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; }
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) { } } }
public DeBoorKnotsGenerator(MathExpression expression) : base(expression) { }
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); } } }