Splines

Spline{T}

Represents a spline function.

Spline(B::BSplineBasis, coefs::AbstractVector)

Construct a spline from a B-spline basis and a vector of B-spline coefficients.

Examples

julia> B = BSplineBasis(BSplineOrder(4), -1:0.2:1);

julia> coefs = rand(length(B));

julia> S = Spline(B, coefs)
13-element Spline{Float64}:
 order: 4
 knots: [-1.0, -1.0, -1.0, -1.0, -0.8, -0.6, -0.4, -0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.0, 1.0, 1.0]
 coefficients: [0.18588655648969699, 0.9029166384444702, 0.9260613807703459, 0.8547964724816131, 0.39474318453198, 0.7014911606231877, 0.7532136707230797, 0.9360833341053749, 0.23429394964461725, 0.8755953969471848, 0.8421116493609568, 0.6943510993657007, 0.3825519047441852]

Spline(undef, B::BSplineBasis, [T=Float64])

Construct a spline with uninitialised vector of coefficients.

(S::Spline)(x)

Evaluate spline at coordinate x.

coefficients(S::Spline)

Get B-spline coefficients of the spline.

eltype(S::Spline)

Returns type of element returned when evaluating the Spline.

length(S::Spline)

Returns the number of coefficients in the spline.

Note that this is equal to the number of basis functions, length(basis(S)).

basis(S::Spline) -> BSplineBasis

Returns the associated B-spline basis.

diff(S::Spline, [deriv::Derivative = Derivative(1)]) -> Spline

Return N-th derivative of spline S as a new spline.

integral(S::Spline)

Returns an antiderivative of the given spline as a new spline.

The algorithm is described in de Boor 2001, p. 127.