Class NurbsBase

This class represents a base class that is common to most curve types.

Inheritance

System.Object

NurbsBase

Inherited Members

System.Object.Equals(System.Object, System.Object)

System.Object.GetType()

System.Object.MemberwiseClone()

System.Object.ReferenceEquals(System.Object, System.Object)

Syntax

public abstract class NurbsBase : IGeometry<NurbsBase>, IEquatable<NurbsBase>, ITransformable<NurbsBase>

Constructors

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NurbsBase()

Declaration

protected NurbsBase()

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NurbsBase(Int32, KnotVector, List<Point4>)

Declaration

protected NurbsBase(int degree, KnotVector knots, List<Point4> controlPoints)

Parameters

Type	Name	Description
System.Int32	degree
KnotVector	knots
System.Collections.Generic.List<Point4>	controlPoints

Properties

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ControlPointLocations

Gets the control points in their rational form.

Declaration

public List<Point3> ControlPointLocations { get; protected set; }

Property Value

Type	Description
System.Collections.Generic.List<Point3>

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ControlPoints

Gets the control points in their homogenized form.

Declaration

public List<Point4> ControlPoints { get; protected set; }

Property Value

Type	Description
System.Collections.Generic.List<Point4>

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Degree

Gets the degree of the curve.

Declaration

public int Degree { get; protected set; }

Property Value

Type	Description
System.Int32

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EndPoint

Declaration

public virtual Point3 EndPoint { get; }

Property Value

Type	Description
Point3

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IsClosed

Checks if a curve is closed.
A curve is closed if the first point and the last are the same.

Declaration

public virtual bool IsClosed { get; }

Property Value

Type	Description
System.Boolean	True if the curve is closed.

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IsPeriodic

Checks if a curve is periodic.
A curve is periodic, where the number of overlapping points is equal the curve degree.

Declaration

public bool IsPeriodic { get; }

Property Value

Type	Description
System.Boolean	True if the curve is periodic.

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Knots

Gets the knots vectors of the curve.

Declaration

public KnotVector Knots { get; protected set; }

Property Value

Type	Description
KnotVector

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Length

Declaration

public virtual double Length { get; }

Property Value

Type	Description
System.Double

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MidPoint

Declaration

public virtual Point3 MidPoint { get; }

Property Value

Type	Description
Point3

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StartPoint

Declaration

public virtual Point3 StartPoint { get; }

Property Value

Type	Description
Point3

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Weights

Gets the list of weight values.

Declaration

public List<double> Weights { get; protected set; }

Property Value

Type	Description
System.Collections.Generic.List<System.Double>

Methods

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ClampEnds()

Converts a curve where the knotVector is clamped.

Declaration

public NurbsBase ClampEnds()

Returns

Type	Description
NurbsBase	A curve with clamped knots.

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Close()

Creates a periodic curve.
This method uses the control point wrapping solution. https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve-closed.html

Declaration

public virtual NurbsBase Close()

Returns

Type	Description
NurbsBase	A periodic curve.

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ClosestParameter(Point3)

Declaration

public virtual double ClosestParameter(Point3 pt)

Parameters

Type	Name	Description
Point3	pt

Returns

Type	Description
System.Double

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ClosestPoint(Point3)

Declaration

public virtual Point3 ClosestPoint(Point3 point)

Parameters

Type	Name	Description
Point3	point

Returns

Type	Description
Point3

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CurvatureAt(Double)

Computes the curvature vector of the curve at the parameter. The vector has length equal to the radius of the curvature circle and with direction to the center of the circle.

Declaration

public Vector3 CurvatureAt(double t)

Parameters

Type	Name	Description
System.Double	t	Evaluation parameter. Parameter should be between 0.0 and 1.0.

Returns

Type	Description
Vector3	The curvature vector.

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DecomposeIntoBeziers()

Decompose a curve into a collection of Beziers curves.

Declaration

public List<NurbsBase> DecomposeIntoBeziers()

Returns

Type	Description
System.Collections.Generic.List<NurbsBase>	A collection of Beziers.

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DerivativeAt(Double, Int32)

Determines the derivatives of a curve at a given parameter.

Declaration

public List<Vector3> DerivativeAt(double t, int numberOfDerivatives = 1)

Parameters

Type	Name	Description
System.Double	t	Parameter on the curve at which the point is to be evaluated. Parameter should be between 0.0 and 1.0.
System.Int32	numberOfDerivatives	The number of derivatives required.

Returns

Type	Description
System.Collections.Generic.List<Vector3>	The derivatives.

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Divide(Double, Boolean)

Divides a curve for a given max segment length, including the end points.
The result is not split curves but a collection of t values and lengths that can be used for splitting.
As with all arc length methods, the result is an approximation.

Declaration

public (List<Point3> Points, List<double> Parameters) Divide(double maxSegmentLength, bool equalSegmentLengths = false)

Parameters

Type	Name	Description
System.Double	maxSegmentLength	The maximum length the segments have to be split in.
System.Boolean	equalSegmentLengths	Force to have all the segments of the same lengths.

Returns

Type	Description
System.ValueTuple<System.Collections.Generic.List<Point3>, System.Collections.Generic.List<System.Double>>	A tuple define the t values where the curve is divided and the lengths between each division.

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Divide(Int32)

Divides a curve for a given number of time, including the end points.
The result is not split curves but a collection of t values and lengths that can be used for splitting.
As with all arc length methods, the result is an approximation.

Declaration

public (List<Point3> Points, List<double> Parameters) Divide(int numberOfSegments)

Parameters

Type	Name	Description
System.Int32	numberOfSegments	The number of parts to split the curve into.

Returns

Type	Description
System.ValueTuple<System.Collections.Generic.List<Point3>, System.Collections.Generic.List<System.Double>>	A tuple define the t values where the curve is divided and the lengths between each division.

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DivideByChordLength(Double)

Divides a curve by a given chord length. Last chord will be of whatever length is left at the end of the curve.

Declaration

public List<double> DivideByChordLength(double chordLength)

Parameters

Type	Name	Description
System.Double	chordLength	Desired chord length.

Returns

Type	Description
System.Collections.Generic.List<System.Double>	Collection of curve parameters along the curve.

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ElevateDegree(Int32)

Elevates the degree of a curve. Implementation of Algorithm A5.9 of The NURBS Book by Piegl and Tiller.

Declaration

public NurbsBase ElevateDegree(int desiredDegree)

Parameters

Type	Name	Description
System.Int32	desiredDegree	The expected final degree. If the supplied degree is less or equal the curve is returned unmodified.

Returns

Type	Description
NurbsBase	The curve after degree elevation.

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Equals(NurbsBase)

Compares two curves for equality.
Two curves are equal when the have same control points, weights, knots and degree.

Declaration

public bool Equals(NurbsBase other)

Parameters

Type	Name	Description
NurbsBase	other	The other curve.

Returns

Type	Description
System.Boolean	Return true if the curves are equal.

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Equals(Object)

Compares if two curves are the same.
Two curves are equal when the have same degree, same control points order and dimension, and same knots.

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
System.Object	obj	The curve object.

Returns

Type	Description
System.Boolean	Return true if the curves are equal.

Overrides

System.Object.Equals(System.Object)

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Extrema()

Computes the parameter values of all local extrema.

Declaration

public IReadOnlyList<double> Extrema()

Returns

Type	Description
System.Collections.Generic.IReadOnlyList<System.Double>	The parameter values of all the local extrema.

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GetBoundingBox()

Gets the bounding box of the curve.

Declaration

public virtual BoundingBox GetBoundingBox()

Returns

Type	Description
BoundingBox

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GetHashCode()

Declaration

public override int GetHashCode()

Returns

Type	Description
System.Int32

Overrides

System.Object.GetHashCode()

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Join(IList<NurbsBase>)

Joins all the curves, if it is possible.

Declaration

public static PolyCurve Join(IList<NurbsBase> curves)

Parameters

Type	Name	Description
System.Collections.Generic.IList<NurbsBase>	curves	The curves to join.

Returns

Type	Description
PolyCurve	The polycurve that is the result of joining all the curves.

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LengthAt(Double)

Declaration

public virtual double LengthAt(double t)

Parameters

Type	Name	Description
System.Double	t

Returns

Type	Description
System.Double

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Offset(Double, Plane)

Computes the offset of the curve.

Declaration

public virtual NurbsBase Offset(double distance, Plane pln)

Parameters

Type	Name	Description
System.Double	distance	The distance of the offset. If negative the offset will be in the opposite side.
Plane	pln	The plane for the offset operation.

Returns

Type	Description
NurbsBase	The offset curve.

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ParameterAtChordLength(Double, Double)

Evaluates a point at a given chord length from a parameter on the curve.

Declaration

public double ParameterAtChordLength(double t, double chordLength)

Parameters

Type	Name	Description
System.Double	t
System.Double	chordLength

Returns

Type	Description
System.Double

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ParameterAtLength(Double)

Computes the parameter along the curve which coincides with a given length.

Declaration

public virtual double ParameterAtLength(double segmentLength)

Parameters

Type	Name	Description
System.Double	segmentLength	Length of segment to measure. Must be less than or equal to the length of the curve.

Returns

Type	Description
System.Double	The parameter on the curve at the given length.

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PerpendicularFrameAt(Double)

Calculates the 3D plane at the given parameter. Defined as the Frenet frame, is constructed from the velocity and the acceleration of the curve. https://janakiev.com/blog/framing-parametric-curves/

Declaration

public Plane PerpendicularFrameAt(double t)

Parameters

Type	Name	Description
System.Double	t	Evaluation parameter. Parameter should be between 0.0 and 1.0.

Returns

Type	Description
Plane	The perpendicular frame.

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PerpendicularFrames(List<Double>, Nullable<Vector3>, Nullable<Vector3>)

Creates rotation minimized perpendicular frames (RMF) at given t parameters along the curve.
Double reflection method taken from Wang, W., J¨uttler, B., Zheng, D., and Liu, Y. 2008. "Computation of rotation minimizing frame."
https://www.microsoft.com/en-us/research/wp-content/uploads/2016/12/Computation-of-rotation-minimizing-frames.pdf

Declaration

public List<Plane> PerpendicularFrames(List<double> uValues, Vector3? startTangent = null, Vector3? endTangent = null)

Parameters

Type	Name	Description
System.Collections.Generic.List<System.Double>	uValues	The curve parameter values to locate perpendicular curve frames
System.Nullable<Vector3>	startTangent	If not null override start tangent vector.
System.Nullable<Vector3>	endTangent	If not null override end tangent vector.

Returns

Type	Description
System.Collections.Generic.List<Plane>	A collection of planes.

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PointAt(Double)

Declaration

public virtual Point3 PointAt(double t)

Parameters

Type	Name	Description
System.Double	t

Returns

Type	Description
Point3

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PointAtLength(Double)

Declaration

public virtual Point3 PointAtLength(double length)

Parameters

Type	Name	Description
System.Double	length

Returns

Type	Description
Point3

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PointAtNormalizedLength(Double)

Evaluates a point at the normalized length.

Declaration

public virtual Point3 PointAtNormalizedLength(double normalizedLength)

Parameters

Type	Name	Description
System.Double	normalizedLength	The length factor is normalized between 0.0 and 1.0.

Returns

Type	Description
Point3	The point at the length.

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ReduceDegree(Double)

Reduce the degree of a NURBS curve. Implementation of Algorithm A5.11 of The NURBS Book by Piegl and Tiller. ToDo: Remove the tolerance, just let reduce and output the max deviation. ToDo: Try this method to reduce the bezier, looks more accurate. https://pomax.github.io/bezierinfo/chapters/reordering/reorder.js

Declaration

public NurbsBase ReduceDegree(double tolerance = 0.001)

Parameters

Type	Name	Description
System.Double	tolerance	Tolerance value declaring if the curve is degree reducible. Default value set to 10e-4, refer to Eq 5.30 for the meaning.

Returns

Type	Description
NurbsBase	The curve after degree reduction, the curve will be degree - 1 from the input.

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Reverse()

Reverses the parametrization of the curve.

Declaration

public virtual NurbsBase Reverse()

Returns

Type	Description
NurbsBase	A reversed curve.

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SplitAt(Double)

Splits a curve into two parts at a given parameter.

Declaration

public List<NurbsBase> SplitAt(double t)

Parameters

Type	Name	Description
System.Double	t	The parameter at which to split the curve.

Returns

Type	Description
System.Collections.Generic.List<NurbsBase>	Two curves.

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SplitAt(Double[])

Splits a curve at given parameters and returns the segments as curves.

Declaration

public List<NurbsBase> SplitAt(double[] parameters)

Parameters

Type	Name	Description
System.Double[]	parameters	The parameters at which to split the curve. Values should be between 0.0 and 1.0.

Returns

Type	Description
System.Collections.Generic.List<NurbsBase>	Collection of curve segments.

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SubCurve(Interval)

Extract sub-curve defined by domain.

Declaration

public NurbsBase SubCurve(Interval domain)

Parameters

Type	Name	Description
Interval	domain	Domain of sub-curve

Returns

Type	Description
NurbsBase	The sub curve.

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TangentAt(Double)

Computes the curve tangent at the given parameter.

Declaration

public virtual Vector3 TangentAt(double t)

Parameters

Type	Name	Description
System.Double	t	The parameter to sample the curve. Parameter should be between 0.0 and 1.0.

Returns

Type	Description
Vector3	The unitized tangent vector at the given parameter.

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ToString()

Implements the override method to string.

Declaration

public override string ToString()

Returns

Type	Description
System.String	The representation of a curve in string.

Overrides

System.Object.ToString()

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Transform(TransformMatrix)

Applies a transformation on the geometry object and returns the transformed geometry.

Declaration

public NurbsBase Transform(TransformMatrix t)

Parameters

Type	Name	Description
TransformMatrix	t	The transformation matrix that represents the transformation.

Returns

Type	Description
NurbsBase	The transformed geometry

Implements

IGeometry<T>

System.IEquatable<T>

ITransformable<T>