Interpolation types

using DataInterpolationsND
using Random
using Plots
Random.seed!(2)

t1 = cumsum(0.5 .+ rand(10))
t2 = cumsum(0.5 .+ rand(10))

t1_eval = collect(range(first(t1), last(t1); length = 100))
t2_eval = collect(range(first(t2), last(t2); length = 100))

u = rand(10, 10)
out = zeros(100, 100)

Linear Interpolation

interp_dims = (
    LinearInterpolationDimension(t1; t_eval = t1_eval),
    LinearInterpolationDimension(t2; t_eval = t2_eval)
)
interp = NDInterpolation(u, interp_dims)
eval_grid!(out, interp)
heatmap(out)

Constant Interpolation

interp_dims = (
    ConstantInterpolationDimension(t1; t_eval = t1_eval),
    ConstantInterpolationDimension(t2; t_eval = t2_eval)
)
interp = NDInterpolation(u, interp_dims)
eval_grid!(out, interp)
heatmap(out)

BSpline Interpolation

interp_dims = (
    BSplineInterpolationDimension(t1, 2; t_eval = t1_eval),
    BSplineInterpolationDimension(t2, 2; t_eval = t2_eval)
)
u_bspline = rand(11, 11) # per dimension this is `sum(multiplicities) - degree - 1 = 11`
u_bspline[1:10, 1:10] = u
interp = NDInterpolation(u_bspline, interp_dims)
eval_grid!(out, interp)
heatmap(out)

NURBS Interpolation

weights = rand(11, 11)
interp = NDInterpolation(u_bspline, interp_dims; cache = NURBSWeights(weights))
eval_grid!(out, interp)
heatmap(out)