
{
if (q == MaxNVert)
{
throw new Exception("Too many vertices");
}
CFaces[q] = new PFace(CFaces[p], G);
q++;
}
}
}
Faces = new PFace[q];
for (int i = 0; i < q; i++)
{
Faces[i] = CFaces[i];
Faces[i].Id = i;
}
foreach (PBaseFace BF in BaseFaces)
{
BF.CloseSMatrixSet();
}
}
private int FindFace(double[] p, double[,] matr)
{
p = PGeom.ApplyMatrix(matr, p);
int r0 = 0;
double d0 = double.MaxValue;
foreach (PFace F in Faces)
{
double v = PGeom.Dist2(p, F.Pole);
if (v < d0)
{
d0 = v; r0 = F.Id;
}
}
return(r0);
}
private void ExpandAxes()
{
int q = BaseAxes.Length;
PAxis[] CAxes = new PAxis[MaxNAxes];
for (int i = 0; i < q; i++)
{
PBaseAxis ax = BaseAxes[i];
ax.Id = i;
ax.ExpandPrimaryTwists();
CAxes[i] = new PAxis(ax); // matrix=id
}
for (int p = 0; p < q; p++)
{
double[] R = CAxes[p].Dir;
foreach (double [] G in Group)
{
double[] v = PGeom.ApplyTwist(G, R);
int j;
bool qr;
for (j = 0; j < q; j++)
{
if (PGeom.AxisEqual(v, CAxes[j].Dir, out qr))
{
break;
}
}
if (j == q)
{
if (q == MaxNAxes)
{
throw new Exception("Too many axes");
}
CAxes[q] = new PAxis(CAxes[p], G);
q++;
}
}
}
Axes = new PAxis[q];
for (int i = 0; i < q; i++)
{
Axes[i] = CAxes[i];
Axes[i].Id = i;
}
}
internal void ExpandPrimaryTwists()
{
const int MaxNTwists = 256;
NPrimaryTwists = Twists.Length;
PBaseTwist[] twst = new PBaseTwist[MaxNTwists];
int q = 0;
foreach (PBaseTwist tw in Twists)
{
twst[q++] = tw;
}
for (int p = 0; p < q; p++)
{
double[] v = twst[p].Dir;
for (int i = 0; i < q; i++)
{
double[] w = PGeom.ApplyTwist(twst[i].Dir, v);
int k;
bool qr;
for (k = 0; k < q; k++)
{
if (PGeom.TwistsEqual(w, twst[k].Dir, out qr))
{
break;
}
}
if (k == q)
{
if (q == MaxNTwists)
{
throw new Exception("Too many planes");
}
twst[q] = new PBaseTwist(w);
q++;
}
}
}
Twists = new PBaseTwist[q];
for (int i = 0; i < q; i++)
{
Twists[i] = twst[i];
}
}
internal double GetRad()
{
double R = 0;
foreach (PBaseFace F in BaseFaces)
{
foreach (PMesh M in F.StickerMesh)
{
if (M.MinBDim == 0)
{
double r = PGeom.VLength(M.Ctr);
if (r > R)
{
R = r;
}
}
}
}
return(R);
}
private int FindAxis(double[] dir)
{
int r0 = 0;
double d0 = double.MaxValue;
foreach (PAxis Ax in Axes)
{
double v = PGeom.Dist2(dir, Ax.Dir);
if (v < d0)
{
d0 = v; r0 = Ax.Id + 1;
}
v = PGeom.Dist2Rev(dir, Ax.Dir);
if (v < d0)
{
d0 = v; r0 = -Ax.Id - 1;
}
}
return(r0);
}
internal int FindNearestAxis(double[] pt, bool qexact)
{
double tbest = qexact ? 0.999999 : -1;
int res = 0;
double ld = PGeom.DotProd(pt, pt);
for (int i = 0; i < Axes.Length; i++)
{
double[] v = Axes[i].Dir;
double x = PGeom.DotProd(pt, v) / Math.Sqrt(ld * PGeom.DotProd(v, v));
if (x > tbest)
{
res = i + 1; tbest = x;
}
if (x < -tbest)
{
res = -i - 1; tbest = -x;
}
}
return(res);
}
internal bool FindTwist(int nf, double[] pt, out int ax, out int tw) // 4D only
{
ax = Faces[nf].RefAxis;
tw = 0;
if (ax == 0)
{
return(false);
}
int iax = Math.Abs(ax) - 1;
double[] actr = Axes[iax].Dir;
double[] rtw = new double[Dim];
double l1 = PGeom.DotProd(pt, actr) / PGeom.DotProd(actr, actr);
for (int i = 0; i < Dim; i++)
{
rtw[i] = pt[i] - l1 * actr[i];
}
double tbest = -1;
double[] p = new double[4];
for (int i = 0; i < Axes[iax].Twists.Length; i++)
{
double[] u = Axes[iax].Twists[i];
p[0] = actr[1] * (u[2] * u[7] - u[3] * u[6]) + actr[2] * (u[3] * u[5] - u[1] * u[7]) + actr[3] * (u[1] * u[6] - u[2] * u[5]);
p[1] = actr[0] * (u[3] * u[6] - u[2] * u[7]) + actr[2] * (u[0] * u[7] - u[3] * u[4]) + actr[3] * (u[2] * u[4] - u[0] * u[6]);
p[2] = actr[0] * (u[1] * u[7] - u[3] * u[5]) + actr[1] * (u[3] * u[4] - u[0] * u[7]) + actr[3] * (u[0] * u[5] - u[1] * u[4]);
p[3] = actr[0] * (u[2] * u[5] - u[1] * u[6]) + actr[1] * (u[0] * u[6] - u[2] * u[4]) + actr[2] * (u[1] * u[4] - u[0] * u[5]);
l1 = -PGeom.DotProd(p, rtw) / Math.Sqrt(PGeom.DotProd(p, p));
if (l1 < -tbest)
{
tbest = -l1; tw = -i - 1;
}
if (l1 > tbest)
{
tbest = l1; tw = i + 1;
}
}
return(true);
}
private int FindAxisInv(double[] dir, double[,] matr)
{
dir = PGeom.ApplyInvMatrix(matr, dir);
return(FindAxis(dir));
}
internal int FindAxis(double[] dir, double[,] matr)
{
dir = PGeom.ApplyMatrix(matr, dir);
return(FindAxis(dir));
}
private void FillFromStrings(string[] descr)
{
int naxis = 0;
int caxis = 0;
PBaseAxis ax = null;
int state = 0;
int nv;
int fline = 0;
QSimplified = false;
try {
while (state >= 0)
{
if (fline == descr.Length)
{
if (state != 7)
{
throw new Exception("Unexpected end");
}
break;
}
string line = descr[fline++];
if (line == "" || line == null || line[0] == '#')
{
continue;
}
string[] str = line.Split(' ', '\t');
if (str.Length == 0 || str[0] == "" || str[0] == null)
{
continue;
}
string cmd = str[0].ToLowerInvariant();
switch (state)
{
case 0:
if (cmd != "dim")
{
throw new Exception("'Dim' required");
}
Dim = int.Parse(str[1]);
break;
case 1:
if (cmd != "naxis")
{
throw new Exception("'NAxis' required");
}
naxis = int.Parse(str[1]);
BaseAxes = new PBaseAxis[naxis];
break;
case 2:
if (cmd != "faces")
{
throw new Exception("'Faces' required");
}
nv = str.Length - 1;
BaseFaces = new PBaseFace[nv];
for (int i = 0; i < nv; i++)
{
BaseFaces[i] = new PBaseFace(GetVector(str[i + 1], Dim));
}
break;
case 3:
if (cmd == "simplified")
{
QSimplified = true; state--; break;
}
if (cmd != "group")
{
throw new Exception("'Group' required");
}
nv = str.Length - 1;
Group = new double[nv][];
for (int i = 0; i < nv; i++)
{
Group[i] = GetVector(str[i + 1], 2 * Dim);
PGeom.GetOrder(Group[i]);
}
if (naxis == 0)
{
state = -2;
}
break;
case 4:
if (cmd != "axis")
{
throw new Exception("'Axis' required");
}
ax = new PBaseAxis(GetVector(str[1], Dim));
break;
case 5:
if (cmd != "twists")
{
throw new Exception("'Twists' required");
}
nv = str.Length - 1;
ax.Twists = new PBaseTwist[nv];
for (int i = 0; i < nv; i++)
{
ax.Twists[i] = new PBaseTwist(GetVector(str[i + 1], 2 * Dim));
}
break;
case 6:
if (cmd != "cuts")
{
throw new Exception("'Cuts' required");
}
nv = str.Length - 1;
ax.Cut = new double[nv];
for (int i = 0; i < nv; i++)
{
ax.Cut[i] = double.Parse(str[i + 1], CultureInfo.InvariantCulture);
}
ax.AdjustCuts();
BaseAxes[caxis++] = ax;
ax = null;
break;
case 7: {
if (cmd == "fixedmask")
{
BaseAxes[caxis - 1].FixedMask = int.Parse(str[1]);
if (caxis == naxis)
{
state = -2;
}
else
{
state = 3;
}
break;
}
if (caxis != naxis)
{
state = 4; goto case 4;
}
state = -2;
break;
}
}
state++;
}
} catch (Exception e) {
throw new Exception("Error: " + e.Message + " in line " + fline + ": " + (descr[fline] ?? "{null}"));
}
}
internal void SetStickers(LMesh M, CutNetwork CN, PAxis[] Axes, double[][] fctrs)
{
int dim = Pole.Length;
NCutAxes = 0;
int nax = Axes.Length;
for (int i = 0; i < nax; i++)
{
if (AxisLayers[i] < 0)
{
NCutAxes++;
}
}
CutAxes = new int[NCutAxes];
int d = 0;
int rnk = 0;
for (int u = 0; u < nax; u++)
{
if (AxisLayers[u] < 0)
{
CutAxes[d++] = u;
}
else
{
rnk += Axes[u].Base.GetRank(AxisLayers[u]);
}
}
NStickers = CN.Nodes.Length;
StickerMask = new byte[NStickers, NCutAxes];
StickerMesh = new PMesh[NStickers];
int nstk = 0;
for (int i = 0; i < NStickers; i++)
{
PMesh xx = CN.GetPMesh(i);
if (fctrs != null)
{
bool qg = false;
foreach (double[] p in fctrs)
{
if (PGeom.VertEqual(p, xx.Ctr))
{
qg = true;
break;
}
}
if (!qg)
{
continue;
}
}
xx.FCtr = Pole;
double[] ctr = xx.GetMCtr();
int rnk1 = rnk;
for (int j = 0; j < NCutAxes; j++)
{
PAxis ax = Axes[CutAxes[j]];
double[] h = ax.Dir;
double lh = PGeom.DotProd(h, h);
double s = 0;
for (int k = 0; k < dim; k++)
{
s += ctr[k] * h[k];
}
s /= lh;
int lv = ax.Base.NLayers - 1;
for (int g = 0; g < lv; g++)
{
if (s > ax.Base.Cut[g])
{
lv = g; break;
}
}
rnk1 += ax.Base.GetRank(lv);
StickerMask[nstk, j] = (byte)lv;
}
xx.Rank = rnk1;
StickerMesh[nstk++] = xx;
}
if (nstk != NStickers)
{
PMesh[] stkm = new PMesh[nstk];
byte[,] stkmsk = new byte[nstk, NCutAxes];
for (int i = 0; i < nstk; i++)
{
stkm[i] = StickerMesh[i];
for (int j = 0; j < NCutAxes; j++)
{
stkmsk[i, j] = StickerMask[i, j];
}
}
StickerMask = stkmsk;
StickerMesh = stkm;
NStickers = nstk;
}
}
private void CutFaces()
{
double RMax = 0;
foreach (PBaseFace F in BaseFaces)
{
RMax = Math.Max(RMax, PGeom.VLength(F.Pole));
}
int minrank = int.MaxValue;
foreach (PBaseFace F in BaseFaces)
{
CutNode face = CutNode.GenCube(Dim, RMax * Dim);
double[] hpln = CutNetwork.GetPlane(F.Pole, 1);
face.Split(1, hpln, false);
face = face.ZeroNode;
int opgen = 1;
foreach (PFace FF in Faces)
{
if (F.Id != FF.Id)
{
hpln = CutNetwork.GetPlane(FF.Pole, 1);
face.Split(++opgen, hpln, true);
if (face.Status != CutNode.STAT_PLUS)
{
throw new Exception("Empty face: Id=" + F.Id);
}
}
}
int nff = face.Children.Length;
double[][] ffpol = new double[nff][];
for (int i = 0; i < nff; i++)
{
ffpol[i] = face.Children[i].Pole;
}
F.FPoles = ffpol;
LMesh m = new LMesh(Dim, true);
face.FillLMesh(++opgen, m);
m.CloseCtr();
F.FaceMesh = new PMesh(m);
F.FaceMesh.FCtr = F.Pole;
double[] verts = m.pts;
int nverts = m.npts;
CutNetwork CN = new CutNetwork(face, Dim, opgen);
double[][] fctrs = null;
if (QSimplified)
{
fctrs = CN.GetCtrs();
}
F.AxisLayers = new int[Axes.Length];
for (int u = 0; u < Axes.Length; u++)
{
PAxis Ax = Axes[u];
double[] D = Ax.Dir;
double lD = PGeom.Dist2(D, new double[Dim]);
double smin = double.MaxValue, smax = double.MinValue;
for (int i = 0; i < nverts; i++)
{
double v = 0;
for (int j = 0; j < Dim; j++)
{
v += D[j] * verts[i * Dim + j];
}
if (v < smin)
{
smin = v;
}
if (v > smax)
{
smax = v;
}
}
smin /= lD; smax /= lD;
bool cs = false, cc = false;
int k = Ax.Base.NLayers - 1;
for (int i = 0; i < Ax.Base.Cut.Length; i++)
{
double p = Ax.Base.Cut[i];
if (p >= smax - 0.0001)
{
continue;
}
if (!cs)
{
k = i; cs = true;
}
if (p <= smin + 0.0001)
{
break;
}
hpln = CutNetwork.GetPlane(Ax.Dir, p);
CN.Split(hpln, false);
cc = true;
}
if (cc)
{
k = -1;
}
F.AxisLayers[u] = k;
}
F.SetStickers(m, CN, Axes, fctrs);
minrank = Math.Min(minrank, F.MinRank());
}
foreach (PBaseFace F in BaseFaces)
{
F.SubRank(minrank);
}
}
internal PBaseFace(double[] pole)
{
Pole = pole;
SMatrices = new ArrayList();
SMatrices.Add(PGeom.MatrixIdentity(pole.Length));
}
internal PFace(PFace src, double[] tw)
{
Base = src.Base;
Pole = PGeom.ApplyTwist(tw, src.Pole);
Matrix = PGeom.ApplyTwist(tw, src.Matrix);
}
internal void InitPuzzle(Puzzle cube)
{
Cube = cube;
int dim = Cube.Str.Dim;
NF = Cube.Str.Faces.Length;
NStk = Cube.Str.NStickers;
SetColorsArray(null);
StFaces = new StkMesh[NF];
FPoles = new double[NF][];
Stks = new StkMesh[NStk];
BPln = new bool[NF];
int[] vn = new int[100000 * 4];
lVN = 0;
double[][][] FFPoles = new double[NF][][];
for (int i = 0; i < NF; i++)
{
PFace F = Cube.Str.Faces[i];
StFaces[i] = new StkMesh(F.Base.FaceMesh, i, F.Matrix);
FPoles[i] = F.Pole;
int fstk = F.FirstSticker;
for (int j = 0; j < F.Base.NStickers; j++)
{
Stks[fstk + j] = new StkMesh(F.Base.StickerMesh[j], i, F.Matrix);
Stks[fstk + j].FCtr = F.Pole;
}
double[][] baseFFP = F.Base.FPoles;
FFPoles[i] = new double[baseFFP.Length][];
for (int j = 0; j < baseFFP.Length; j++)
{
FFPoles[i][j] = PGeom.ApplyMatrix(F.Matrix, baseFFP[j]);
}
}
for (int i = 0; i < NF; i++)
{
StFaces[i].SetCoord(1, 1);
}
for (int i = 1; i < NF; i++)
{
for (int j = 0; j < i; j++)
{
double[][] pi = FFPoles[i], pj = FFPoles[j];
foreach (double[] vi in pi)
{
foreach (double[] vj in pj)
{
if (PtEq(vi, vj, dim))
{
goto _1;
}
}
}
continue;
_1:
StkMesh Fi = StFaces[i], Fj = StFaces[j];
float[] fpi = Fi.Coords, fpj = Fj.Coords;
for (int i1 = 0; i1 < fpi.Length; i1 += dim)
{
for (int j1 = 0; j1 < fpj.Length; j1 += dim)
{
if (PtEq(fpi, i1, fpj, j1, dim))
{
vn[lVN++] = i;
vn[lVN++] = i1;
vn[lVN++] = j;
vn[lVN++] = j1;
break;
}
}
}
}
}
VertNetwork = new int[lVN];
Buffer.BlockCopy(vn, 0, VertNetwork, 0, lVN * sizeof(int));
}
internal PBaseTwist(double[] dir)
{
Dir = dir;
Order = PGeom.GetOrder(Dir);
}