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Knot Vectors

Knot vectors are fundamental data structures that define the parametric domain and behavior of B-spline and NURBS bases.

Constructor

TinyGismo.KnotVector — Type
KnotVector(knots::Vector{Float64})

Construct a knot vector from a vector of knot values.

Arguments

  • knots: A vector of knot values (non-decreasing)

Returns

A knot vector object

Details

A knot vector is a non-decreasing sequence of real numbers that define the parametric domain and behavior of B-spline and NURBS bases.

Examples

knots = [0.0, 0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0, 1.0]
kv = KnotVector(knots)
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Query Functions

Base.size — Method
Base.size(kv::KnotVector)

Get the total number of knots in the knot vector (including multiplicities).

Alias for the C++ size() method.

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TinyGismo.uSize — Function
uSize(knotVector::KnotVector)

Get the number of unique knot values.

Arguments

  • knotVector: The knot vector

Returns

The number of unique knots

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TinyGismo.unique — Function
unique(knotVector::KnotVector)

Get the unique knot values from the knot vector.

Arguments

  • knotVector: The knot vector

Returns

A vector of unique knot values in ascending order

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TinyGismo.multiplicities — Function
multiplicities(knotVector::KnotVector)

Get the multiplicity of each unique knot value.

Arguments

  • knotVector: The knot vector

Returns

A vector of multiplicities corresponding to each unique knot

Details

The multiplicity of a knot indicates how many times that knot value appears in the knot vector. Higher multiplicity reduces continuity at that knot.

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TinyGismo.knotContainer — Function
knotContainer(knotVector::KnotVector)

Get the underlying knot values as an array.

Arguments

  • knotVector: The knot vector

Returns

A const array view of the knot values

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Degree Operations

These operations are documented in the Basis Functions section.

Refinement

Refinement operations for knot vectors are documented in the Basis Functions - Refinement section.