/// <summary>
/// Creates a interpolated curve through a set of points.<br/>
/// <em>Refer to Algorithm A9.1 on The NURBS Book, pp.369-370 for details.</em>
/// </summary>
/// <param name="pts">The set of points to interpolate.</param>
/// <param name="degree">The Curve degree.</param>
/// <param name="startTangent">The tangent vector for the first point.</param>
/// <param name="endTangent">The tangent vector for the last point.</param>
/// <param name="centripetal">True use the chord as per knot spacing, false use the squared chord.</param>
/// <returns>A the interpolated curve.</returns>
public static NurbsBase Interpolated(List <Point3> pts, int degree, Vector3?startTangent = null,
Vector3?endTangent = null, bool centripetal = false)
{
if (pts.Count < degree + 1)
{
throw new Exception($"You must supply at least degree + 1 points. You supplied {pts.Count} pts.");
}
// Gets uk parameters.
List <double> uk = CurveHelpers.Parametrization(pts, centripetal);
// Compute knot vectors.
bool hasTangents = startTangent != null && endTangent != null;
KnotVector knots = ComputeKnotsForInterpolation(uk, degree, hasTangents);
// Global interpolation.
// Build matrix of basis function coefficients.
Matrix coeffMatrix = BuildCoefficientsMatrix(pts, degree, hasTangents, uk, knots);
// Solve for each points.
List <Point4> ctrlPts = (hasTangents)
? SolveCtrlPtsWithTangents(knots, pts, coeffMatrix, degree, new Vector3(startTangent.Value), new Vector3(endTangent.Value))
: SolveCtrlPts(pts, coeffMatrix);
return(new NurbsCurve(degree, knots, ctrlPts));
}
public void It_Refines_The_Curve_Knot(double val, int insertion)
{
// Arrange
int degree = 3;
List <double> newKnots = new List <double>();
for (int i = 0; i < insertion; i++)
{
newKnots.Add(val);
}
List <Point3> pts = new List <Point3>();
for (int i = 0; i <= 12 - degree - 2; i++)
{
pts.Add(new Point3(i, 0.0, 0.0));
}
NurbsCurve curve = new NurbsCurve(pts, degree);
// Act
NurbsBase curveAfterRefine = KnotVector.Refine(curve, newKnots);
Point3 p0 = curve.PointAt(2.5);
Point3 p1 = curveAfterRefine.PointAt(2.5);
// Assert
(curve.Knots.Count + insertion).Should().Be(curveAfterRefine.Knots.Count);
(pts.Count + insertion).Should().Be(curveAfterRefine.ControlPointLocations.Count);
(p0 == p1).Should().BeTrue();
}
public void It_Returns_A_Derive_Basic_Function_Given_NI()
{
// Arrange
// Values and formulas from The Nurbs Book p.69 & p.72
int degree = 2;
int span = 4;
int order = 2;
double parameter = 2.5;
KnotVector knots = new KnotVector {
0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5
};
double[,] expectedResult = new double[, ] {
{ 0.125, 0.75, 0.125 }, { -0.5, 0.0, 0.5 }, { 1.0, -2.0, 1.0 }
};
// Act
List <Vector> resultToCheck = GShark.Evaluate.Curve.DerivativeBasisFunctionsGivenNI(span, parameter, degree, order, knots);
// Assert
resultToCheck[0][0].Should().BeApproximately(expectedResult[0, 0], GSharkMath.MaxTolerance);
resultToCheck[0][1].Should().BeApproximately(expectedResult[0, 1], GSharkMath.MaxTolerance);
resultToCheck[0][2].Should().BeApproximately(expectedResult[0, 2], GSharkMath.MaxTolerance);
resultToCheck[1][0].Should().BeApproximately(expectedResult[1, 0], GSharkMath.MaxTolerance);
resultToCheck[1][1].Should().BeApproximately(expectedResult[1, 1], GSharkMath.MaxTolerance);
resultToCheck[1][2].Should().BeApproximately(expectedResult[1, 2], GSharkMath.MaxTolerance);
resultToCheck[2][0].Should().BeApproximately(expectedResult[2, 0], GSharkMath.MaxTolerance);
resultToCheck[2][1].Should().BeApproximately(expectedResult[2, 1], GSharkMath.MaxTolerance);
resultToCheck[2][2].Should().BeApproximately(expectedResult[2, 2], GSharkMath.MaxTolerance);
resultToCheck.Count.Should().Be(order + 1);
resultToCheck[0].Count.Should().Be(degree + 1);
}
/// <summary>
/// Computes the non-vanishing basis functions.<br/>
/// <em>Implementation of Algorithm A2.2 from The NURBS Book by Piegl and Tiller.<br/>
/// Uses recurrence to compute the basis functions, also known as Cox - deBoor recursion formula.</em>
/// </summary>
/// <param name="degree">Degree of a curve.</param>
/// <param name="knots">Set of knots.</param>
/// <param name="span">Index span of knots.</param>
/// <param name="knot">knot value.</param>
/// <returns>List of non-vanishing basis functions.</returns>
internal static List <double> BasisFunction(int degree, KnotVector knots, int span, double knot)
{
Vector left = Vector.Zero1d(degree + 1);
Vector right = Vector.Zero1d(degree + 1);
// N[0] = 1.0 by definition;
Vector N = Vector.Zero1d(degree + 1);
N[0] = 1.0;
for (int j = 1; j < degree + 1; j++)
{
left[j] = knot - knots[span + 1 - j];
right[j] = knots[span + j] - knot;
double saved = 0.0;
for (int r = 0; r < j; r++)
{
double temp = N[r] / (right[r + 1] + left[j - r]);
N[r] = saved + right[r + 1] * temp;
saved = left[j - r] * temp;
}
N[j] = saved;
}
return(N);
}
protected NurbsBase(int degree, KnotVector knots, List <Point4> controlPoints)
{
if (controlPoints is null)
{
throw new ArgumentNullException(nameof(controlPoints));
}
if (knots is null)
{
throw new ArgumentNullException(nameof(knots));
}
if (degree < 1)
{
throw new ArgumentException("Degree must be greater than 1!");
}
if (knots.Count != controlPoints.Count + degree + 1)
{
throw new ArgumentException("Number of controlPoints + degree + 1 must equal knots length!");
}
if (!knots.IsValid(degree, controlPoints.Count))
{
throw new ArgumentException("Invalid knot format! Should begin with degree + 1 repeats and end with degree + 1 repeats!");
}
Weights = Point4.GetWeights(controlPoints);
Degree = degree;
Knots = knots;
ControlPointLocations = Point4.PointDehomogenizer1d(controlPoints);
ControlPoints = controlPoints;
}
/// <summary>
/// Compute R - Eqn 9.67.
/// </summary>
private static List <Point3> ComputeValuesR(KnotVector knots, List <double> curveParameters, List <Point3> Rk, int degree, int numberOfCtrPts)
{
List <Vector> vectorR = new List <Vector>();
for (int i = 1; i < numberOfCtrPts - 1; i++)
{
List <Vector> ruTemp = new List <Vector>();
for (int j = 0; j < Rk.Count; j++)
{
double tempBasisVal = Evaluate.Curve.OneBasisFunction(degree, knots, i, curveParameters[j + 1]);
ruTemp.Add(Rk[j] * tempBasisVal);
}
Vector tempVec = Vector.Zero1d(ruTemp[0].Count);
for (int g = 0; g < ruTemp[0].Count; g++)
{
foreach (Vector vec in ruTemp)
{
tempVec[g] += vec[g];
}
}
vectorR.Add(tempVec);
}
return(vectorR.Select(v => new Point3(v[0], v[1], v[2])).ToList());
}
/// <summary>
/// Computes Rk - Eqn 9.63.
/// </summary>
private static List <Point3> ComputesValuesRk(KnotVector knots, List <double> curveParameters, int degree, List <Point3> pts, int numberOfCtrPts)
{
Point3 pt0 = pts[0]; // Q0
Point3 ptm = pts[pts.Count - 1]; // Qm
List <Point3> Rk = new List <Point3>();
for (int i = 1; i < pts.Count - 1; i++)
{
Point3 pti = pts[i];
double n0p = Evaluate.Curve.OneBasisFunction(degree, knots, 0, curveParameters[i]);
double nnp = Evaluate.Curve.OneBasisFunction(degree, knots, numberOfCtrPts - 1, curveParameters[i]);
Point3 elem2 = pt0 * n0p;
Point3 elem3 = ptm * nnp;
Point3 tempVec = new Point3();
for (int j = 0; j < 3; j++)
{
tempVec[j] = (pti[j] - elem2[j] - elem3[j]);
}
tempVec.X = pti.X - elem2.X - elem3.X;
tempVec.Y = pti.Y - elem2.Y - elem3.Y;
tempVec.Z = pti.Z - elem2.Z - elem3.Z;
Rk.Add(tempVec);
}
return(Rk);
}
/// <summary>
/// This method evaluate a B-spline span using the deBoor algorithm.
/// https://github.com/mcneel/opennurbs/blob/2b96cf31429dab25bf8a1dbd171227c506b06f88/opennurbs_evaluate_nurbs.cpp#L1249
/// This method is not implemented for clamped knots.
/// </summary>
/// <param name="controlPts">The control points of the curve.</param>
/// <param name="knots">The knot vector of the curve.</param>
/// <param name="degree">The value degree of the curve.</param>
/// <param name="parameter">The parameter value where the curve is evaluated.</param>
internal static void DeBoor(ref List <Point4> controlPts, KnotVector knots, int degree, double parameter)
{
if (Math.Abs(knots[degree] - knots[degree - 1]) < GSharkMath.Epsilon)
{
throw new Exception($"DeBoor evaluation failed: {knots[degree]} == {knots[degree + 1]}");
}
// deltaT = {knot[order-1] - t, knot[order] - t, .. knot[2*order-3] - t}
List <double> deltaT = new List <double>();
for (int k = 0; k < degree; k++)
{
deltaT.Add(knots[degree + 1 + k] - parameter);
}
for (int i = degree; i > 0; --i)
{
for (int j = 0; j < i; j++)
{
double k0 = knots[degree + 1 - i + j];
double k1 = knots[degree + 1 + j];
double alpha0 = deltaT[j] / (k1 - k0);
double alpha1 = 1.0 - alpha0;
Point4 cv1 = controlPts[j + 1];
Point4 cv0 = controlPts[j];
controlPts[j] = (cv0 * alpha0) + (cv1 * alpha1);
}
}
}
/// <summary>
/// Constructs a nurbs curve representation of this polyline.
/// </summary>
/// <returns>A Nurbs curve shaped like this polyline.</returns>
private void ToNurbs()
{
double lengthSum = 0;
List <double> weights = new List <double>();
KnotVector knots = new KnotVector {
0, 0
};
List <Point4> ctrlPts = new List <Point4>();
for (int i = 0; i < ControlPointLocations.Count - 1; i++)
{
lengthSum += Segments[i].Length;
knots.Add(lengthSum);
weights.Add(1.0);
ctrlPts.Add(new Point4(ControlPointLocations[i], 1.0));
}
knots.Add(lengthSum);
weights.Add(1.0);
ctrlPts.Add(new Point4(ControlPointLocations.Last(), 1.0));
Weights = weights;
Knots = knots.Normalize();
Degree = 1;
ControlPoints = ctrlPts;
}
/// <summary>
/// Computes the knot vectors used to calculate a curve global interpolation.
/// </summary>
private static KnotVector ComputeKnotsForInterpolation(List <double> curveParameters, int degree, bool hasTangents)
{
// Start knot vectors.
KnotVector knots = CollectionHelpers.RepeatData(0.0, degree + 1).ToKnot();
// If we have tangent values we need two more control points and knots.
int start = (hasTangents) ? 0 : 1;
int end = (hasTangents) ? curveParameters.Count - degree + 1 : curveParameters.Count - degree;
// Use averaging method (Eqn 9.8) to compute internal knots in the knot vector.
for (int i = start; i < end; i++)
{
double weightSum = 0.0;
for (int j = 0; j < degree; j++)
{
weightSum += curveParameters[i + j];
}
knots.Add((1.0 / degree) * weightSum);
}
// Add end knot vectors.
knots.AddRange(CollectionHelpers.RepeatData(1.0, degree + 1));
return(knots);
}
/// <summary>
/// Defines the control points defining the tangent values for the first and last points.
/// </summary>
private static List <Point4> SolveCtrlPtsWithTangents(KnotVector knots, List <Point3> pts, Matrix coeffMatrix, int degree, Vector3 startTangent, Vector3 endTangent)
{
Matrix matrixLu = Matrix.Decompose(coeffMatrix, out int[] permutation);
Matrix ptsSolved = new Matrix();
// Equations 9.11
double mult0 = knots[degree + 1] / degree;
// Equations 9.12
double mult1 = (1 - knots[knots.Count - degree - 2]) / degree;
// Solve for each dimension.
for (int i = 0; i < 3; i++)
{
Vector b = new Vector {
pts[0][i], startTangent[i] * mult0
};
// Insert the tangents at the second and second to last index.
// Equations 9.11
b.AddRange(pts.Skip(1).Take(pts.Count - 2).Select(pt => pt[i]));
// Equations 9.12
b.Add(endTangent[i] * mult1);
b.Add(pts[pts.Count - 1][i]);
Vector solution = Matrix.Solve(matrixLu, permutation, b);
ptsSolved.Add(solution);
}
return(ptsSolved.Transpose().Select(pt => new Point4(pt[0], pt[1], pt[2], 1)).ToList());
}
/// <summary>
/// Constructs a NURBS surface from a 2D grid of points.<br/>
/// The grid of points should be organized as, the V direction from left to right and the U direction increases from bottom to top.
/// </summary>
/// <param name="degreeU">Degree of surface in U direction.</param>
/// <param name="degreeV">Degree of surface in V direction.</param>
/// <param name="points">Points locations.</param>
/// <param name="weight">A 2D collection of weights.</param>
/// <returns>A NURBS surface.</returns>
public static NurbsSurface FromPoints(int degreeU, int degreeV, List <List <Point3> > points, List <List <double> > weight = null)
{
KnotVector knotU = new KnotVector(degreeU, points.Count);
KnotVector knotV = new KnotVector(degreeV, points[0].Count);
var controlPts = points.Select((pts, i) => pts.Select((pt, j) => weight != null ? new Point4(pt, weight[i][j]) : new Point4(pt)).ToList()).ToList();
return(new NurbsSurface(degreeU, degreeV, knotU, knotV, controlPts));
}
[InlineData(new double[] { -0.666, -0.333, 0, 0.333, 0.666, 1, 1.333, 1.666 }, 2, 5, true)] // Periodic
public void It_Checks_If_The_Knots_Are_Valid(double[] knots, int degree, int ctrlPts, bool expectedResult)
{
// Act
KnotVector knot = new KnotVector(knots);
// Assert
knot.IsValid(degree, ctrlPts).Should().Be(expectedResult);
}
public void It_Returns_True_If_KnotVector_Is_Clamped(double[] knots, int degree, bool expectedResult)
{
// Act
KnotVector knotVector = new KnotVector(knots);
// Assert
knotVector.IsClamped(degree).Should().Be(expectedResult);
}
public void It_Checks_If_Knots_Is_Periodic(double[] knots, int degree, bool expectedResult)
{
// Act
KnotVector knot = new KnotVector(knots);
// Assert
knot.IsPeriodic(degree).Should().Be(expectedResult);
}
protected NurbsBase()
{
Weights = new List <double>();
Degree = 0;
Knots = new KnotVector();
ControlPointLocations = new List <Point3>();
ControlPoints = new List <Point4>();
}
/// <summary>
/// Computes the value of a basis function for a single value.<br/>
/// <em>Implementation of Algorithm A2.4 from The NURBS Book by Piegl and Tiller.</em><br/>
/// </summary>
/// <param name="degree">Degree of a curve.</param>
/// <param name="knots">Set of knots.</param>
/// <param name="span">Index span of knots.</param>
/// <param name="knot">knot value.</param>
/// <returns>The single parameter value of the basis function.</returns>
public static double OneBasisFunction(int degree, KnotVector knots, int span, double knot)
{
// Special case at boundaries.
if ((span == 0 && Math.Abs(knot - knots[0]) < GSharkMath.MaxTolerance) ||
(span == knots.Count - degree - 2) && Math.Abs(knot - knots[knots.Count - 1]) < GSharkMath.MaxTolerance)
{
return(1.0);
}
// Local property, parameter is outside of span range.
if (knot < knots[span] || knot >= knots[span + degree + 1])
{
return(0.0);
}
List <double> N = CollectionHelpers.RepeatData(0.0, degree + span + 1);
// Initialize the zeroth degree basic functions.
for (int j = 0; j < degree + 1; j++)
{
if (knot >= knots[span + j] && knot < knots[span + j + 1])
{
N[j] = 1.0;
}
}
// Compute triangular table of basic functions.
for (int k = 1; k < degree + 1; k++)
{
double saved = 0.0;
if (N[0] != 0.0)
{
saved = ((knot - knots[span]) * N[0]) / (knots[span + k] - knots[span]);
}
for (int j = 0; j < degree - k + 1; j++)
{
double uLeft = knots[span + j + 1];
double uRight = knots[span + j + k + 1];
if (N[j + 1] == 0.0)
{
N[j] = saved;
saved = 0.0;
}
else
{
double temp = N[j + 1] / (uRight - uLeft);
N[j] = saved + (uRight - knot) * temp;
saved = (knot - uLeft) * temp;
}
}
}
return(N[0]);
}
public virtual NurbsBase Reverse()
{
List <Point4> controlPts = new List <Point4>(ControlPoints);
controlPts.Reverse();
KnotVector knots = KnotVector.Reverse(Knots);
return(new NurbsCurve(Degree, knots, controlPts));
}
/// <summary>
/// Bezier degree reduction.
/// <em>Refer to The NURBS Book by Piegl and Tiller at page 220.</em>
/// </summary>
private static double BezierDegreeReduce(Point4[] bpts, int degree, out Point4[] rbpts)
{
// Eq. 5.40
int r = (int)Math.Floor(((double)degree - 1) / 2);
Point4[] P = new Point4[degree];
P[0] = bpts[0];
P[P.Length - 1] = bpts.Last();
bool isDegreeOdd = degree % 2 != 0;
int r1 = (isDegreeOdd) ? r - 1 : r;
// Eq. 5.41
for (int i = 1; i <= r1; i++)
{
double alphaI = (double)i / degree;
P[i] = (bpts[i] - (P[i - 1] * alphaI)) / (1 - alphaI);
}
for (int i = degree - 2; i >= r + 1; i--)
{
double alphaI = (double)(i + 1) / degree;
P[i] = (bpts[i + 1] - (P[i + 1] * (1 - alphaI))) / alphaI;
}
/* Equations (5.43) and (5.44) express the parametric error {distance between points at corresponding parameter values);
* the maximums of geometric and parametric errors are not necessarily at the same u value.
* For p even the maximum error occurs at u = 1/2; for p odd the error is zero at u = 1/2, and it has two peaks a bit to the left and
* right of u = 1/2. */
// Eq. 5.43 p even.
KnotVector knots = new KnotVector(degree - 1, P.Length);
int span = knots.Span(degree - 1, 0.5);
List <double> Br = Evaluate.Curve.BasisFunction(degree - 1, knots, span, 0.5);
double parametricError = bpts[r + 1].DistanceTo((P[r] + P[r + 1]) * 0.5) * Br[r + 1];
// Eq. 5.42
if (isDegreeOdd)
{
double alphaR = (double)r / degree;
Point4 PLeft = (bpts[r] - (P[r - 1] * alphaR)) / (1 - alphaR);
double alphaR1 = (double)(r + 1) / degree;
Point4 PRight = (bpts[r + 1] - (P[r + 1] * (1 - alphaR1))) / alphaR1;
P[r] = (PLeft + PRight) * 0.5;
// Eq. 5.44 p odd.
parametricError = ((1 - alphaR) * 0.5) * ((Br[r] - Br[r + 1]) * PLeft.DistanceTo(PRight));
}
rbpts = P;
return(parametricError);
}
public void CreateUniformPeriodicKnotVector_Throws_An_Exception_If_Are_Not_Valid_Inputs(int degree, int numberOfControlPts)
{
// Are identifies as not valid inputs when:
// Degree and control points count is less than 2.
// Degree is bigger than the control points count.
// Act
Func <KnotVector> funcResult = () => KnotVector.UniformPeriodic(degree, numberOfControlPts);
// Assert
funcResult.Should().Throw <Exception>();
}
public void It_Throws_An_Exception_If_Input_Knot_Vector_Is_Empty()
{
// Assert
KnotVector knots = new KnotVector();
// Act
Func <KnotVector> func = () => knots.Normalize();
// Arrange
func.Should().Throw <Exception>().WithMessage("Input knot vector cannot be empty");
}
/// <summary>
/// Samples a curve in an adaptive way. <br/>
/// <em>Corresponds to this algorithm http://ariel.chronotext.org/dd/defigueiredo93adaptive.pdf </em>
/// </summary>
/// <param name="curve">The curve to sampling.</param>
/// <param name="tolerance">The tolerance for the adaptive division.</param>
/// <returns>A tuple collecting the parameter where it was sampled and the points.</returns>
public static (List <double> tValues, List <Point3> pts) AdaptiveSample(NurbsBase curve, double tolerance = GSharkMath.MinTolerance)
{
if (curve.Degree != 1)
{
return(AdaptiveSampleRange(curve, curve.Knots[0], curve.Knots[curve.Knots.Count - 1], tolerance));
}
KnotVector copyKnot = new KnotVector(curve.Knots);
copyKnot.RemoveAt(0);
copyKnot.RemoveAt(copyKnot.Count - 1);
return(copyKnot, curve.ControlPointLocations);
}
public void KnotMultiplicity_Returns_Knot_Multiplicity_At_The_Given_Index(double knot, int expectedMultiplicity)
{
// Arrange
KnotVector knots = new KnotVector {
0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3.3, 4, 4, 4
};
// Act
int multiplicity = knots.Multiplicity(knot);
// Assert
multiplicity.Should().Be(expectedMultiplicity);
}
public void It_Creates_A_Copy_Of_The_Knot_Vector()
{
// Assert
KnotVector knotVector = new KnotVector {
0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3.3, 4, 4, 4
};
// Act
KnotVector knotVectorCopy = knotVector.Copy();
// Arrange
knotVectorCopy.Should().NotBeSameAs(knotVector);
knotVectorCopy.Should().BeEquivalentTo(knotVector);
}
public void It_Returns_The_KnotSpan_Given_A_Parameter(int expectedValue, double parameter)
{
// Arrange
KnotVector knotVector = new KnotVector {
0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5
};
int degree = 2;
// Act
int result = knotVector.Span(knotVector.Count - degree - 2, 2, parameter);
// Assert
result.Should().Be(expectedValue);
}
public virtual NurbsBase Close()
{
// Wrapping control points
List <Point4> pts = new List <Point4>(ControlPoints);
for (int i = 0; i < Degree; i++)
{
pts.Add(pts[i]);
}
KnotVector knots = KnotVector.UniformPeriodic(Degree, pts.Count);
return(new NurbsCurve(Degree, knots, pts));
}
/// <summary>
/// Internal constructor used to validate the NURBS surface.
/// </summary>
/// <param name="degreeU">The degree in the U direction.</param>
/// <param name="degreeV">The degree in the V direction.</param>
/// <param name="knotsU">The knotVector in the U direction.</param>
/// <param name="knotsV">The knotVector in the V direction.</param>
/// <param name="controlPts">Two dimensional array of points.</param>
internal NurbsSurface(int degreeU, int degreeV, KnotVector knotsU, KnotVector knotsV, List <List <Point4> > controlPts)
{
if (controlPts == null)
{
throw new ArgumentNullException("Control points array connot be null!");
}
if (degreeU < 1)
{
throw new ArgumentException("DegreeU must be greater than 1!");
}
if (degreeV < 1)
{
throw new ArgumentException("DegreeV must be greater than 1!");
}
if (knotsU == null)
{
throw new ArgumentNullException("KnotU cannot be null!");
}
if (knotsV == null)
{
throw new ArgumentNullException("KnotV cannot be null!");
}
if (knotsU.Count != controlPts.Count() + degreeU + 1)
{
throw new ArgumentException("Points count + degreeU + 1 must equal knotsU count!");
}
if (knotsV.Count != controlPts.First().Count() + degreeV + 1)
{
throw new ArgumentException("Points count + degreeV + 1 must equal knotsV count!");
}
if (!knotsU.IsValid(degreeU, controlPts.Count()))
{
throw new ArgumentException("Invalid knotsU!");
}
if (!knotsV.IsValid(degreeV, controlPts.First().Count()))
{
throw new ArgumentException("Invalid knotsV!");
}
DegreeU = degreeU;
DegreeV = degreeV;
KnotsU = (Math.Abs(knotsU.GetDomain(degreeU).Length - 1.0) > GSharkMath.Epsilon) ? knotsU.Normalize() : knotsU;
KnotsV = (Math.Abs(knotsV.GetDomain(degreeV).Length - 1.0) > GSharkMath.Epsilon) ? knotsV.Normalize() : knotsV;
Weights = Point4.GetWeights2d(controlPts);
ControlPointLocations = Point4.PointDehomogenizer2d(controlPts);
ControlPoints = controlPts;
DomainU = new Interval(KnotsU.First(), KnotsU.Last());
DomainV = new Interval(KnotsV.First(), KnotsV.Last());
}
public void It_Creates_An_Unclamped_Uniform_KnotVector()
{
// Arrange
int degree = 3;
int ctrlPts = 5;
KnotVector expectedKnotVector = new KnotVector {
0.0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1.0
};
// Act
KnotVector knots = new KnotVector(degree, ctrlPts, false);
// Assert
knots.Should().BeEquivalentTo(expectedKnotVector);
}
public void It_Reverses_A_Knot_Vectors()
{
// Assert
KnotVector knotVector = new KnotVector {
0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3.3, 4, 4, 4
};
KnotVector expectedKnotVector = new KnotVector {
0, 0, 0, 0.7000000000000002, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4
};
// Act
KnotVector reversedKnots = KnotVector.Reverse(knotVector);
// Arrange
reversedKnots.Should().BeEquivalentTo(expectedKnotVector);
}
public void It_Returns_A_Normalized_Knot_Vector()
{
// Arrange
KnotVector knots = new KnotVector {
-5, -5, -3, -2, 2, 3, 5, 5
};
KnotVector knotsExpected = new KnotVector {
0.0, 0.0, 0.2, 0.3, 0.7, 0.8, 1.0, 1.0
};
// Act
KnotVector normalizedKnots = knots.Normalize();
// Assert
normalizedKnots.Should().BeEquivalentTo(knotsExpected);
}