/// <summary>
/// Determines the derivatives of a curve at a given parameter.<br/>
/// <em>Corresponds to algorithm 3.2 from The NURBS Book by Piegl and Tiller.</em>
/// </summary>
/// <param name="curve">The curve object.</param>
/// <param name="parameter">Parameter on the curve at which the point is to be evaluated.</param>
/// <param name="numberDerivs">Integer number of basis functions - 1 = knots.length - degree - 2.</param>
/// <returns>The derivatives.</returns>
internal static List <Point4> CurveDerivatives(NurbsBase curve, double parameter, int numberDerivs)
{
List <Point4> curveHomogenizedPoints = curve.ControlPoints;
int n = curve.Knots.Count - curve.Degree - 2;
int derivateOrder = numberDerivs < curve.Degree ? numberDerivs : curve.Degree;
Point4[] ck = new Point4[numberDerivs + 1];
int knotSpan = curve.Knots.Span(n, curve.Degree, parameter);
List <Vector> derived2d = DerivativeBasisFunctionsGivenNI(knotSpan, parameter, curve.Degree, derivateOrder, curve.Knots);
for (int k = 0; k < derivateOrder + 1; k++)
{
for (int j = 0; j < curve.Degree + 1; j++)
{
double valToMultiply = derived2d[k][j];
Point4 pt = curveHomogenizedPoints[knotSpan - curve.Degree + j];
for (int i = 0; i < pt.Size; i++)
{
ck[k][i] = ck[k][i] + (valToMultiply * pt[i]);
}
}
}
return(ck.ToList());
}
public void It_Returns_A_Circle3D_With_Its_Nurbs_Representation()
{
// Arrange
var ptsExpected = new List <Point3>
{
new Point3(74.264416, 36.39316, -1.884313),
new Point3(62.298962, 25.460683, 1.083287),
new Point3(73.626287, 13.863582, 4.032316),
new Point3(84.953611, 2.266482, 6.981346),
new Point3(96.919065, 13.198959, 4.013746),
new Point3(108.884519, 24.131437, 1.046146),
new Point3(97.557194, 35.728537, -1.902883),
new Point3(86.22987, 47.325637, -4.851913),
new Point3(74.264416, 36.39316, -1.88431)
};
// Act
NurbsBase circleNurbs = _circle3D;
// Assert
circleNurbs.Knots.GetDomain(circleNurbs.Degree).Length.Should().Be(1.0);
for (int ptIndex = 0; ptIndex < ptsExpected.Count; ptIndex++)
{
circleNurbs.ControlPointLocations[ptIndex].EpsilonEquals(ptsExpected[ptIndex], GSharkMath.MaxTolerance);
}
}
/// <summary>
/// Approximates the parameter at a given length on a curve.
/// </summary>
/// <param name="curve">The curve object.</param>
/// <param name="segmentLength">The arc length for which to do the procedure.</param>
/// <param name="tolerance">If set less or equal 0.0, the tolerance used is 1e-10.</param>
/// <returns>The parameter on the curve.</returns>
internal static double ParameterAtLength(NurbsBase curve, double segmentLength, double tolerance = -1)
{
if (segmentLength < GSharkMath.Epsilon)
{
return(curve.Knots[0]);
}
if (Math.Abs(curve.Length - segmentLength) < GSharkMath.Epsilon)
{
return(curve.Knots[curve.Knots.Count - 1]);
}
List <NurbsBase> curves = Modify.Curve.DecomposeIntoBeziers(curve);
int i = 0;
double curveLength = -GSharkMath.Epsilon;
double segmentLengthLeft = segmentLength;
// Iterate through the curves consuming the bezier's, summing their length along the way.
while (curveLength < segmentLength && i < curves.Count)
{
double bezierLength = BezierLength(curves[i]);
curveLength += bezierLength;
if (segmentLength < curveLength + GSharkMath.Epsilon)
{
return(BezierParameterAtLength(curves[i], segmentLengthLeft, tolerance));
}
i++;
segmentLengthLeft -= bezierLength;
}
return(-1);
}
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_Curve_Where_Degree_Is_Reduced_From_5_To_4()
{
// Arrange
// Followed example Under C1 constrain condition https://www.hindawi.com/journals/mpe/2016/8140427/tab1/
List <Point3> pts = new List <Point3>
{
new Point3(-5.0, 0.0, 0.0),
new Point3(-7.0, 2.0, 0.0),
new Point3(-3.0, 5.0, 0.0),
new Point3(2.0, 6.0, 0.0),
new Point3(5.0, 3.0, 0.0),
new Point3(3.0, 0.0, 0.0)
};
int degree = 5;
double tolerance = 10e-2;
NurbsCurve curve = new NurbsCurve(pts, degree);
Point3 ptOnCurve0 = curve.PointAt(0.5);
Point3 ptOnCurve1 = curve.PointAt(0.25);
// Act
NurbsBase reducedCurve = curve.ReduceDegree(tolerance);
Point3 ptOnReducedDegreeCurve0 = reducedCurve.PointAt(0.5);
Point3 ptOnReducedDegreeCurve1 = reducedCurve.PointAt(0.25);
// Assert
reducedCurve.Degree.Should().Be(degree - 1);
ptOnCurve0.DistanceTo(ptOnReducedDegreeCurve0).Should().BeLessThan(GSharkMath.MinTolerance);
ptOnCurve1.DistanceTo(ptOnReducedDegreeCurve1).Should().BeLessThan(tolerance);
}
/// <summary>
/// Samples a curve at equally spaced parametric intervals.
/// </summary>
/// <param name="curve">The curve object.</param>
/// <param name="numSamples">Number of samples.</param>
/// <returns>A tuple with the set of points and the t parameter where the point was evaluated.</returns>
internal static (List <double> tvalues, List <Point3> pts) RegularSample(NurbsBase curve, int numSamples)
{
if (numSamples < 1)
{
throw new Exception("Number of sample must be at least 1 and not negative.");
}
double start = curve.Knots[0];
double end = curve.Knots[curve.Knots.Count - 1];
double span = (end - start) / (numSamples - 1);
List <Point3> pts = new List <Point3>();
List <double> tValues = new List <double>();
for (int i = 0; i < numSamples; i++)
{
double t = start + span * i;
Point3 ptEval = curve.PointAt(t);
pts.Add(ptEval);
tValues.Add(t);
}
return(tValues, pts);
}
/// <summary>
/// Computes the intersection between a curve and a plane.<br/>
/// https://www.parametriczoo.com/index.php/2020/03/31/plane-and-curve-intersection/
/// </summary>
/// <param name="crv">The curve to intersect.</param>
/// <param name="pl">The plane to intersect with the curve.</param>
/// <param name="tolerance">Tolerance set per default at 1e-6.</param>
/// <returns>If intersection found a collection of <see cref="CurvePlaneIntersectionResult"/> otherwise the result will be empty.</returns>
public static List <CurvePlaneIntersectionResult> CurvePlane(NurbsBase crv, Plane pl, double tolerance = 1e-6)
{
List <NurbsBase> bBoxRoot = BoundingBoxOperations.BoundingBoxPlaneIntersection(new LazyCurveBBT(crv), pl);
List <CurvePlaneIntersectionResult> intersectionResults = bBoxRoot.Select(
x => IntersectionRefiner.CurvePlaneWithEstimation(crv, pl, x.Knots[0], x.Knots[0], tolerance)).ToList();
return(intersectionResults);
}
/// <summary>
/// Divides a curve for a given number of time, including the end points.<br/>
/// The result is not split curves but a collection of t values and lengths that can be used for splitting.<br/>
/// As with all arc length methods, the result is an approximation.
/// </summary>
/// <param name="curve">The curve object to divide.</param>
/// <param name="divisions">The number of parts to split the curve into.</param>
/// <returns>A tuple define the t values where the curve is divided and the lengths between each division.</returns>
internal static List <double> ByCount(NurbsBase curve, int divisions)
{
double approximatedLength = Analyze.Curve.Length(curve);
double arcLengthSeparation = approximatedLength / divisions;
var divisionByLength = ByLength(curve, arcLengthSeparation);
var tValues = divisionByLength.tValues;
return(tValues);
}
/// <summary>
/// Computes the self intersections of a curve.
/// </summary>
/// <param name="crv">The curve for self-intersections.</param>
/// <param name="tolerance">Tolerance set per default at 1e-6.</param>
/// <returns>If intersection found a collection of <see cref="CurvesIntersectionResult"/> otherwise the result will be empty.</returns>
public static List <CurvesIntersectionResult> CurveSelf(NurbsBase crv, double tolerance = 1e-6)
{
List <Tuple <NurbsBase, NurbsBase> > bBoxTreeIntersections = BoundingBoxOperations.BoundingBoxTreeIntersection(new LazyCurveBBT(crv), 0);
List <CurvesIntersectionResult> intersectionResults = bBoxTreeIntersections
.Select(x => IntersectionRefiner.CurvesWithEstimation(x.Item1, x.Item2, x.Item1.Knots[0], x.Item2.Knots[0], tolerance))
.Where(crInRe => Math.Abs(crInRe.ParameterA - crInRe.ParameterB) > tolerance)
.Unique((a, b) => Math.Abs(a.ParameterA - b.ParameterA) < tolerance * 5);
return(intersectionResults);
}
public void It_Returns_Parameter_At_The_Given_Length(double segmentLength, double tValueExpected)
{
// Arrange
NurbsBase curve = NurbsCurveCollection.PlanarCurveDegreeThree();
// Act
double parameter = curve.ParameterAtLength(segmentLength);
// Assert
parameter.Should().BeApproximately(tValueExpected, GSharkMath.MinTolerance);
}
public void It_Returns_True_If_The_NurbsBase_Form_Of_A_Line_Is_Correct()
{
//Act
NurbsBase nurbsLine = _exampleLine;
// Assert
nurbsLine.ControlPointLocations.Count.Should().Be(2);
nurbsLine.ControlPointLocations[0].Equals(_exampleLine.StartPoint).Should().BeTrue();
nurbsLine.ControlPointLocations[1].Equals(_exampleLine.EndPoint).Should().BeTrue();
nurbsLine.Degree.Should().Be(1);
}
public void It_Returns_The_Segment_At_Length(double length, int segmentIndex)
{
//Arrange
NurbsBase expectedSegment = _polycurve.Segments[segmentIndex];
//Act
NurbsBase segmentResult = _polycurve.SegmentAtLength(length);
//Assert
segmentResult.Should().BeSameAs(expectedSegment);
}
/// <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 It_Returns_The_Length_Of_The_Curve()
{
// Arrange
NurbsBase curve = NurbsCurveCollection.PlanarCurveDegreeThree();
double expectedLength = 50.334675;
// Act
double crvLength = curve.Length;
// Assert
crvLength.Should().BeApproximately(expectedLength, GSharkMath.MinTolerance);
}
public void Returns_The_Surface_Isocurve_At_U_Direction()
{
// Arrange
NurbsSurface surface = NurbsSurfaceCollection.SurfaceFromPoints();
Point3 expectedPt = new Point3(3.591549, 10, 4.464789);
// Act
NurbsBase Isocurve = surface.IsoCurve(0.3, SurfaceDirection.U);
// Assert
Isocurve.ControlPointLocations[1].DistanceTo(expectedPt).Should().BeLessThan(GSharkMath.MinTolerance);
}
/// <summary>
/// Refines an intersection pair for two curves given an initial guess.<br/>
/// This is an unconstrained minimization, so the caller is responsible for providing a very good initial guess.
/// </summary>
/// <param name="crv0">The first curve.</param>
/// <param name="crv1">The second curve.</param>
/// <param name="firstGuess">The first guess parameter.</param>
/// <param name="secondGuess">The second guess parameter.</param>
/// <param name="tolerance">The value tolerance for the intersection.</param>
/// <returns>The results collected into the object <see cref="CurvesIntersectionResult"/>.</returns>
internal static CurvesIntersectionResult CurvesWithEstimation(NurbsBase crv0, NurbsBase crv1,
double firstGuess, double secondGuess, double tolerance)
{
IObjectiveFunction objectiveFunctions = new CurvesIntersectionObjectives(crv0, crv1);
Minimizer min = new Minimizer(objectiveFunctions);
MinimizationResult solution = min.UnconstrainedMinimizer(new Vector {
firstGuess, secondGuess
}, tolerance * tolerance);
// These are not the same points, also are used to filter where the intersection is not happening.
Point3 pt1 = crv0.PointAt(solution.SolutionPoint[0]);
Point3 pt2 = crv1.PointAt(solution.SolutionPoint[1]);
return(new CurvesIntersectionResult(pt1, pt2, solution.SolutionPoint[0], solution.SolutionPoint[1]));
}
public void It_Returns_The_Closest_Point_And_Parameter(double[] ptToCheck, double[] ptExpected, double tValExpected)
{
// Arrange
NurbsBase curve = NurbsCurveCollection.PlanarCurveDegreeThree();
Point3 testPt = new Point3(ptToCheck[0], ptToCheck[1], ptToCheck[2]);
Point3 expectedPt = new Point3(ptExpected[0], ptExpected[1], ptExpected[2]);
// Act
Point3 pt = curve.ClosestPoint(testPt);
double parameter = curve.ClosestParameter(testPt);
// Assert
parameter.Should().BeApproximately(tValExpected, GSharkMath.MaxTolerance);
pt.EpsilonEquals(expectedPt, GSharkMath.MaxTolerance).Should().BeTrue();
}
public void Returns_The_Surface_Isocurve_At_V_Direction()
{
// Arrange
NurbsSurface surface = NurbsSurfaceCollection.SurfaceFromPoints();
Point3 expectedPt = new Point3(5, 4.615385, 2.307692);
Point3 expectedPtAt = new Point3(5, 3.913043, 1.695652);
// Act
NurbsBase Isocurve = surface.IsoCurve(0.3, SurfaceDirection.V);
Point3 ptAt = Isocurve.PointAt(0.5);
// Assert
Isocurve.ControlPointLocations[1].DistanceTo(expectedPt).Should().BeLessThan(GSharkMath.MinTolerance);
ptAt.DistanceTo(expectedPtAt).Should().BeLessThan(GSharkMath.MinTolerance);
}
/// <summary>
/// Computes the approximate length of a rational bezier curve by gaussian quadrature - assumes a smooth curve.
/// </summary>
/// <param name="curve">The curve object.</param>
/// <param name="u">The parameter at which to approximate the length.</param>
/// <param name="gaussDegIncrease">
/// the degree of gaussian quadrature to perform.
/// A higher number yields a more exact result, default set to 17.
/// </param>
/// <returns>The approximate length of a bezier.</returns>
internal static double BezierLength(NurbsBase curve, double u = -1.0, int gaussDegIncrease = 17)
{
double uSet = u < 0.0 ? curve.Knots.Last() : u;
double z = (uSet - curve.Knots[0]) / 2;
double sum = 0.0;
int gaussDegree = curve.Degree + gaussDegIncrease;
for (int i = 0; i < gaussDegree; i++)
{
double cu = z * LegendreGaussData.tValues[gaussDegree][i] + z + curve.Knots[0];
List <Vector3> tan = Evaluate.Curve.RationalDerivatives(curve, cu);
sum += LegendreGaussData.cValues[gaussDegree][i] * tan[1].Length;
}
return(z * sum);
}
/// <summary>
/// Refines an intersection between a curve and a plane given an initial guess.<br/>
/// This is an unconstrained minimization, so the caller is responsible for providing a very good initial guess.
/// </summary>
/// <param name="crv">The curve to intersect.</param>
/// <param name="plane">The plane to intersect with the curve.</param>
/// <param name="firstGuess">The first guess parameter.</param>
/// <param name="secondGuess">The second guess parameter.</param>
/// <param name="tolerance">The value tolerance for the intersection.</param>
/// <returns>The results collected into the object <see cref="CurvePlaneIntersectionResult"/>.</returns>
internal static CurvePlaneIntersectionResult CurvePlaneWithEstimation(NurbsBase crv, Plane plane,
double firstGuess, double secondGuess, double tolerance)
{
IObjectiveFunction objectiveFunctions = new CurvePlaneIntersectionObjectives(crv, plane);
Minimizer min = new Minimizer(objectiveFunctions);
MinimizationResult solution = min.UnconstrainedMinimizer(new Vector {
firstGuess, secondGuess
}, tolerance * tolerance);
Point3 pt = crv.PointAt(solution.SolutionPoint[0]);
(double u, double v)parameters = plane.ClosestParameters(pt);
Vector uv = new Vector {
parameters.u, parameters.v, 0.0
};
return(new CurvePlaneIntersectionResult(pt, solution.SolutionPoint[0], uv));
}
public void It_Returns_True_If_The_NurbsBase_Form_Of_A_Polygon_Is_Correct()
{
// Arrange
PolyLine polygon = new Polygon(Planar2D);
double lengthSum = 0.0;
// Act
NurbsBase polygonCurve = polygon;
// Assert
polygonCurve.Degree.Should().Be(1);
polygonCurve.ControlPointLocations[0]
.EpsilonEquals(polygonCurve.ControlPointLocations.Last(), GSharkMath.MinTolerance).Should().BeTrue();
for (int i = 0; i < polygon.SegmentsCount; i++)
{
lengthSum += polygon.Segments[i].Length;
polygon.ControlPointLocations[i + 1].EpsilonEquals(polygonCurve.PointAtLength(lengthSum), GSharkMath.MaxTolerance).Should().BeTrue();
}
}
/// <summary>
/// Decompose a curve into a collection of bezier curves.<br/>
/// </summary>
/// <param name="curve">The curve object.</param>
/// <param name="normalize">Set as per default false, true normalize the knots between 0 to 1.</param>
/// <returns>Collection of curve objects, defined by degree, knots, and control points.</returns>
internal static List <NurbsBase> DecomposeIntoBeziers(NurbsBase curve, bool normalize = false)
{
int degree = curve.Degree;
List <Point4> controlPoints = curve.ControlPoints;
KnotVector knots = curve.Knots;
// Find all of the unique knot values and their multiplicity.
// For each, increase their multiplicity to degree + 1.
Dictionary <double, int> knotMultiplicities = knots.Multiplicities();
int reqMultiplicity = degree + 1;
// Insert the knots.
foreach (KeyValuePair <double, int> kvp in knotMultiplicities)
{
if (kvp.Value >= reqMultiplicity)
{
continue;
}
List <double> knotsToInsert = CollectionHelpers.RepeatData(kvp.Key, reqMultiplicity - kvp.Value);
NurbsBase curveTemp = new NurbsCurve(degree, knots, controlPoints);
NurbsBase curveResult = KnotRefine(curveTemp, knotsToInsert);
knots = curveResult.Knots;
controlPoints = curveResult.ControlPoints;
}
int crvKnotLength = reqMultiplicity * 2;
List <NurbsBase> curves = new List <NurbsBase>();
int i = 0;
while (i < controlPoints.Count)
{
KnotVector knotsRange = (normalize)
? knots.GetRange(i, crvKnotLength).ToKnot().Normalize()
: knots.GetRange(i, crvKnotLength).ToKnot();
List <Point4> ptsRange = controlPoints.GetRange(i, reqMultiplicity);
NurbsBase tempCrv = new NurbsCurve(degree, knotsRange, ptsRange);
curves.Add(tempCrv);
i += reqMultiplicity;
}
return(curves);
}
/// <summary>
/// Computes the approximate length of a rational curve by gaussian quadrature - assumes a smooth curve.
/// </summary>
/// <param name="curve">The curve object.</param>
/// <param name="u">The parameter at which to approximate the length.</param>
/// <param name="gaussDegIncrease">
/// The degree of gaussian quadrature to perform.
/// A higher number yields a more exact result, default set to 17.
/// </param>
/// <returns>The approximate length.</returns>
internal static double Length(NurbsBase curve, double u = -1.0, int gaussDegIncrease = 17)
{
double uSet = u < 0.0 ? curve.Knots.Last() : u;
List <NurbsBase> crvs = Modify.Curve.DecomposeIntoBeziers(curve);
double sum = 0.0;
foreach (NurbsBase bezier in crvs)
{
if (!(bezier.Knots[0] + GSharkMath.Epsilon < uSet))
{
break;
}
double param = Math.Min(bezier.Knots.Last(), uSet);
sum += BezierLength(bezier, param, gaussDegIncrease);
}
return(sum);
}
/// <summary>
/// Computes the curve parameter at a given length.
/// </summary>
/// <param name="curve">The curve object.</param>
/// <param name="segmentLength">The length to find the parameter.</param>
/// <param name="tolerance">If set less or equal 0.0, the tolerance used is 1e-10.</param>
/// <returns>The parameter at the given length.</returns>
internal static double BezierParameterAtLength(NurbsBase curve, double segmentLength, double tolerance)
{
if (segmentLength < 0)
{
return(curve.Knots[0]);
}
// We compute the whole length.
double curveLength = BezierLength(curve);
if (segmentLength > curveLength)
{
return(curve.Knots[curve.Knots.Count - 1]);
}
// Divide and conquer.
double setTolerance = tolerance <= 0.0 ? GSharkMath.Epsilon : tolerance;
double startT = curve.Knots[0];
double startLength = 0.0;
double endT = curve.Knots[curve.Knots.Count - 1];
double endLength = curveLength;
while (endLength - startLength > setTolerance)
{
double midT = (startT + endT) / 2;
double midLength = BezierLength(curve, midT);
if (midLength > segmentLength)
{
endT = midT;
endLength = midLength;
}
else
{
startT = midT;
startLength = midLength;
}
}
return((startT + endT) / 2);
}
/// <summary>
/// Divides a curve for a given length, including the end points.<br/>
/// The result is not split curves but a collection of t values and lengths that can be used for splitting.<br/>
/// As with all arc length methods, the result is an approximation.
/// </summary>
/// <param name="curve">The curve object to divide.</param>
/// <param name="length">The length separating the resultant samples.</param>
/// <returns>A tuple define the t values where the curve is divided and the lengths between each division.</returns>
internal static (List <double> tValues, List <double> lengths) ByLength(NurbsBase curve, double length)
{
List <NurbsBase> curves = Modify.Curve.DecomposeIntoBeziers(curve);
List <double> curveLengths = curves.Select(NurbsBase => Analyze.Curve.BezierLength(NurbsBase)).ToList();
double totalLength = curveLengths.Sum();
List <double> tValues = new List <double> {
curve.Knots[0]
};
List <double> divisionLengths = new List <double> {
0.0
};
if (length > totalLength)
{
return(tValues, divisionLengths);
}
int i = 0;
double sum = 0.0;
double sum2 = 0.0;
double segmentLength = length;
while (i < curves.Count)
{
sum += curveLengths[i];
while (segmentLength < sum + GSharkMath.Epsilon)
{
double t = Analyze.Curve.BezierParameterAtLength(curves[i], segmentLength - sum2, GSharkMath.MinTolerance);
tValues.Add(t);
divisionLengths.Add(segmentLength);
segmentLength += length;
}
sum2 += curveLengths[i];
i++;
}
return(tValues, divisionLengths);
}
public void It_Is_A_Curve_Representation_Of_ExampleArc3D()
{
// Arrange
double[] weightChecks = { 1.0, 0.7507927793532885, 1.0, 0.7507927793532885, 1.0, 0.7507927793532885, 1.0 };
Point3[] ptChecks =
{
new Point3(74.264416, 36.39316, -1.8843129999999997),
new Point3(63.73736394529969, 26.774907230101093, 0.7265431054950776),
new Point3(72.2808868605866, 15.429871621311115, 3.6324963299804987),
new Point3(80.8244097758736, 4.084836012521206, 6.538449554465901),
new Point3(93.52800280921122, 10.812836698886068, 4.6679117389561),
new Point3(106.23159584254901, 17.54083738525103, 2.797373923446271),
new Point3(100.92443, 30.599893, -0.5851159999999997)
};
// Act
NurbsBase arc = _exampleArc3D;
// Assert
arc.ControlPointLocations.Count.Should().Be(7);
arc.Degree.Should().Be(2);
for (int i = 0; i < ptChecks.Length; i++)
{
arc.ControlPointLocations[i].EpsilonEquals(ptChecks[i], GSharkMath.MaxTolerance).Should().BeTrue();
arc.ControlPoints[i].W.Should().Be(weightChecks[i]);
if (i < 3)
{
arc.Knots[i].Should().Be(0);
arc.Knots[i + 7].Should().Be(1);
}
else if (i < 5)
{
arc.Knots[i].Should().Be(0.3333333333333333);
}
else
{
arc.Knots[i].Should().Be(0.6666666666666666);
}
}
}
public void It_Returns_A_Curve_Where_Degree_Is_Elevated_From_1_To_Elevated_Degree_Value(int finalDegree)
{
// Arrange
List <Point3> pts = new List <Point3>
{
new Point3(0.0, 0.0, 1.0),
new Point3(7.0, 3.0, -10),
new Point3(5.2, 5.2, -5),
};
int degree = 1;
NurbsCurve curve = new NurbsCurve(pts, degree);
Point3 ptOnCurve = curve.PointAt(0.5);
// Act
NurbsBase elevatedDegreeCurve = curve.ElevateDegree(finalDegree);
Point3 ptOnElevatedDegreeCurve = elevatedDegreeCurve.PointAt(0.5);
// Assert
elevatedDegreeCurve.Degree.Should().Be(finalDegree);
ptOnElevatedDegreeCurve.DistanceTo(ptOnCurve).Should().BeLessThan(GSharkMath.MinTolerance);
}
/// <summary>
/// Calculates all the extrema on a curve.<br/>
/// Extrema are calculated for each dimension, rather than for the full curve, <br/>
/// so that the result is not the number of convex/concave transitions, but the number of those transitions for each separate dimension.
/// </summary>
/// <param name="curve">Curve where the extrema are calculated.</param>
/// <returns>The extrema.</returns>
internal static Extrema ComputeExtrema(NurbsBase curve)
{
var derivPts = DerivativeCoordinates(curve.ControlPointLocations);
Extrema extrema = new Extrema();
int dim = derivPts[0][0].Size;
for (int j = 0; j < dim; j++)
{
List <double> p0 = new List <double>();
for (int i = 0; i < derivPts[0].Count; i++)
{
p0.Add(derivPts[0][i][j]);
}
List <double> result = new List <double>(DerivativesRoots(p0));
if (curve.Degree == 3)
{
IList <double> p1 = new List <double>();
for (int i = 0; i < derivPts[1].Count; i++)
{
p1.Add(derivPts[1][i][j]);
}
result = result.Concat(DerivativesRoots(p1).ToList()).ToList();
}
result = result.Where((t) => t >= 0 && t <= 1).ToList();
result.Sort();
extrema[j] = result;
}
extrema.Values = extrema[0].Union(extrema[1]).Union(extrema[2]).OrderBy(x => x).ToList();
return(extrema);
}
/// <summary>
/// Performs a knot refinement on a surface by inserting knots at various parameters.<br/>
/// <em>Implementation of Algorithm A5.5 of The NURBS Book by Piegl and Tiller.</em>
/// </summary>
internal static NurbsSurface SurfaceKnotRefine(NurbsSurface surface, IList <double> knotsToInsert, SurfaceDirection direction)
{
List <List <Point4> > modifiedControlPts = new List <List <Point4> >();
List <List <Point4> > controlPts = surface.ControlPoints;
KnotVector knots = surface.KnotsV;
int degree = surface.DegreeV;
if (direction != SurfaceDirection.V)
{
controlPts = CollectionHelpers.Transpose2DArray(surface.ControlPoints);
knots = surface.KnotsU;
degree = surface.DegreeU;
}
NurbsBase curve = null;
foreach (List <Point4> pts in controlPts)
{
curve = Curve.KnotRefine(new NurbsCurve(degree, knots, pts), knotsToInsert);
modifiedControlPts.Add(curve.ControlPoints);
}
if (curve == null)
{
throw new Exception(
"The refinement was not be able to be completed. A problem occur refining the internal curves.");
}
if (direction != SurfaceDirection.V)
{
var reversedControlPts = CollectionHelpers.Transpose2DArray(modifiedControlPts);
return(new NurbsSurface(surface.DegreeU, surface.DegreeV, curve.Knots, surface.KnotsV.Copy(),
reversedControlPts));
}
return(new NurbsSurface(surface.DegreeU, surface.DegreeV, surface.KnotsU.Copy(), curve.Knots,
modifiedControlPts));
}
/// <summary>
/// Samples a curve in an adaptive way. <br/>
/// <em>Corresponds to this algorithm http://ariel.chronotext.org/dd/defigueiredo93adaptive.pdf <br/>
/// https://www.modelical.com/en/grasshopper-scripting-107/ </em>
/// </summary>
/// <param name="curve">The curve to sampling.</param>
/// <param name="start">The start parameter for sampling.</param>
/// <param name="end">The end parameter for sampling.</param>
/// <param name="tolerance">Tolerance for the adaptive scheme. The default tolerance is set as (1e-6).</param>
/// <returns>A tuple with the set of points and the t parameter where the point was evaluated.</returns>
public static (List <double> tValues, List <Point3> pts) AdaptiveSampleRange(NurbsBase curve, double start, double end, double tolerance = GSharkMath.MinTolerance)
{
// Sample curve at three pts.
Random random = new Random();
double t = 0.5 + 0.2 * random.NextDouble();
double mid = start + (end - start) * t;
Point3 pt1 = Point4.PointDehomogenizer(Evaluate.Curve.PointAt(curve, start));
Point3 pt2 = Point4.PointDehomogenizer(Evaluate.Curve.PointAt(curve, mid));
Point3 pt3 = Point4.PointDehomogenizer(Evaluate.Curve.PointAt(curve, end));
Vector3 diff = pt1 - pt3;
Vector3 diff2 = pt1 - pt2;
if ((Vector3.DotProduct(diff, diff) < tolerance && Vector3.DotProduct(diff2, diff2) > tolerance) ||
!Trigonometry.ArePointsCollinear(pt1, pt2, pt3, tolerance))
{
// Get the exact middle value or a random value start + (end - start) * (0.45 + 0.1 * random.NextDouble());
double tMiddle = start + (end - start) * 0.5;
// Recurse the two halves.
(List <double> tValues, List <Point3> pts)leftHalves = AdaptiveSampleRange(curve, start, tMiddle, tolerance);
(List <double> tValues, List <Point3> pts)rightHalves = AdaptiveSampleRange(curve, tMiddle, end, tolerance);
leftHalves.tValues.RemoveAt(leftHalves.tValues.Count - 1);
List <double> tMerged = leftHalves.tValues.Concat(rightHalves.tValues).ToList();
leftHalves.pts.RemoveAt(leftHalves.pts.Count - 1);
List <Point3> ptsMerged = leftHalves.pts.Concat(rightHalves.pts).ToList();
return(tMerged, ptsMerged);
}
return(new List <double> {
start, end
}, new List <Point3> {
pt1, pt3
});
}
