public BiquarticHermiteSpline(SurfaceDimension uDimension,
SurfaceDimension vDimension, KnotsGenerator knotsGenerator,
Derivation derivation = Derivation.Zero)
: base(uDimension, vDimension,
new BiquarticKnotsGenerator(knotsGenerator), derivation)
{
}
protected Spline(SurfaceDimension uDimension,
SurfaceDimension vDimension,
InterpolativeMathFunction interpolativeMathFunction,
Derivation derivation = Derivation.Zero)
: this(uDimension, vDimension,
new DirectKnotsGenerator(interpolativeMathFunction), derivation)
{
}
public BiquarticHermiteSpline(SurfaceDimension uDimension,
SurfaceDimension vDimension,
InterpolativeMathFunction interpolativeMathFunction,
Derivation derivation = Derivation.Zero)
: this(uDimension, vDimension,
new DirectKnotsGenerator(interpolativeMathFunction), derivation)
{
}
public BiquarticHermiteSpline(SurfaceDimension uDimension,
SurfaceDimension vDimension, MathExpression mathExpression,
Derivation derivation = Derivation.Zero)
: this(uDimension, vDimension,
InterpolativeMathFunction.FromExpression(mathExpression),
derivation)
{
}
protected Spline(SurfaceDimension uDimension,
SurfaceDimension vDimension,
MathExpression mathExpression,
Derivation derivation = Derivation.Zero)
: this(uDimension, vDimension,
InterpolativeMathFunction.FromExpression(mathExpression),
derivation)
{
Name = mathExpression.Expression;
}
public MathFunctionSurface(SurfaceDimension uDimension,
SurfaceDimension vDimension,
MathExpression mathExpression,
Derivation derivation = Derivation.Zero)
: this(
uDimension, vDimension, mathExpression.Interpret(), derivation
)
{
Name = mathExpression.Expression;
}
protected Spline(SurfaceDimension uDimension,
SurfaceDimension vDimension,
KnotsGenerator knotsGenerator,
Derivation derivation = Derivation.Zero)
{
KnotsGenerator = knotsGenerator;
UDimension = uDimension;
VDimension = vDimension;
Derivation = derivation;
Segments =
CreateMesh(knotsGenerator.GenerateKnots(uDimension, vDimension));
}
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;
}
public MathFunctionSurface(SurfaceDimension uDimension,
SurfaceDimension vDimension,
MathFunction function, Derivation derivation = Derivation.Zero)
{
Derivation = derivation;
if (derivation != Derivation.Zero)
{
var interpolativeFunction =
new InterpolativeMathFunction(function);
switch (Derivation)
{
case Derivation.X:
function = interpolativeFunction.Dx;
break;
case Derivation.Y:
function = interpolativeFunction.Dy;
break;
case Derivation.XY:
function = interpolativeFunction.Dxy;
break;
case Derivation.SecondXY:
function =
new InterpolativeMathFunction(
interpolativeFunction.Dxy).Dxy;
break;
}
}
UDimension = uDimension;
VDimension = vDimension;
var uCount_min_1 = uDimension.KnotCount - 1;
//surface.UKnotsCount-1;
var vCount_min_1 = vDimension.KnotCount - 1;
//surface.VKnotsCount-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, function);
segments.Add(segment);
}
}
Segments = segments;
}
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;
}
private void DrawButton_OnClick(object sender, RoutedEventArgs e)
{
InterpolativeMathFunction mathFunction;
SurfaceDimension uDim, vDim;
try
{
uDim = new SurfaceDimension(
double.Parse(HermiteUMinTextBox.Text),
double.Parse(HermiteUMaxTextBox.Text),
int.Parse(HermiteUCountTextBox.Text)
);
vDim = new SurfaceDimension(
double.Parse(HermiteVMinTextBox.Text),
double.Parse(HermiteVMaxTextBox.Text),
int.Parse(HermiteVCountTextBox.Text));
mathFunction = InterpolativeMathFunction.FromExpression(MathExpressionTextBox.Text,"x","y");
}
catch (Exception)
{
MessageBox.Show("Invalid input.");
return;
}
SplineFactory createSpline;
KnotsGeneratorFactory createKnotsGenerator;
if (_splineSubtractionClicked)
{
//createSpline = (x);
var minuendGenerator = _minuendKnotsFactory(mathFunction);
var subtrahendGenerator = ((KnotsGeneratorFactory) KnotsGeneratorComboBox.SelectedValue)(mathFunction);
createKnotsGenerator = (mf)=>minuendGenerator-subtrahendGenerator;
createSpline = (u,v,k,d)=>new BicubicHermiteSpline(u,v,k,d);
//_splineSubtractionClicked = false;
}
else
{
createSpline = (SplineFactory)InterpolationTypeComboBox.SelectedValue;
createKnotsGenerator = (KnotsGeneratorFactory)KnotsGeneratorComboBox.SelectedValue;
}
var shape = createSpline(uDim, vDim, createKnotsGenerator(mathFunction));
// var fdshape = createSpline(uDim, vDim, createKnotsGenerator(mathFunction), Derivation.XY);
// var sdshape = createSpline(uDim, vDim, createKnotsGenerator(mathFunction), Derivation.SecondXY);
if (_splineSubtractionClicked)
{
shape.Name += "DIFF";
DisableSplineChaining();
}
Color color;
if (ColorCheckBox.IsChecked.HasValue && !ColorCheckBox.IsChecked.Value)
color = ColorUtils.RandomShade((float)ColorSlider.Value);
else
color = _colorWheel.Next;
//ShapesComboBox.Foreground = new SolidColorBrush(System.Windows.Media.Color.FromArgb(255, color.R, color.G, color.B));
shape.ColoredByShades(color);
shape.DrawStyle = DrawStyle.Surface;
shape.Name = MathExpressionTextBox.Text;
var currentSelectedIndex = ShapesComboBox.SelectedIndex;
_functionScene.Add(shape,false);
ShapesComboBoxItems.Add(new ShapeComboBoxItem(shape.Name,color));
ShapesComboBox.ItemsSource = null;
ShapesComboBox.ItemsSource = ShapesComboBoxItems;
ShapesComboBox.SelectedIndex = currentSelectedIndex;
ShapesComboBox_OnSelectedItem(ShapesComboBox,null);
if (ShapesComboBox.SelectedIndex < 0)
ShapesComboBox.SelectedIndex = 0;
AutoScale();
}
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)
{
}
}
}
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);
}
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);
}
}
}
