/// <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);
}
public static Point3D[] GetCloudPoints(MouldCurve c)
{
Point3D[] pnts;
Vect2 uv = new Vect2();
Vect3 xyz = new Vect3();
pnts = new Point3D[c.FitPoints.Length];
double s;
for (int i = 0; i < c.FitPoints.Length; i++)
{
s = c[i].S;
c.xVal(s, ref uv, ref xyz);
Utilities.Vect3ToPoint3D(ref pnts[i], xyz);
}
return pnts;
}
/// <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>
/// inserts additional points into the geo-point arrays to ensure a smooth, linear geo
/// </summary>
/// <param name="g">the curve object to spline</param>
/// <param name="sFits">in: the initial set of geo-points s-positions, out: an interpolated set of geo-point s-pos</param>
/// <param name="uFits">in: the initial set of geo-points u-positions, out: an interpolated set of geo-point u-pos</param>
static void RefineGeo(MouldCurve g, ref double[] sFits, ref Vect2[] uFits)
{
int NumFits = sFits.Length;
List<double> sPos = new List<double>(NumFits * 10);
int uAdd, xAdd, sAdd;
double s, dau;
Vect2 uv = new Vect2();//, um = new Vect2(), up = new Vect2();
Vect2 dmu = new Vect2(), dpu = new Vect2();
Vect3 xyz = new Vect3(), dmx = new Vect3(), dpx = new Vect3();
sPos.Add(sFits[0]);
for (int i = 1; i < NumFits; i++)
{
s = (sFits[i - 1] + sFits[i]) / 2.0;
g.xVal(s, ref uv, ref xyz);
dmu = uFits[i - 1] - uv;
dpu = uFits[i] - uv;
dau = Math.Acos(-(dmu.Dot(dpu)) / dmu.Magnitude / dpu.Magnitude);
uAdd = (int)(dau / (Math.PI / 180.0) + 1);
g.xVal(uFits[i - 1], ref dmx);
g.xVal(uFits[i], ref dpx);
dmx = dmx - xyz;
dpx = dpx - xyz;
dau = Math.Acos(-(dmx.Dot(dpx)) / dmx.Magnitude / dpx.Magnitude);
xAdd = (int)(dau / (Math.PI / 180.0) + 1);
sAdd = Math.Max(xAdd, uAdd);
for (int iS = 1; iS <= sAdd; iS++)
{
s = BLAS.interpolate((double)iS / (double)sAdd, sFits[i], sFits[i - 1]);
sPos.Add(s);//add evenly spaced s points
}
}
uFits = new Vect2[sPos.Count];
sFits = new double[sPos.Count];
int iA = 0;
foreach (double sA in sPos)
{
uFits[iA] = new Vect2();
g.uVal(sA, ref uFits[iA]);
sFits[iA] = sA;
iA++;
}
}
/// <summary>
/// Fits a multi-segement geodesic between the specified fitpoints optionally specifying which segments to girth
/// </summary>
/// <param name="points">the array of fitpoints, must be more than 2</param>
/// <param name="bGirths">an array specifying which segments to girth and which to spline
/// count is 1 less than the fitpoints count
/// can be null which defaults to first and last segment girths</param>
/// <returns>true if successful, false otherwise</returns>
internal static bool Geo(MouldCurve g, IFitPoint[] points)
{
if (points == null || points.Length < 2)
return false;
else if (points.Length == 2 && g.IsGirth(0))
return Geo(g, points[0], points[1]);
//compiled piecewise values
List<double> S = new List<double>();
List<Vect2> U = new List<Vect2>();
//segment values
double[] spos = null;
Vect2[] upos = null;
Vect3 xyz = new Vect3(), xyp = new Vect3();
//initialize S and U
points[0].S = 0;
S.Add(0);
U.Add(points[0].UV);
for (int i = 1; i < points.Length; i++)
{
//span a geo between the fitpoints
//if (i % 2 == 1)
if( g.IsGirth(i-1) )
{
if (!GeoSegment(g, points[i - 1], points[i], ref spos, ref upos))
return false;
for (int nS = 1; nS < spos.Length; nS++)
{
//scale the spos by length to get distance
S.Add(spos[nS] * g.Length + points[i - 1].S);
//copy the upos
U.Add(upos[nS]);
}
}
else// if (i % 2 == 0)
{
g.xVal(points[i - 1].UV, ref xyp);
g.xVal(points[i].UV, ref xyz);
S.Add(xyz.Distance(xyp) + points[i-1].S);
U.Add(points[i].UV);
}
points[i].S = S.Last();//store the curent length for paramterization
}
//reparamaterize
g.Length = S.Last();
for (int i = 0; i < S.Count; i++)
S[i] /= g.Length;
for (int i = 0; i < points.Length; i++)
points[i].S /= g.Length;
//spline the combined points
g.ReSpline(S.ToArray(), U.ToArray());
g.FitPoints = points;
return true;
}
/// <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;
}
/// <summary>
/// Fits a geodesic between the start and end points and returns the geo fit arrays for post-processing
/// </summary>
/// <param name="g">the curve object to fit with</param>
/// <param name="start">the starting point of the segment</param>
/// <param name="end">the end point of the segment</param>
/// <param name="sFits">in: null, out: the segment s-positions of each geo fitting point</param>
/// <param name="uFits">in: null, out: the segment u-positions of each geo fitting point</param>
/// <returns>true if successful, false otherwise</returns>
internal static bool GeoSegment(MouldCurve g, IFitPoint start, IFitPoint end, ref double[] sFits, ref Vect2[] uFits)
{
if (start == end || start.UV == end.UV || (start is SlidePoint && end is SlidePoint))
return false;
//start.S = 0;
//end.S = 1;
int REZ = 9;
int END = REZ - 1;
int i;
double d = 0, sguess;
Vect3 xI = new Vect3(), xs = new Vect3(), xe = new Vect3();
Vect2 utemp = new Vect2();
uFits = new Vect2[REZ];
sFits = new double[REZ];
//attempt a better starting slide position
if (start is SlidePoint)
{
g.xVal(end.UV, ref xI);
sguess = (start as SlidePoint).SCurve;
if ((start as SlidePoint).Curve.xClosest(ref sguess, ref utemp, ref xI, ref d, 1e-9, false))
(start as SlidePoint).SCurve = sguess;
}
sFits[0] = 0;
uFits[0] = new Vect2(start.UV);
//attempt a better starting slide position
if (end is SlidePoint)
{
g.xVal(uFits[0], ref xI);
sguess = (end as SlidePoint).SCurve;
if ((end as SlidePoint).Curve.xClosest(ref sguess, ref utemp, ref xI, ref d, 1e-9, false))
(end as SlidePoint).SCurve = sguess;
}
sFits[END] = 1;
uFits[END] = new Vect2(end.UV);
//interpolate 8 internal points in xyz
g.xVal(uFits[0], ref xs);
g.xVal(uFits[END], ref xe);
for (i = 1; i < END; i++)
{
uFits[i] = new Vect2();
sFits[i] = (double)i / (double)END;
for (int j = 0; j < 3; j++)
xI[j] = BLAS.interpolate(sFits[i], xe[j], xs[j]);
for (int j = 0; j < 2; j++)//interpolate starting uv guess
uFits[i][j] = BLAS.interpolate(sFits[i], uFits[END][j], uFits[0][j]);
if (!g.Surface.xClosest(ref uFits[i], ref xI, ref d, 1e-5))
for (int j = 0; j < 2; j++)//default to uv interp if xyz fails
uFits[i][j] = BLAS.interpolate(sFits[i], uFits[END][j], uFits[0][j]);
}
if (!FitGeo(g, start, end, sFits, uFits))
return false;
RefineGeo(g, ref sFits, ref uFits);
return FitGeo(g, start, end, sFits, uFits);
}
