private double FitCurve()
{
if (m_Group == null || m_Group.Count < 5)
return 0;
Vect2 uv = new Vect2();
Vect3 xyz = new Vect3(), xprev = new Vect3();
List<IFitPoint> fit = new List<IFitPoint>(m_Group.Count);
//get target point on starting yarn
//yar0.xVal(m_sPos, ref uv, ref xyz);
double s1 = m_sPos, d = 0;
//fit.Add(new FixedPoint(uv));
double length = 0, h=0;
Vect2 v;
List<Vect2> combs = new List<Vect2>(m_Group.Count);
for (int i = 0; i < m_Group.Count; i++)
{
m_Group[i].xVal(s1, ref uv, ref xprev);
fit.Add(new FixedPoint(uv[0], uv[1]));
//find closest point on yar1 to the target point on yar0;
if (i < m_Group.Count - 1)
{
xyz.Set(xprev);
//find the spacing to the next yarn
if (!CurveTools.xClosest(m_Group[i + 1], ref s1, ref uv, ref xyz, ref d, 1e-6, true))
Logger.logger.Instance.Log("xClosest failed in DensityComb");
//throw new Exception("xClosest failed in DensityComb");
h = xyz.Distance(xprev);
//store the spacing and x-distance
v = new Vect2();
v[0] = length;
v[1] = m_Group.InverseSpacing(h);
combs.Add(v);
length += h;//accumulate length
}
}
Length = length;
//convert x-distance to s-spacing
for (int i = 0; i < combs.Count; i++)
fit[i][0] = combs[i][0] /= length;
combs.Add(new Vect2(1, m_Group.InverseSpacing(h)));//add endpoint with spacing to previous curve
//fit to the intersection points
SurfaceCurve.SimpleFit(this, fit.ToArray());
FitComb(combs.ToArray());
return DPI = m_Group.YarnDenier * .0254 * (m_Group.Count - 1) / length;
}
public bool xClosest(ref Vect2 uv, ref Vect3 xyzTarget, ref double dist, double tol)
{
Vect3 x = new Vect3(xyzTarget);
Vect3 dxu = new Vect3(), dxv = new Vect3();
Vect3 ddxu = new Vect3(), ddxv = new Vect3(), dduv = new Vect3();
Vect3 h = new Vect3();
Vect2 c = new Vect2();
Vect2 res = new Vect2();
Vect2 a = new Vect2(), b = new Vect2();
double det, r;
Vect2 d = new Vect2();
int loop = 0, max_loops = 150;
while (loop++ < max_loops)
{
xCvt(uv, ref x, ref dxu, ref dxv, ref ddxu, ref ddxv, ref dduv);
h = x - xyzTarget;
//h = BLAS.subtract(x, xyzTarget);
dist = h.Magnitude;
//e[0] = s;
c[0] = h.Dot(dxu);// BLAS.dot(h, dxu); // error, dot product is 0 at pi/2
c[1] = h.Dot(dxv);// BLAS.dot(h, dxv); // error, dot product is 0 at pi/2
if (Math.Abs(c[0]) < tol && Math.Abs(c[1]) < tol) // error is less than the tolerance
{
xyzTarget.Set(x);// return point to caller
return true;
}
a[0] = dxu.Norm + h.Dot(ddxu);
a[1] = b[0] = dxu.Dot(dxv) + h.Dot(dduv);
b[1] = dxv.Norm + h.Dot(ddxv);
//a[0] = BLAS.dot(dxu, dxu) + BLAS.dot(h, ddxu);
//a[1] = BLAS.dot(dxu, dxv) + BLAS.dot(h, dduv);
//b[0] = a[1];
//b[1] = BLAS.dot(dxv, dxv) + BLAS.dot(h, ddxv);
det = a.Cross(b);
//det = BLAS.cross2d(a, b);
d[0] = c.Cross(b) / det;
d[1] = a.Cross(c) / det;
//d[0] = BLAS.cross2d(c, b) / det;
//d[1] = BLAS.cross2d(a, c) / det;
c[0] = 0.01 > Math.Abs(d[0]) ? 1 : 0.01 / Math.Abs(d[0]);
c[1] = 0.01 > Math.Abs(d[1]) ? 1 : 0.01 / Math.Abs(d[1]);
//enforce maximum increment
r = Math.Min(c[0], c[1]);
//increment uv by scaled residuals
//uv = BLAS.subtract(uv, BLAS.scale(d, r));
uv = uv - d * r;
//logger.write_format_line("%.5g\t%.5g\t%.5g\t%.5g\t%.5g\t", x[ox], x[oy], e[ox], e[oy], dist);
}
//s = s0;
return false;
}
public virtual List<Entity> CreateEntities(bool bFitPoints, double TolAngle, out double[] sPos)
{
if (!AllFitPointsValid())
{
sPos = null;
return new List<Entity>();
}
List<double> spos = new List<double>();
const int TEST = 8;
int FitLength = FitPoints.Length;
double[] stest = new double[(FitLength - 1) * TEST];
Vect3[] xtest = new Vect3[(FitLength - 1) * TEST];
Vect2 uv = new Vect2();
Vect3 xyz = new Vect3();
Vect3 dxp = new Vect3(), dxm = new Vect3();
//initial 8 subdivisions per segment
int nFit, nTest = 0;
for (nFit = 1; nFit < FitLength; nFit++)
{
for (int i = 0; i < TEST; i++, nTest++)
{
stest[nTest] = BLAS.interpolate(i, TEST, FitPoints[nFit].S, FitPoints[nFit - 1].S);
xtest[nTest] = new Vect3();
xVal(stest[nTest], ref uv, ref xtest[nTest]);
}
}
//test the midpoint of each subsegment to determine required # of points
int[] nAdd = new int[stest.Length];
double cosA;
double smid;
int nTotal = FitLength;
for (nTest = 1; nTest < stest.Length; nTest++)
{
//midpoint position
smid = (stest[nTest] + stest[nTest - 1]) / 2.0;
xVal(smid, ref uv, ref xyz);
//forward and backward tangents
dxp = xtest[nTest] - xyz;
dxm = xtest[nTest - 1] - xyz;
//change in angle between for and aft tans
cosA = -(dxp.Dot(dxm)) / (dxp.Magnitude * dxm.Magnitude);
Utilities.LimitRange(-1, ref cosA, 1);
cosA = Math.Acos(cosA);
//determine additional points and sum total
nTotal += nAdd[nTest] = (int)(cosA / TolAngle + 1);
}
m_Length = 0;
Vect3 xprev = new Vect3();
Vect3 dx = new Vect3();
List<Point3D> pnts = new List<Point3D>();
List<Vect3> tans = new List<Vect3>();
xVal(stest[0], ref uv, ref xprev);
pnts.Add(new Point3D(xprev.ToArray()));
spos.Add(stest[0]);
for (nTest = 1; nTest < stest.Length; nTest++)
{
for (int i = 1; i <= nAdd[nTest]; i++)
{
smid = ((nAdd[nTest] - i) * stest[nTest - 1] + i * stest[nTest]) / nAdd[nTest];
xVec(smid, ref uv, ref xyz, ref dx);
spos.Add(smid);
pnts.Add(new Point3D(xyz.ToArray()));
tans.Add(new Vect3(dx));
m_Length += xyz.Distance(xprev);
xprev.Set(xyz);
}
}
if (EXTENDENTITY)
{
//add for-cast/back-cast points
for (int i = 0; i < 2; i++)
{
for (nTest = 0; nTest < 10; nTest++)
{
smid = BLAS.interpolant(nTest, 10) * 0.05;//scale down to .1 cast
if (i == 0)
smid = -smid;
else
smid += 1.0;
xVal(smid, ref uv, ref xyz);
if (i == 0)
pnts.Insert(0, new Point3D(xyz.ToArray()));
else
pnts.Add(new Point3D(xyz.ToArray()));
}
}
}
LinearPath lp = new LinearPath(pnts);
lp.EntityData = this;
//lp.LineWeight = 3.0f;
//lp.LineWeightMethod = colorMethodType.byEntity;
List<Entity> tanpaths = new List<Entity>();
tanpaths.Add(lp);
if (bFitPoints)
{
//LinearPath path;
//int npnt = 0;
//foreach (Vect3 pnt in tans)
//{
// pnt.Magnitude = 2;
// xyz = new Vect3(pnts[npnt].ToArray());
// xyz += pnt;
// path = new LinearPath(pnts[npnt], new Point3D(xyz.ToArray()));
// path.EntityData = this;
// tanpaths.Add(path);
// npnt++;
// //xVal(pnt.UV, ref xyz);
// //pnts.Add(new Point3D(xyz.ToArray()));
//}
pnts = new List<Point3D>();
foreach (IFitPoint pnt in FitPoints)
{
xVal(pnt.UV, ref xyz);
pnts.Add(new Point3D(xyz.ToArray()));
}
PointCloud pc = new PointCloud(pnts, 8f);
pc.EntityData = this;
tanpaths.Add(pc);
}
sPos = spos.ToArray();
return tanpaths;
}
/// <summary>
/// Interpolates intermediate points in uv and fits a curve
/// </summary>
/// <param name="c">the curve to fit</param>
/// <param name="points">points to fit to, minimum 2</param>
internal static void InterpoFit(MouldCurve c, IFitPoint[] points)
{
if (points.Length <= 1 || points.Length >= 5)//need at least 2 points to fit a curve, can't interpolate more than 4
return;
//recalculate s-positions based on xyz-values
//if (RePos)
//{
// Vect2 uv = new Vect2();
// Vect3 x0 = new Vect3();
// Vect3 x1 = new Vect3();
// fits[0][0] = 0;//initialize s paramter
// Surface.xVal(fits[0].UV, ref x0);//initialize starting x point
// for (int nFit = 1; nFit < fits.Length; nFit++)
// {
// Surface.xVal(fits[nFit].UV, ref x1);
// fits[nFit][0] = fits[nFit - 1][0] + x1.Distance(x0);
// x1.Set(x0);//store previous x point
// }
// for (int nFit = 0; nFit < fits.Length; nFit++)
// fits[nFit][0] /= fits.Last()[0];//convert length to position
// fits.Last()[0] = 1;//enforce unit length
//}
//linear uv interpolation to match minimum 5 points required
double[][] uFits = new double[2][];
double[] sFits = new double[5];
uFits[0] = new double[5];
uFits[1] = new double[5];
double p;
int i, nint = 0;
Vect3 x2 = new Vect3(), x1 = new Vect3();
Vect2 umid = new Vect2();
Dictionary<int, int> FitstoSFits = new Dictionary<int, int>();
if (points.Length == 4)
{
//store fitpoints
sFits[nint] = points[nint][0] = 0;
uFits[0][nint] = points[nint][1];
uFits[1][nint] = points[nint][2];
c.xVal(points[nint].UV, ref x1);
FitstoSFits[nint] = nint;
nint++;
//store fitpoints
//sFits[nint] = fits[nint][0];
uFits[0][nint] = points[nint][1];
uFits[1][nint] = points[nint][2];
c.xVal(points[nint].UV, ref x2);
sFits[nint] = x2.Distance(x1) + sFits[nint - 1];
FitstoSFits[nint] = nint;
nint++;
//insert midpoint
//sFits[nint] = (fits[nint][0] + fits[nint - 1][0]) / 2.0;
umid = points[nint].UV + points[nint - 1].UV;
umid /= 2;
uFits[0][nint] = umid[0];
uFits[1][nint] = umid[1];
c.xVal(umid, ref x1);
sFits[nint] = x2.Distance(x1) + sFits[nint - 1];
nint++;
//store fitpoints
//sFits[nint] = fits[nint-1][0];
uFits[0][nint] = points[nint - 1][1];
uFits[1][nint] = points[nint - 1][2];
c.xVal(points[nint - 1].UV, ref x2);
sFits[nint] = x2.Distance(x1) + sFits[nint - 1];
FitstoSFits[nint - 1] = nint;
nint++;
//store fitpoints
//sFits[nint] = fits[nint-1][0];
uFits[0][nint] = points[nint - 1][1];
uFits[1][nint] = points[nint - 1][2];
c.xVal(points[nint - 1].UV, ref x1);
sFits[nint] = x2.Distance(x1) + sFits[nint - 1];
FitstoSFits[nint - 1] = nint;
nint++;
}
else
{
int num = (5 - points.Length) / (points.Length - 1);//insertion points
num = num < 1 ? 1 : num;
for (i = 0; i < points.Length - 1; i++)
{
//store fitpoints
//sFits[nint] = fits[i][0];
uFits[0][nint] = points[i][1];
uFits[1][nint] = points[i][2];
FitstoSFits[i] = nint;
c.xVal(points[i].UV, ref x1);
if (i == 0)
{
sFits[nint] = 0;
}
else
{
sFits[nint] = x2.Distance(x1) + sFits[nint - 1];
}
x2.Set(x1);//store xprev
nint++;
for (int j = 1; j <= num; j++)
{
//interpolate insertion points and store
p = BLAS.interpolant(j, num + 2);
//sFits[nint] = BLAS.interpolate(p, fits[i + 1][0], fits[i][0]);
umid[0] = uFits[0][nint] = BLAS.interpolate(p, points[i + 1][1], points[i][1]);
umid[1] = uFits[1][nint] = BLAS.interpolate(p, points[i + 1][2], points[i][2]);
c.xVal(umid, ref x1);
sFits[nint] = x2.Distance(x1) + sFits[nint - 1];
x2.Set(x1);//store xprev
nint++;
}
}
//endpoint
//sFits[nint] = 1;
uFits[0][nint] = points[i][1];
uFits[1][nint] = points[i][2];
c.xVal(points[i].UV, ref x1);
sFits[nint] = x2.Distance(x1) + sFits[nint - 1];
System.Diagnostics.Debug.Assert(nint == 4);
FitstoSFits[i] = nint;
}
for (i = 0; i < sFits.Length; i++)
sFits[i] /= sFits.Last();
//sFits[sFits.Length - 1] = 1;
foreach (int key in FitstoSFits.Keys)
points[key][0] = sFits[FitstoSFits[key]];
c.FitPoints = points;
c.ReSpline(sFits, uFits);
}
/// <summary>
/// fit a curve to the specified points
/// requires S parameter specified for each point
/// requires at least 5 points
/// </summary>
/// <param name="points">points to fit to, minimum 5</param>
internal static void SimpleFit(MouldCurve c, IFitPoint[] points)
{
Vect2 uv = new Vect2();
Vect3 x0 = new Vect3();
Vect3 x1 = new Vect3();
double[][] uFits = new double[2][];
double[] sFits = new double[points.Length];
uFits[0] = new double[points.Length];
uFits[1] = new double[points.Length];
//complile fitpoints to fitting arrays
sFits[0] = 0;
points[0][0] = 0;
c.xVal(points[0].UV, ref x0);//initialize starting x point
for (int nFit = 0; nFit < points.Length; nFit++)
{
//sFits[nFit] = fits[nFit][0];
uFits[0][nFit] = points[nFit][1];
uFits[1][nFit] = points[nFit][2];
if (nFit > 0)
{
c.xVal(points[nFit].UV, ref x1);
points[nFit][0] = points[nFit - 1][0] + x1.Distance(x0);
x0.Set(x1);//store previous x point
}
}
for (int nFit = 0; nFit < points.Length; nFit++)
sFits[nFit] = points[nFit][0] /= points.Last()[0];//convert length to position
//sFits[sFits.Length-1] = fits.Last()[0] = 1;//enforce unit length
c.FitPoints = points;
c.ReSpline(sFits, uFits);
}
/// <summary>
/// using the start, end and passed geo fit points will slide the points along their normals to achieve a geodesic
/// </summary>
/// <param name="g">the curve object to spline</param>
/// <param name="start">the starting point of this segment</param>
/// <param name="end">the ending point of this segment</param>
/// <param name="sFits">the s-positons of each geo-point</param>
/// <param name="uFits">the u-positons of each geo-point</param>
/// <returns>true if successful, false otherwise</returns>
static bool FitGeo(MouldCurve g, IFitPoint start, IFitPoint end, double[] sFits, Vect2[] uFits)
{
int NumFits = sFits.Length;
int INC = NumFits - 1;
int i;
Vect2[] uNor = new Vect2[NumFits];
Vect3 xyz = new Vect3(), dxu = new Vect3(), dxv = new Vect3();
Vect2 ut = new Vect2(), un = new Vect2();
double a11, a12, a22, det;
//calculate insurface normals at each fitpoint
uNor[0] = new Vect2();//fixed endpoint doesnt need normal
for (i = 1; i < INC; i++)
{
g.Surface.xVec(uFits[i], ref xyz, ref dxu, ref dxv);
//covariant metric tensor components
a11 = dxu.Norm;
a12 = dxu.Dot(dxv);
a22 = dxv.Norm;
det = Math.Sqrt(a11 * a22 - a12 * a12);
//tangent(secant) vector u components
ut = uFits[i + 1] - uFits[i - 1];
//contravariant normal vector components in the surface plane
un[0] = (a12 * ut[0] + a22 * ut[1]) / det;
un[1] = -(a11 * ut[0] + a12 * ut[1]) / det;
//store unit normal u components
un.Magnitude = 1;
uNor[i] = new Vect2(un);
}
uNor[INC] = new Vect2();//fixed endpoint doesnt need normal
Vect3 xPrev = new Vect3();
Vect3 ddxu = new Vect3(), ddxv = new Vect3(), dduv = new Vect3();
Vect3[] xNor = new Vect3[NumFits];
Vect3[] dxNor = new Vect3[NumFits];
Vect3[] xTan = new Vect3[NumFits];
double[] xLen = new double[NumFits];
bool Conver = false;
int nNwt; Vector x; DenseVector sNor;
for (nNwt = 0; nNwt < 50; nNwt++)
{
xNor[0] = new Vect3();
//update startpoint slide position
if (start is SlidePoint)
{
dxNor[0] = new Vect3();
(start as SlidePoint).Curve.xCvt((start as SlidePoint).SCurve, ref uFits[0], ref xPrev, ref xNor[0], ref dxNor[0]);
//uFits[0][0] = FitPoints[0][1];
//uFits[0][1] = FitPoints[0][2];
}
else
g.xVal(uFits[0], ref xPrev);
//update endpoint slide position
if (end is SlidePoint)
{
uFits[INC][0] = end[1];
uFits[INC][1] = end[2];
}
xLen[0] = 0;
//calc internal point vectors
for (i = 1; i < NumFits; i++)
{
g.Surface.xCvt(uFits[i], ref xyz, ref dxu, ref dxv, ref ddxu, ref ddxv, ref dduv);
a11 = uNor[i][0] * uNor[i][0];
a12 = uNor[i][0] * uNor[i][1] * 2;
a22 = uNor[i][1] * uNor[i][1];
// insurface normal x components
dxu.Scale(uNor[i][0]);
dxv.Scale(uNor[i][1]);
xNor[i] = dxu + dxv;
//insurface normal x derivatives
ddxu.Scale(a11);
dduv.Scale(a12);
ddxv.Scale(a22);
dxNor[i] = ddxu + dduv + ddxv;
//forward facing tangent vector
xTan[i] = xyz - xPrev;
xPrev.Set(xyz);
xLen[i] = xTan[i].Magnitude;//segment length
xLen[0] += xLen[i];//accumulate total length
xTan[i].Magnitude = 1;//unit tangent vector
}
//update endpoint slide position
if (end is SlidePoint)
{
(end as SlidePoint).Curve.xCvt((end as SlidePoint).SCurve, ref uFits[INC], ref xyz, ref xNor[INC], ref dxNor[INC]);
}
DenseMatrix A = new DenseMatrix(NumFits);
sNor = new DenseVector(NumFits);
double p0, pp, d, d0, dp, gm, g0, gp; int ix;
//slide startpoint
if (start is SlidePoint)
{
//mid point normal vector dotted with end point tangent vectors
pp = xNor[0].Dot(xTan[1]);
for (g0 = gp = 0, ix = 0; ix < 3; ix++)
{
//midpoint tangent and curavture variantion
dp = (xNor[0][ix] - pp * xTan[1][ix]) / xLen[1];
//mid and top point gradients
g0 += -dp * xNor[0][ix] + xTan[1][ix] * dxNor[0][ix];
gp += dp * xNor[1][ix];
}
//geodesic residual and gradients
A[0, 0] = g0;
A[0, 1] = gp;
sNor[0] = pp;
}
else//fixed start point
{
A[0, 0] = 1;
sNor[0] = 0;
}
for (i = 1; i < INC; i++)//internal points
{
//midpoint normal dotted with tangents
p0 = xNor[i].Dot(xTan[i]);// BLAS.dot(xNor[i], xTan[i]);
pp = xNor[i].Dot(xTan[i + 1]);//BLAS.dot(xNor[i], xTan[i + 1]);
for (gm = g0 = gp = 0, ix = 0; ix < 3; ix++)
{
//midpoint curvature vector
d = xTan[i + 1][ix] - xTan[i][ix];
//midpoint tangent and curavture variantion
d0 = (xNor[i][ix] - p0 * xTan[i][ix]) / xLen[i];
dp = (xNor[i][ix] - pp * xTan[i + 1][ix]) / xLen[i + 1];
//bottom, mid and top point gradients
gm += d0 * xNor[i - 1][ix];
g0 += (-d0 - dp) * xNor[i][ix] + d * dxNor[i][ix];
gp += dp * xNor[i + 1][ix];
}
A[i, i - 1] = gm;
A[i, i] = g0;
A[i, i + 1] = gp;
sNor[i] = -p0 + pp;
}
if (end is SlidePoint)//slide endpoint
{
p0 = xNor[i].Dot(xTan[i]);
for (gm = g0 = 0, ix = 0; ix < 3; ix++)
{
//midpoint tangent and curavture variantion
d0 = (xNor[i][ix] - p0 * xTan[i][ix]) / xLen[i];
//bottom, mid and top point gradients
gm += d0 * xNor[i - 1][ix];
g0 += -d0 * xNor[i][ix] - xTan[i][ix] * dxNor[i][ix];
}
A[i, i - 1] = gm;
A[i, i] = g0;
sNor[i] = -p0;
}
else//fixed endpoint
{
A[i, i] = 1;
sNor[i] = 0;
}
LU decomp = A.LU();
x = (Vector)decomp.Solve(sNor);
double Reduce = Math.Min(1, .05 / x.AbsoluteMaximum());
if( start is SlidePoint)
(start as SlidePoint).SCurve -= x[0] * Reduce;
if( end is SlidePoint)
(end as SlidePoint).SCurve -= x[INC] * Reduce;
for (i = 1; i < NumFits; i++)//increment uv points
{
uFits[i][0] -= x[i] * uNor[i][0] * Reduce;
uFits[i][1] -= x[i] * uNor[i][1] * Reduce;
}
if (nNwt < 5)
{
//keep initial (s)-increments within bounds
if (start is SlidePoint)
(start as SlidePoint).SCurve = Utilities.LimitRange(0, (start as SlidePoint).SCurve, 1);
if (end is SlidePoint)
(end as SlidePoint).SCurve = Utilities.LimitRange(0, (end as SlidePoint).SCurve, 1);
// keep initial (u)-increments within bounds
for (i = 1; i < NumFits - 1; i++)
{
uFits[i][0] = Utilities.LimitRange(0, uFits[i][0], 1);
uFits[i][1] = Utilities.LimitRange(-.125, uFits[i][1], 1.125);
}
}
double xmax = x.AbsoluteMaximum();
double smax = sNor.AbsoluteMaximum();
if (Conver = (x.AbsoluteMaximum() < 1e-8 && sNor.AbsoluteMaximum() < 1e-7))
break;
}
if (!Conver)
return false;
g.Length = xLen[0];//store length
//calculate unit length (s)-parameter values
sFits[0] = 0;
for (i = 1; i < NumFits; i++)
sFits[i] = sFits[i - 1] + xLen[i] / xLen[0];
//g.m_uvs = uFits;
g.ReSpline(sFits, uFits);
return true;
}
