protected virtual void FillXDerivations(KnotMatrix values)
{
for (var j = 0; j < values.Columns; j++)
{
FillXDerivations(j, values);
}
}
private static void OriginalKnots(KnotMatrix newKnots,
KnotMatrix oldKnots)
{
for (var i = 0; i < oldKnots.Rows; i++)
{
for (var j = 0; j < oldKnots.Columns; j++)
{
newKnots[2*i, 2*j] = oldKnots[i, j];
}
}
}
public override KnotMatrix GenerateKnots(
SurfaceDimension uDimension, SurfaceDimension vDimension)
{
var afvOld = _baseGenerator.GenerateKnots(uDimension/2,
vDimension/2);
var uCountNew = uDimension.KnotCount;
var vCountNew = vDimension.KnotCount;
var afvNew = new KnotMatrix(uCountNew, vCountNew);
FillNewKnots(afvNew, afvOld);
return afvNew;
}
protected virtual void FillXYDerivations(int columnIndex,
KnotMatrix values,
double[] lowerDiagonal = null, double[] mainDiagonal = null,
double[] upperDiagonal = null)
{
var unknownsCount = values.Rows - 2;
if (unknownsCount == 0) return;
Action<int, double> dset =
(idx, value) => values[idx, columnIndex].Dxy = value;
Func<int, double> rget = idx => values[idx, columnIndex].Dy;
var h = values[1, 0].X - values[0, 0].X;
var dlast = values[values.Rows - 1, columnIndex].Dxy;
var dfirst = values[0, columnIndex].Dxy;
SolveTridiagonal(rget, h, dfirst, dlast, unknownsCount, dset,
lowerDiagonal, mainDiagonal, upperDiagonal);
}
protected override void FillXYDerivations(KnotMatrix values)
{
base.FillXYDerivations(0, values,
LowerDiagonal(values.Rows - 2), MainDiagonal(values.Rows - 2),
UpperDiagonal(values.Rows - 2));
base.FillXYDerivations(values.Columns - 1, values,
LowerDiagonal(values.Rows - 2), MainDiagonal(values.Rows - 2),
UpperDiagonal(values.Rows - 2));
base.FillYXDerivations(0, values,
LowerDiagonal(values.Columns - 2),
MainDiagonal(values.Columns - 2),
UpperDiagonal(values.Columns - 2));
base.FillYXDerivations(values.Rows - 1, values,
LowerDiagonal(values.Columns - 2),
MainDiagonal(values.Columns - 2),
UpperDiagonal(values.Columns - 2));
}
internal IEnumerable<ISurface> CreateMesh(KnotMatrix knots)
{
var uCount_min_1 = knots.Rows - 1;
var vCount_min_1 = knots.Columns - 1;
var segments = new List<ISurface>(uCount_min_1*vCount_min_1);
for (var i = 0; i < uCount_min_1; i++)
{
for (var j = 0; j < vCount_min_1; j++)
{
var segment = CreateSegment(i, j, knots);
segments.Add(segment);
}
}
return segments;
}
protected override void FillXDerivations(KnotMatrix values)
{
var h = values[1, 0].X - values[0, 0].X;
var oneDivH = 1/h;
var threeDiv4H = 0.75*oneDivH;
for (var j = 0; j < values.Columns; j++)
{
FillXDerivations(j, values);
for (var i = 1; i < values.Rows - 1; i += 2)
{
values[i, j].Dx = threeDiv4H
*(values[i + 1, j].Z - values[i - 1, j].Z)
- 0.25
*(values[i + 1, j].Dx
+ values[i - 1, j].Dx);
}
}
}
public override KnotMatrix GenerateKnots(SurfaceDimension uDimension,
SurfaceDimension vDimension)
{
if (uDimension.KnotCount < 4
|| vDimension.KnotCount < 4)
{
return
new DirectKnotsGenerator(Function).GenerateKnots(
uDimension, vDimension);
}
var values = new KnotMatrix(uDimension.KnotCount,
vDimension.KnotCount);
InitializeKnots(uDimension, vDimension, values);
FillXDerivations(values);
FillXYDerivations(values);
FillYDerivations(values);
FillYXDerivations(values);
return values;
}
protected override void FillYDerivations(KnotMatrix values)
{
var h = values[0, 1].Y - values[0, 0].Y;
var oneDivH = 1/h;
var threeDiv4H = 0.75*oneDivH;
for (var i = 0; i < values.Rows; i++)
{
FillYDerivations(i, values);
//for (var j = 1; j < values.Columns - 1; j += 2)
//{
// values[i, j].Dy = threeDiv4H * (values[i, j + 1].Z - values[i, j - 1].Z)
// - 0.25 * (values[i, j + 1].Dy + values[i, j - 1].Dy);
//}
}
for (var i = 0; i < values.Rows; i++)
{
for (var j = 1; j < values.Columns - 1; j += 2)
{
values[i, j].Dy = threeDiv4H
*(values[i, j + 1].Z - values[i, j - 1].Z)
- 0.25
*(values[i, j + 1].Dy
+ values[i, j - 1].Dy);
}
}
}
using System;
using HermiteInterpolation.MathFunctions;
using HermiteInterpolation.Numerics;
using HermiteInterpolation.SplineKnots;
using HermiteInterpolation.Utils;
namespace HermiteInterpolation.Shapes.SplineInterpolation
{
public class BiquarticHermiteSurface : BicubicHermiteSurface
{
private class BiquarticKnotsGenerator : KnotsGenerator
{
private readonly KnotsGenerator _baseGenerator;
public BiquarticKnotsGenerator(KnotsGenerator baseGenerator)
: base(baseGenerator.Function)
{
_baseGenerator = baseGenerator;
}
public override KnotMatrix GenerateKnots(SurfaceDimension uDimension, SurfaceDimension vDimension)
{
var afvOld = _baseGenerator.GenerateKnots(uDimension/2, vDimension/2);
var uCountNew = uDimension.KnotCount;
var vCountNew = vDimension.KnotCount;
var afvNew = new KnotMatrix(uCountNew, vCountNew);
FillNewKnots(afvNew, afvOld);
return afvNew;
}
private void FillNewKnots(KnotMatrix newKnots,
KnotMatrix oldKnots)
{
// z, dx, dy, dxy initialization
OriginalKnots(newKnots, oldKnots);
// z, dx, deltay, deltaxy
VerticalKnots(newKnots);
// z, Dx, dy, Dxy
HorizontalKnots(newKnots);
// z, Dx, deltay, deltaxy
InnerKnots(newKnots);
}
private void InnerKnots(KnotMatrix newKnots)
{
for (int i = 1; i < newKnots.Rows; i += 2)
{
for (int j = 1; j < newKnots.Columns; j += 2)
{
var u0v0 = newKnots[i - 1,j - 1];
var u1v0 = newKnots[i,j - 1];
var u2v0 = newKnots[i + 1,j - 1];
var u0v1 = newKnots[i - 1,j];
var u1v1 = new Knot();
var u2v1 = newKnots[i + 1,j];
var u0v2 = newKnots[i - 1,j + 1];
var u1v2 = newKnots[i,j + 1];
var u2v2 = newKnots[i + 1,j + 1];
var hx = Math.Abs(u2v0.X - u0v0.X) / 2;
var hx4 = hx * 4;
var hy = Math.Abs(u0v2.Y - u0v0.Y) / 2;
var hy4 = hy * 4;
var x = u0v1.X + hx;
var y = u1v0.Y + hy;
u1v1.X = x;
u1v1.Y = y;
u1v1.Z = Function.Z(x, y);
u1v1.Dx = -(3 * (u0v1.Z - u2v1.Z) + hx * (u0v1.Dx + u2v1.Dx)) /
hx4;
u1v1.Dy = -(3 * (u1v0.Z - u1v2.Z) + hx * (u1v0.Dx + u1v2.Dx)) /
hy4;
u1v1.Dxy = (u0v0.Dxy + u2v0.Dxy + u0v2.Dxy + u2v2.Dxy +
(3 *
((u0v0.Dy - u2v0.Dy + u0v2.Dy - u2v2.Dy) / hx +
(u0v0.Dx + u2v0.Dx - u0v2.Dx - u2v2.Dx) / hy +
(3 * (u0v0.Z - u2v0.Z - u0v2.Z + u2v2.Z)) / (hx * hy)))) /
16;
newKnots[i,j] = u1v1;
}
}
}
private void HorizontalKnots(KnotMatrix newKnots)
{
for (int i = 1; i < newKnots.Rows; i += 2)
{
for (int j = 0; j < newKnots.Columns; j += 2)
{
var u0 = newKnots[i - 1,j];
var u1 = new Knot();
// finished
var u2 = newKnots[i + 1,j];
var hx = Math.Abs(u2.X - u0.X) / 2;
var hx4 = hx * 4;
var x = u0.X + hx;
var y = u0.Y;
u1.X = x;
u1.Y = y;
u1.Z = Function.Z(x, y);
u1.Dy = Function.Dy(x, y);
u1.Dx = -(3 * (u0.Z - u2.Z) + hx * (u0.Dx + u2.Dx)) /
hx4;
u1.Dxy = -(3 * (u0.Dy - u2.Dy) + hx * (u0.Dxy + u2.Dxy)) /
hx4;
// finished
newKnots[i,j] = u1;
}
}
}
private void VerticalKnots(KnotMatrix newKnots)
{
for (int i = 0; i < newKnots.Rows; i += 2)
{
for (int j = 1; j < newKnots.Columns; j += 2)
{
var v0 = newKnots[i,j - 1];
var v1 = new Knot();
// finished
var v2 = newKnots[i,j + 1];
var hy = Math.Abs(v2.Y - v0.Y) / 2;
var hy4 = hy * 4;
var x = v0.X;
var y = v0.Y + hy;
v1.X = x;
v1.Y = y;
v1.Z = Function.Z(x, y);
v1.Dx = Function.Dx(x, y);
v1.Dy = -(3 * (v0.Z - v2.Z) + hy * (v0.Dy + v2.Dy)) /
hy4;
v1.Dxy = -(3 * (v0.Dx - v2.Dx) + hy * (v0.Dxy + v2.Dxy)) /
hy4;
// finished
newKnots[i,j] = v1;
}
}
}
private static void OriginalKnots(KnotMatrix newKnots, KnotMatrix oldKnots)
{
for (var i = 0; i < oldKnots.Rows; i++)
{
for (var j = 0; j < oldKnots.Columns; j++)
{
newKnots[2 * i,2 * j] = oldKnots[i,j];
}
}
}
}
public BiquarticHermiteSurface(SurfaceDimension uDimension, SurfaceDimension vDimension, MathExpression mathExpression, Derivation derivation = Derivation.Zero) : this(uDimension, vDimension, InterpolativeMathFunction.FromExpression(mathExpression), derivation)
{
}
public BiquarticHermiteSurface(SurfaceDimension uDimension, SurfaceDimension vDimension, InterpolativeMathFunction interpolativeMathFunction, Derivation derivation = Derivation.Zero) : this(uDimension, vDimension, new DirectKnotsGenerator(interpolativeMathFunction), derivation)
{
}
public BiquarticHermiteSurface(SurfaceDimension uDimension, SurfaceDimension vDimension, KnotsGenerator knotsGenerator, Derivation derivation = Derivation.Zero) : base(uDimension, vDimension, new BiquarticKnotsGenerator(knotsGenerator), derivation)
{
}
}
}
private void VerticalKnots(KnotMatrix newKnots)
{
for (var i = 0; i < newKnots.Rows; i += 2)
{
for (var j = 1; j < newKnots.Columns; j += 2)
{
var v0 = newKnots[i, j - 1];
var v1 = new Knot();
// finished
var v2 = newKnots[i, j + 1];
var hy = Math.Abs(v2.Y - v0.Y)/2;
var hy4 = hy*4;
var x = v0.X;
var y = v0.Y + hy;
v1.X = x;
v1.Y = y;
v1.Z = Function.Z(x, y);
v1.Dx = Function.Dx(x, y);
v1.Dy = -(3*(v0.Z - v2.Z) + hy*(v0.Dy + v2.Dy))/
hy4;
v1.Dxy = -(3*(v0.Dx - v2.Dx) + hy*(v0.Dxy + v2.Dxy))/
hy4;
// finished
newKnots[i, j] = v1;
}
}
}
protected virtual void FillXYDerivations(KnotMatrix values)
{
FillXYDerivations(0, values);
FillXYDerivations(values.Columns - 1, values);
}
private void FillNewKnots(KnotMatrix newKnots,
KnotMatrix oldKnots)
{
// z, dx, dy, dxy initialization
OriginalKnots(newKnots, oldKnots);
// z, dx, deltay, deltaxy
VerticalKnots(newKnots);
// z, Dx, dy, Dxy
HorizontalKnots(newKnots);
// z, Dx, deltay, deltaxy
InnerKnots(newKnots);
}
protected virtual void InitializeKnots(SurfaceDimension uDimension,
SurfaceDimension vDimension, KnotMatrix values)
{
var uSize = Math.Abs(uDimension.Max - uDimension.Min)
/(uDimension.KnotCount - 1);
var vSize = Math.Abs(vDimension.Max - vDimension.Min)
/(vDimension.KnotCount - 1);
var u = uDimension.Min;
for (var i = 0; i < uDimension.KnotCount; i++, u += uSize)
{
var v = vDimension.Min;
for (var j = 0; j < vDimension.KnotCount; j++, v += vSize)
{
var z = Function.Z.SafeCall(u, v);
values[i, j] = new Knot(u, v, z);
}
}
// Init Dx
var uKnotCountMin1 = uDimension.KnotCount - 1;
for (var j = 0; j < vDimension.KnotCount; j++)
{
values[0, j].Dx = Function.Dx.SafeCall(values[0, j].X,
values[0, j].Y);
values[uKnotCountMin1, j].Dx =
Function.Dx.SafeCall(values[uKnotCountMin1, j].X,
values[uKnotCountMin1, j].Y);
}
// Init Dy
var vKnotCountMin1 = vDimension.KnotCount - 1;
for (var i = 0; i < uDimension.KnotCount; i++)
{
values[i, 0].Dy = Function.Dy.SafeCall(values[i, 0].X,
values[i, 0].Y);
values[i, vKnotCountMin1].Dy =
Function.Dy.SafeCall(values[i, vKnotCountMin1].X,
values[i, vKnotCountMin1].Y);
}
// Init Dxy
values[0, 0].Dxy = Function.Dxy.SafeCall(values[0, 0].X,
values[0, 0].Y);
values[uKnotCountMin1, 0].Dxy =
Function.Dxy.SafeCall(values[uKnotCountMin1, 0].X,
values[uKnotCountMin1, 0].Y);
values[0, vKnotCountMin1].Dxy =
Function.Dxy.SafeCall(values[0, vKnotCountMin1].X,
values[0, vKnotCountMin1].Y);
values[uKnotCountMin1, vKnotCountMin1].Dxy =
Function.Dxy.SafeCall(values[uKnotCountMin1, vKnotCountMin1].X,
values[uKnotCountMin1, vKnotCountMin1].Y);
}
protected virtual void FillYXDerivations(int rowIndex, KnotMatrix values,
double[] lowerDiagonal = null, double[] mainDiagonal = null,
double[] upperDiagonal = null)
{
var unknownsCount = values.Columns - 2;
if (unknownsCount == 0) return;
Action<int, double> dset =
(idx, value) => values[rowIndex, idx].Dxy = value;
Func<int, double> rget = idx => values[rowIndex, idx].Dx;
var h = values[0, 1].Y - values[0, 0].Y;
var dfirst = values[rowIndex, 0].Dxy;
var dlast = values[rowIndex, values.Columns - 1].Dxy;
SolveTridiagonal(rget, h, dfirst, dlast, unknownsCount, dset,
lowerDiagonal, mainDiagonal, upperDiagonal);
}
protected virtual void FillYXDerivations(KnotMatrix values)
{
for (var i = 0; i < values.Rows; i++)
{
FillYXDerivations(i, values);
}
}
private void InnerKnots(KnotMatrix newKnots)
{
for (var i = 1; i < newKnots.Rows; i += 2)
{
for (var j = 1; j < newKnots.Columns; j += 2)
{
var u0v0 = newKnots[i - 1, j - 1];
var u1v0 = newKnots[i, j - 1];
var u2v0 = newKnots[i + 1, j - 1];
var u0v1 = newKnots[i - 1, j];
var u1v1 = new Knot();
var u2v1 = newKnots[i + 1, j];
var u0v2 = newKnots[i - 1, j + 1];
var u1v2 = newKnots[i, j + 1];
var u2v2 = newKnots[i + 1, j + 1];
var hx = Math.Abs(u2v0.X - u0v0.X)/2;
var hx4 = hx*4;
var hy = Math.Abs(u0v2.Y - u0v0.Y)/2;
var hy4 = hy*4;
var x = u0v1.X + hx;
var y = u1v0.Y + hy;
u1v1.X = x;
u1v1.Y = y;
u1v1.Z = Function.Z(x, y);
u1v1.Dx =
-(3*(u0v1.Z - u2v1.Z) + hx*(u0v1.Dx + u2v1.Dx))/
hx4;
u1v1.Dy =
-(3*(u1v0.Z - u1v2.Z) + hx*(u1v0.Dx + u1v2.Dx))/
hy4;
u1v1.Dxy = (u0v0.Dxy + u2v0.Dxy + u0v2.Dxy + u2v2.Dxy +
(3*
((u0v0.Dy - u2v0.Dy + u0v2.Dy - u2v2.Dy)/hx
+
(u0v0.Dx + u2v0.Dx - u0v2.Dx - u2v2.Dx)/hy
+
(3*(u0v0.Z - u2v0.Z - u0v2.Z + u2v2.Z))
/(hx*hy))))/
16;
newKnots[i, j] = u1v1;
}
}
}
protected abstract ISurface CreateSegment(int uIdx, int vIdx,
KnotMatrix knots);
private double[] RightSideCross(KnotMatrix knots, int i, double dfirst,
double dlast,
int unknownsCount)
{
var even = unknownsCount%2 == 0;
var equationsCount = even ? unknownsCount/2 - 1 : unknownsCount/2;
var eta = even ? -4 : 1;
var rs = new double[equationsCount];
var oneDiv7 = 1/7;
var hx = knots[1, 0].X - knots[0, 0].X;
var hy = knots[0, 1].Y - knots[0, 0].Y;
var oneDivHx = 1d/hx;
var oneDivHy = 1d/hy;
var threeDivHx = 3/hx;
var threeDivHy = 3/hy;
var threeDiv7hx = oneDiv7*threeDivHx;
var threeDiv7hy = oneDiv7*threeDivHy;
var threeDiv7hxhy = threeDiv7hy/hy;
var columns = knots.Columns;
var iMin1 = i - 1;
var iMin2 = i - 2;
for (int k = 0, j = 4; k < equationsCount - 1; k++, j += 2)
{
rs[k] = oneDiv7
*(knots[iMin2, j + 2].Dxy + knots[iMin2, j - 2].Dxy)
- 2*knots[iMin1, j].Dxy
+ threeDiv7hx
*(knots[iMin1, j + 2].Dy + knots[iMin1, j - 2].Dy) +
threeDiv7hy
*(-knots[iMin2, j + 2].X + knots[iMin2, j - 2].X)
+ 3*threeDivHx*(knots[i, j + 2].Dy + knots[i, j - 2].Dy)
+
3*threeDiv7hxhy
*(-knots[iMin2, j + 2].Z + knots[iMin2, j - 2].Z)
+ 4*threeDiv7hx
*(-knots[iMin1, j + 2].Dy - knots[iMin1, j - 2].Dy) +
4*threeDiv7hy
*(knots[iMin2, j + 1].X - knots[iMin2, j - 1].X)
+ threeDiv7hy*(knots[i, j + 2].Dx + knots[i, j - 2].Dx)
+
9*threeDiv7hxhy*(-knots[i, j + 2].Z + knots[i, j - 2].Z)
-
12*threeDiv7hxhy*
(knots[iMin1, j + 2].Z - knots[iMin1, j - 2].Z
+ knots[iMin2, j + 1].Z - knots[iMin2, j - 1].Z)
- 6*oneDivHx*knots[iMin2, j].Dy
+ 12*oneDivHy*(knots[i, j + 1].Dx + knots[i, j - 1].Dx)
+
36*threeDiv7hxhy*(knots[i, j + 1].Z + knots[i, j - 1].Z)
- 18*oneDivHx*knots[i, j].Dy
+ 48*threeDiv7hxhy
*(-knots[iMin1, j + 1].Z + knots[iMin1, j - 1].Z) +
24*oneDivHx*knots[iMin1, j].Z;
}
rs[0] -= dfirst;
rs[equationsCount - 1] = oneDiv7
*(knots[iMin2, columns - 1].Dxy
+ knots[iMin2, columns - 5].Dxy) -
2*knots[iMin1, columns - 3].Dxy
+ threeDiv7hx
*(knots[iMin1, columns - 1].Dy
+ knots[iMin1, columns - 5].Dy) +
threeDiv7hy
*(-knots[iMin2, columns - 1].X
+ knots[iMin2, columns - 5].X)
+ 3*threeDivHx
*(knots[i, columns - 1].Dy
+ knots[i, columns - 5].Dy) +
3*threeDiv7hxhy
*(-knots[iMin2, columns - 1].Z
+ knots[iMin2, columns - 5].Z)
+
4*threeDiv7hx
*(-knots[iMin1, columns - 1].Dy
- knots[iMin1, columns - 5].Dy) +
4*threeDiv7hy
*(knots[iMin2, columns - 2].X
- knots[iMin2, columns - 4].X)
+ threeDiv7hy
*(knots[i, columns - 1].Dx
+ knots[i, columns - 5].Dx) +
9*threeDiv7hxhy
*(-knots[i, columns - 1].Z
+ knots[i, columns - 5].Z)
-
12*threeDiv7hxhy*
(knots[iMin1, columns - 1].Z
- knots[iMin1, columns - 5].Z +
knots[iMin2, columns - 2].Z
- knots[iMin2, columns - 4].Z)
- 6*oneDivHx*knots[iMin2, columns - 3].Dy +
12*oneDivHy
*(knots[i, columns - 2].Dx
+ knots[i, columns - 4].Dx) +
36*threeDiv7hxhy
*(knots[i, columns - 2].Z
+ knots[i, columns - 4].Z)
- 18*oneDivHx*knots[i, columns - 3].Dy +
48*threeDiv7hxhy
*(-knots[iMin1, columns - 2].Z
+ knots[iMin1, columns - 4].Z) +
24*oneDivHx*knots[iMin1, columns - 3].Z
- eta*dlast;
return rs;
}
protected override void FillYXDerivations(int rowIndex,
KnotMatrix values,
double[] lowerDiagonal = null, double[] mainDiagonal = null,
double[] upperDiagonal = null)
{
var unknownsCount = values.Columns - 2;
if (unknownsCount == 0) return;
var h = values[0, 1].Y - values[0, 0].Y;
var dfirst = values[rowIndex, 0].Dxy;
var dlast = values[rowIndex, values.Columns - 1].Dxy;
lowerDiagonal = lowerDiagonal ?? LowerDiagonal(unknownsCount);
mainDiagonal = mainDiagonal ?? MainDiagonal(unknownsCount);
upperDiagonal = upperDiagonal ?? UpperDiagonal(unknownsCount);
var result = RightSideCross(values, rowIndex, dfirst, dlast,
unknownsCount);
LinearSystems.SolveTridiagonalSystem(lowerDiagonal, mainDiagonal,
upperDiagonal, result);
for (var i = 0; i < result.Length; i++)
{
values[rowIndex, 2*i + 1].Dxy = result[i];
}
}
protected override void FillYXDerivations(KnotMatrix values)
{
for (var i = 2; i < values.Rows - 1; i += 2)
{
FillYXDerivations(i, values);
}
var oneDiv16 = 1d/16d;
var threeDiv16 = oneDiv16*3;
var hx = values[1, 0].X - values[0, 0].X;
var hy = values[0, 1].Y - values[0, 0].Y;
var oneDivHx = 1d/hx;
var oneDivHy = 1d/hy;
for (var i = 1; i < values.Rows - 1; i += 2)
{
for (var j = 1; j < values.Columns - 1; j += 2)
{
values[i, j].Dxy = oneDiv16*
(values[i + 1, j + 1].Dxy
+ values[i + 1, j - 1].Dxy
+ values[i - 1, j + 1].Dxy +
values[i - 1, j - 1].Dxy)
-
threeDiv16*oneDivHy*
(values[i + 1, j + 1].Dx
+ values[i + 1, j - 1].Dx
+ values[i - 1, j + 1].Dx +
values[i - 1, j - 1].Dx)
-
threeDiv16*oneDivHx*
(values[i + 1, j + 1].Dy
+ values[i + 1, j - 1].Dy
+ values[i - 1, j + 1].Dy +
values[i - 1, j - 1].Dy)
+
3*threeDiv16*oneDivHx*oneDivHy*
(values[i + 1, j + 1].Dy
- values[i + 1, j - 1].Dy
- values[i - 1, j + 1].Dy*
values[i - 1, j - 1].Dy);
}
}
for (var j = 2; j < values.Columns - 2; j += 2)
{
values[1, j].Dxy = 0.75*oneDivHy
*(values[1, j + 1].Dx - values[1, j - 1].Dx)
- 0.25
*(values[1, j + 1].Dxy - values[1, j - 1].Dxy);
}
for (var i = 2; i < values.Rows - 2; i += 2)
{
for (var j = 2; j < values.Columns - 2; j += 2)
{
values[i + 1, j].Dxy = 0.75*oneDivHy
*(values[i + 1, j + 1].Dx
- values[i + 1, j - 1].Dx)
- 0.25
*(values[i + 1, j + 1].Dxy
- values[i + 1, j - 1].Dxy);
}
for (var j = 1; j < values.Columns - 2; j += 2)
{
values[i, j].Dxy = 0.75*oneDivHy
*(values[i, j + 1].Dx
- values[i, j - 1].Dx)
- 0.25
*(values[i, j + 1].Dxy
- values[i, j - 1].Dxy);
}
}
}
using System;
using System.Collections.Generic;
using HermiteInterpolation.MathFunctions;
using HermiteInterpolation.Numerics;
using HermiteInterpolation.Primitives;
using HermiteInterpolation.SplineKnots;
using MathNet.Numerics.LinearAlgebra;
using Microsoft.Xna.Framework;
namespace HermiteInterpolation.Shapes.SplineInterpolation
{
public class BicubicHermiteSurface :Spline
{
public BicubicHermiteSurface(SurfaceDimension uDimension, SurfaceDimension vDimension, MathExpression mathExpression, Derivation derivation = Derivation.Zero) : base(uDimension, vDimension, mathExpression, derivation)
{
}
public BicubicHermiteSurface(SurfaceDimension uDimension, SurfaceDimension vDimension, InterpolativeMathFunction interpolativeMathFunction, Derivation derivation = Derivation.Zero) : base(uDimension, vDimension, interpolativeMathFunction, derivation)
{
}
public BicubicHermiteSurface(SurfaceDimension uDimension, SurfaceDimension vDimension, KnotsGenerator knotsGenerator, Derivation derivation = Derivation.Zero) : base(uDimension, vDimension, knotsGenerator, derivation)
{
}
protected delegate Vector<double> BasisVector(double t, double t0, double t1);
/// <summary>
///
/// </summary>
/// <param name="uIdx"></param>
/// <param name="vIdx"></param>
/// <param name="knots"></param>
/// <returns></returns>
protected override ISurface CreateSegment(int uIdx, int vIdx, KnotMatrix knots)
{
var u0 = knots[uIdx,vIdx].X;
var u1 = knots[uIdx+1,vIdx].X;
var v0 = knots[uIdx,vIdx].Y;
var v1 = knots[uIdx,vIdx+1].Y;
var meshDensity = Constants.MeshDensity;
var uKnotsDistance = Math.Abs(u1-u0);
var xCount = Math.Ceiling(uKnotsDistance/meshDensity);
var yKnotDistance = Math.Abs(v1 - v0);
var yCount = Math.Ceiling(yKnotDistance / meshDensity);
var verticesCount = (int)((++xCount) * (++yCount));
var segmentMeshVertices = new VertexPositionNormalColor[verticesCount];
var basisCalculator = new BicubicBasis(knots,Derivation);//BasisFactory.CreateBasis(Surface.Type);
var phi = basisCalculator.Matrix(uIdx, vIdx);
var k = 0;
var x = (float) u0 ;
for (var i = 0; i < xCount; i++,x += meshDensity)
{
x = x < u1 ? x : (float)u1;
var lambda1 = basisCalculator.Vector(x, u0, u1);
var basis = phi.LeftMultiply(lambda1);
var y = (float) v0;
for (var j = 0; j < yCount; j++,y += meshDensity)
{
y = y < v1 ? y : (float)v1;
var lambda2 = basisCalculator.Vector(y, v0, v1);
var zv = basis.PointwiseMultiply(lambda2);
var z = (float) zv.Sum();
z = MathHelper.Clamp(z, -Constants.MaxSceneZDifference, Constants.MaxSceneZDifference);
segmentMeshVertices[k++] = new VertexPositionNormalColor(new Vector3(x, y, z), DefaultNormal,
DefaultColor);
}
}
return new SimpleSurface(segmentMeshVertices, (int)xCount, (int)yCount);
}
}
}
public BiquarticBasis(KnotMatrix knots, Derivation derivation)
: base(knots, derivation)
{
}
private void HorizontalKnots(KnotMatrix newKnots)
{
for (var i = 1; i < newKnots.Rows; i += 2)
{
for (var j = 0; j < newKnots.Columns; j += 2)
{
var u0 = newKnots[i - 1, j];
var u1 = new Knot();
// finished
var u2 = newKnots[i + 1, j];
var hx = Math.Abs(u2.X - u0.X)/2;
var hx4 = hx*4;
var x = u0.X + hx;
var y = u0.Y;
u1.X = x;
u1.Y = y;
u1.Z = Function.Z(x, y);
u1.Dy = Function.Dy(x, y);
u1.Dx = -(3*(u0.Z - u2.Z) + hx*(u0.Dx + u2.Dx))/
hx4;
u1.Dxy = -(3*(u0.Dy - u2.Dy) + hx*(u0.Dxy + u2.Dxy))/
hx4;
// finished
newKnots[i, j] = u1;
}
}
}
