PointDiscretizedBoxMap

A generalization of MonteCarloBoxMap and GridBoxMap can be defined as follows:

1. we provide a "global" set of test points within the unit cube $[-1,1]^d$.
2. For each box Box(c,r), we rescale the global test points to lie within the box by calculating c .+ r .* p for each global test point p.

BoxMap(:pointdiscretized, map, domain, points) -> SampledBoxMap

Example

julia> using StaticArrays
       # create a map that tests the vertices of a box
julia> global_test_points = SVector{2,Float64}[
           (1,  1),
           (1, -1),
           (-1, 1),
           (-1, -1)
       ]4-element Vector{SVector{2, Float64}}:
 [1.0, 1.0]
 [1.0, -1.0]
 [-1.0, 1.0]
 [-1.0, -1.0]
julia> F = BoxMap(:pointdiscretized, f, domain, global_test_points)SampledBoxMap with 4 sample points
julia> p = plot!(
           p, F(B),
           color=RGBA(1.,0.,0.,0.5),
           lab="Images of test points along the vertices",
       )Plot{Plots.GRBackend() n=4}