API Reference › core-geometry› Bspline › KnotVector

KnotVector Class

Array of non-decreasing numbers acting as a knot vector for B-spline curves and surfaces.

  • Essential identity: numKnots = numPoles + order - 2 = numPoles + degree - 1
  • Various B-spline libraries have confusion over how many "end knots" are needed. Many libraries (including MicroStation and Parasolid) demand order knots at each end for clamping. However, only order-1 are really needed. This class uses the order-1 convention.
  • A span is a single interval of the knots.
  • The left knot of the span with index k>=0 is the knot with index k+degree-1.
  • A knot vector is clamped when the first degree knots are equal and the last degree knots are equal.
  • The "active knot interval" is the subset of the knot vector sans its first and last degree-1 knots, and serves as the parametric domain of the associated B-spline object.
  • This class provides queries to convert among spanIndex, knotIndex, spanFraction, fraction of knot range, and knot.
  • Callers need to distinguish core computational inputs such as left knot index, knot value, span index, and span fraction.

Methods

Name Description
baseKnotFractionToKnot(knotIndex0: number, localFraction: number): number Convert localFraction within the interval following an indexed knot to a knot value.  
clone(): KnotVector Copy degree and knots to a new KnotVector.  
copyKnots(includeExtraEndKnot: boolean): number[] Return a simple array form of the knots.  
createBasisArray(): Float64Array Return an array of size degree + 1, e.g., to hold the set of relevant basis function values at a parameter.  
evaluateBasisFunctions(knotIndex0: number, u: number, f: Float64Array): boolean Evaluate the B-spline basis functions f[] at a parameter u in a knot span.  
evaluateBasisFunctions1(knotIndex0: number, u: number, f: Float64Array, df: Float64Array, ddf?: Float64Array): boolean Evaluate basis functions f[], derivatives df[], and optional second derivatives ddf[] at a parameter u  
fractionToKnot(fraction: number): number Return fraction of active knot range to knot value.  
getKnotMultiplicity(knot: number): number Compute the multiplicity of the input knot, or zero if not a knot.  
getKnotMultiplicityAtIndex(knotIndex: number): number Compute the multiplicity of the knot at the given index.  
grevilleKnot(knotIndex: number): number Return the average of degree consecutive knots beginning at knotIndex.  
isAlmostEqual(other: KnotVector): boolean Test matching degree and knot values.  
isIndexOfRealSpan(spanIndex: number): boolean Given a span index, test if it is within range and has nonzero length.  
knotToLeftKnotIndex(u: number): number Find the knot span bracketing knots[i] <= u < knots[i+1] and return i.  
normalize(): boolean Transform knots such that the active knot range becomes [0,1].  
reflectKnots(): void Reflect all knots so leftKnot and rightKnot are maintained but interval lengths are reversed.  
setKnots(knots: Float64Array | number[], skipFirstAndLast?: boolean): void Install knot values from an array, optionally ignoring first and last.  
setKnotsCapture(knots: Float64Array): void Set knots to input array (CAPTURED).  
spanFractionToFraction(spanIndex: number, localFraction: number): number Convert localFraction within an indexed bezier span to fraction of active knot range.  
spanFractionToKnot(spanIndex: number, localFraction: number): number Convert localFraction within an indexed bezier span to a knot value.  
spanIndexToLeftKnotIndex(spanIndex: number): number Given a span index, return the index of the knot at its left.  
spanIndexToSpanLength(spanIndex: number): number Return the knot interval length of indexed bezier span.  
testClosable(mode?: BSplineWrapMode): boolean Returns true if all numeric values have wraparound conditions that allow the knots to be closed with specified  
copyKnots(knots: Float64Array | number[], degree: number, includeExtraEndKnot?: boolean, wrapMode?: BSplineWrapMode): number[] Static Return a simple array form of the knots.  
create(knotArray: Float64Array | number[], degree: number, skipFirstAndLast?: boolean): KnotVector Static Create knot vector with given knot values and degree.  
createUniformClamped(numPoles: number, degree: number, a0: number, a1: number): KnotVector Static Create knot vector with {degree-1} replicated knots at start and end, and uniform knots between.  
createUniformWrapped(numInterval: number, degree: number, a0: number, a1: number): KnotVector Static Create knot vector with wraparound knots at start and end, and uniform knots between.  

Properties

Name Type Description
degree number The degree of basis functions defined in these knots.  
knotLength01 Accessor ReadOnly number Return the length of the active knot interval.  
knots Float64Array The simple array of knot values.  
knotTolerance Static Readonly "1e-9" Tolerance for considering two knots to be the same.  
leftKnot Accessor ReadOnly number Return the leftmost knot value (of the active interval, ignoring unclamped leading knots).  
leftKnotIndex Accessor ReadOnly number Return the index of the leftmost knot of the active interval.  
numSpans Accessor ReadOnly number Return the number of Bezier spans.  
rightKnot Accessor ReadOnly number Return the rightmost knot value (of the active interval, ignoring unclamped leading knots).  
rightKnotIndex Accessor ReadOnly number Return the index of the rightmost knot of the active interval.  
wrappable Accessor BSplineWrapMode Whether this KnotVector was created by converting legacy periodic data during deserialization.  

Defined in

Last Updated: 21 February, 2025