Eval

verb.eval.Eval

CLASS

Source code

Eval provides all of the core algorithms for evaluating points and derivatives on NURBS curves and surfaces. Most of the time, it makes more sense to use the tools in verb.geom for this, but in some cases this will make more sense.

Eval also provides experimental tools for evaluating points in NURBS volumes.

Many of these algorithms owe their implementation to Piegl & Tiller's "The NURBS Book"

rationalCurveTangent

STATIC METHOD

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rationalCurveTangent(curve : NurbsCurveData, u : Float) : Array<Float>

Compute the tangent at a point on a NURBS curve

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rationalSurfaceNormal

STATIC METHOD

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rationalSurfaceNormal(surface : NurbsSurfaceData, u : Float, v : Float) : Array<Float>

Compute the derivatives at a point on a NURBS surface

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rationalSurfaceDerivatives

STATIC METHOD

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rationalSurfaceDerivatives(surface : NurbsSurfaceData, u : Float, v : Float, numDerivs : Int) : Array<Array<Array<Float>>>

Compute the derivatives at a point on a NURBS surface

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rationalSurfacePoint

STATIC METHOD

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rationalSurfacePoint(surface : NurbsSurfaceData, u : Float, v : Float) : Point

Compute a point on a NURBS surface

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rationalCurveDerivatives

STATIC METHOD

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rationalCurveDerivatives(curve : NurbsCurveData, u : Float, numDerivs : Int) : Array<Point>

Determine the derivatives of a NURBS curve at a given parameter

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rationalCurvePoint

STATIC METHOD

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rationalCurvePoint(curve : NurbsCurveData, u : Float) : Point

Compute a point on a NURBS curve

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surfaceDerivatives

STATIC METHOD

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surfaceDerivatives(surface : NurbsSurfaceData, u : Float, v : Float, numDerivs : Int) : Array<Array<Point>>

Compute the derivatives on a non-uniform, non-rational B spline surface

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surfaceDerivativesGivenNM

STATIC METHOD

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surfaceDerivativesGivenNM(n : Int, m : Int, surface : NurbsSurfaceData, u : Float, v : Float, numDerivs : Int) : Array<Array<Point>>

Compute the derivatives on a non-uniform, non-rational B spline surface (corresponds to algorithm 3.6 from The NURBS book, Piegl & Tiller 2nd edition)

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surfacePoint

STATIC METHOD

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surfacePoint(surface : NurbsSurfaceData, u : Float, v : Float) : Point

Compute a point on a non-uniform, non-rational B-spline surface

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surfacePointGivenNM

STATIC METHOD

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surfacePointGivenNM(n : Int, m : Int, surface : NurbsSurfaceData, u : Float, v : Float) : Point

Compute a point on a non-uniform, non-rational B spline surface (corresponds to algorithm 3.5 from The NURBS book, Piegl & Tiller 2nd edition)

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curveDerivatives

STATIC METHOD

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curveDerivatives(crv : NurbsCurveData, u : Float, numDerivs : Int) : Array<Point>

Determine the derivatives of a non-uniform, non-rational B-spline curve at a given parameter

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curveDerivativesGivenN

STATIC METHOD

Source code

curveDerivativesGivenN(n : Int, curve : NurbsCurveData, u : Float, numDerivs : Int) : Array<Point>

Determine the derivatives of a non-uniform, non-rational B-spline curve at a given parameter (corresponds to algorithm 3.1 from The NURBS book, Piegl & Tiller 2nd edition)

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curvePoint

STATIC METHOD

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curvePoint(curve : NurbsCurveData, u : Float)

Compute a point on a non-uniform, non-rational b-spline curve

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areValidRelations

STATIC METHOD

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areValidRelations(degree : Int, num_controlPoints : Int, knots_length : Int) : Bool

Confirm the relations between degree (p), number of control points(n+1), and the number of knots (m+1) via The NURBS Book (section 3.2, Second Edition)

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curvePointGivenN

STATIC METHOD

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curvePointGivenN(n : Int, curve : NurbsCurveData, u : Float) : Point

Compute a point on a non-uniform, non-rational b-spline curve (corresponds to algorithm 3.1 from The NURBS book, Piegl & Tiller 2nd edition)

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volumePoint

STATIC METHOD

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volumePoint(volume : VolumeData, u : Float, v : Float, w : Float) : Point

Compute a point in a non-uniform, non-rational B spline volume

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volumePointGivenNML

STATIC METHOD

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volumePointGivenNML(volume : VolumeData, n : Int, m : Int, l : Int, u : Float, v : Float, w : Float) : Point

Compute a point in a non-uniform, non-rational B spline volume

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derivativeBasisFunctions

STATIC METHOD

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derivativeBasisFunctions(u : Float, degree : Int, knots : KnotArray) : Array<Array<Float>>

Compute the non-vanishing basis functions and their derivatives

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derivativeBasisFunctionsGivenNI

STATIC METHOD

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derivativeBasisFunctionsGivenNI(knotSpan_index : Int, u : Float, p : Int, n : Int, knots : KnotArray) : Array<Array<Float>>

Compute the non-vanishing basis functions and their derivatives (corresponds to algorithm 2.3 from The NURBS book, Piegl & Tiller 2nd edition)

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basisFunctions

STATIC METHOD

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basisFunctions(u : Float, degree : Int, knots : KnotArray)

Compute the non-vanishing basis functions

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basisFunctionsGivenKnotSpanIndex

STATIC METHOD

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basisFunctionsGivenKnotSpanIndex(knotSpan_index : Int, u : Float, degree : Int, knots : KnotArray)

Compute the non-vanishing basis functions (corresponds to algorithm 2.2 from The NURBS book, Piegl & Tiller 2nd edition)

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knotSpan

STATIC METHOD

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knotSpan(degree : Int, u : Float, knots : Array<Float>) : Int

Find the span on the knot Array without supplying n

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knotSpanGivenN

STATIC METHOD

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knotSpanGivenN(n : Int, degree : Int, u : Float, knots : Array<Float>) : Int

Find the span on the knot Array knots of the given parameter (corresponds to algorithm 2.1 from The NURBS book, Piegl & Tiller 2nd edition)

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dehomogenize

STATIC METHOD

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dehomogenize(homoPoint : Point) : Point

Dehomogenize a point

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rational1d

STATIC METHOD

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rational1d(homoPoints : Array<Point>) : Array<Point>

Obtain the point from a point in homogeneous space without dehomogenization, assuming all are the same length

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rational2d

STATIC METHOD

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rational2d(homoPoints : Array<Array<Point>>) : Array<Array<Point>>

Obtain the weight from a collection of points in homogeneous space, assuming all are the same dimension

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weight1d

STATIC METHOD

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weight1d(homoPoints : Array<Point>) : Array<Float>

Obtain the weight from a collection of points in homogeneous space, assuming all are the same dimension

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weight2d

STATIC METHOD

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weight2d(homoPoints : Array<Array<Point>>) : Array<Array<Float>>

Obtain the weight from a collection of points in homogeneous space, assuming all are the same dimension

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dehomogenize1d

STATIC METHOD

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dehomogenize1d(homoPoints : Array<Point>) : Array<Point>

Dehomogenize an array of points

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dehomogenize2d

STATIC METHOD

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dehomogenize2d(homoPoints : Array<Array<Point>>) : Array<Array<Point>>

Dehomogenize a 2d array of pts

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homogenize1d

STATIC METHOD

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homogenize1d(controlPoints : Array<Point>, weights : Array<Float>) : Array<Point>

Transform a 1d array of points into their homogeneous equivalents

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homogenize2d

STATIC METHOD

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homogenize2d(controlPoints : Array<Array<Point>>, weights : Array<Array<Float>>) : Array<Array<Point>>

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