ImmersedSplines

active_splines(U::TensorProduct{2, <:SplineSpace}, E::Array)

Determine the active B-splines and boundary B-splines given a distance function ϕ.

A[k] == 0 => no physical elements in support of the function A[k] == 1 => boundary function with a physical cut element in its support A[k] == 2 => at least one physical element is fully inside support A[k] == 3 => all physical elements are fully inside support

active_splines(U::TensorProduct{Dim, <:SplineSpace}, E::Array)

Determine the active B-splines and boundary B-splines given a distance function ϕ.

A[k] == 0 => no physical elements in support of the function A[k] == 1 => boundary function with a physical cut element in its support A[k] == 2 => at least one physical element is fully inside support A[k] == 3 => all physical elements are fully inside support

active_splines(U::TensorProduct{2, <:SplineSpace}, E::Array)

Determine the active B-splines and boundary B-splines given a distance function ϕ.

A[k] == 0 => no physical elements in support of the function A[k] == 1 => boundary function with a physical cut element in its support A[k] == 2 => at least one physical element is fully inside support A[k] == 3 => all physical elements are fully inside support

compute_extension_coefficients(p, kts, span, k)

Compute the extension coefficients using dual functionals. This works for general non-uniform knot vectors and is based on the paper [Höllig, Klaus, and Ulrich Reif. "Nonuniform web-splines." Computer Aided Geometric Design 20, no. 5 (2003): 277-294.]

elementisinside(Y::Matrix{Bool})

Return a boolean array that specifies whether an element is inside or outside, respectively

find_extension_indices(active_functions, gperm, mi)

Find the extension indices that are closest to the boundary function with CartesianIndex mi.

find_extension_indices(active_functions, gperm, mi)

Find the extension indices that are closest to the boundary function with CartesianIndex mi.

pointisinside(phi, partition::CartesianProduct)

Return a boolean array that specifies whether a point is inside or outside, respectively

spline_extension_operator(U::TensorProduct{2, <:SplineSpace}, F)

Compute an extension operator that stabilizes the splinespace according to the definition of [Höllig, Klaus, Ulrich Reif, and Joachim Wipper. "Weighted extended B-spline approximation of Dirichlet problems." SIAM Journal on Numerical Analysis 39, no. 2 (2001): 442-462.]

ClosestExtensionArray(F, U::TensorProduct{Dim,<:SplineSpace})

Defines a closest index array, according to the definition of [Höllig, Klaus, Ulrich Reif, and Joachim Wipper. "Weighted extended B-spline approximation of Dirichlet problems." SIAM Journal on Numerical Analysis 39, no. 2 (2001): 442-462.]

ClosestExtensionArray(F, U::TensorProduct{Dim,<:SplineSpace})

Computes a closest index array, according to the definition of [Höllig, Klaus, Ulrich Reif, and Joachim Wipper. "Weighted extended B-spline approximation of Dirichlet problems." SIAM Journal on Numerical Analysis 39, no. 2 (2001): 442-462.]

GeneratePerimeter{Dim,Indices}

Datastructure that allows iteration over active neighborhoods of boundary functions

IPerm{Dim,Indices}

Iterator that returns active neighborhoods around a B-spline.

ImmersedQuadRule(map::AlgoimMapping, xa::Real, ya::Real, xb::Real, yb::Real, qo::Int64)

Compute a algoim quadrature rule in bounding box [xa, ya] × [xb, yb] based on a Gauss-Legendre rule of qo points.