update README

README.md

@@ -13,22 +13,48 @@ julia> using PhotosplineReader.FITSIO
 
 julia> fpath = "PhotosplineReader.jl/test/examples/IceCube_data_release_202209013_kdes/E_dec_photospline_v006_3D.fits";
 
-julia> spt = FITS(fpath) do f
-           SplineTable(f)
-       end
+julia> spt = SplineTable( fpath )
 3-dimensional SplineTable of b-spline orders [1, 1, 3],
-with extents: 
-	 (0.83, 10.21) 
-	 (-0.17, 1.00) 
-	 (0.57, 4.42) 
-
+with extents:
+    (0.83, 10.21)
+    (-0.17, 1.00)
+    (0.57, 4.42)
 
 julia> x = [ 2.8, 0.2, 3.0 ]
 3-element Vector{Float64}:
  2.8
  0.2
  3.0
 
-julia> evaluate_simple( x, spt )
+julia> spt(x)
+0.7973871961087491
+
+julia> spt(x...)
 0.7973871961087491
 ```
+
+## Interfacing with Interpolations.jl
+```julia
+julia> using Interpolations
+
+julia> spt = SplineTable( fpath )
+3-dimensional SplineTable of b-spline orders [1, 1, 3],
+with extents:
+    (0.83, 10.21)
+    (-0.17, 1.00)
+    (0.57, 4.42)
+
+julia> itp = spline_interpolation( spt );
+
+julia> typeof( itp )
+Interpolations.FilledExtrapolation{Float64, 3, ScaledInterpolation{Float32, 3, Interpolations.BSplineInterpolation{Float32, 3, Array{Float32, 3}, Tuple{BSpline{Linear{Throw{OnGrid}}}, BSpline{Linear{Throw{OnGrid}}}, BSpline{Cubic{Line{OnGrid}}}}, Tuple{Base.Slice{UnitRange{Int64}}, Base.Slice{UnitRange{Int64}}, Base.Slice{UnitRange{Int64}}}}, Tuple{BSpline{Linear{Throw{OnGrid}}}, BSpline{Linear{Throw{OnGrid}}}, BSpline{Cubic{Line{OnGrid}}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}, Tuple{BSpline{Linear{Throw{OnGrid}}}, BSpline{Linear{Throw{OnGrid}}}, BSpline{Cubic{Line{OnGrid}}}}, Float64}
+
+julia> itp( x... )
+0.7973871961087493
+
+julia> Interpolations.gradient( itp, x... )
+3-element StaticArraysCore.SVector{3, Float64} with indices SOneTo(3):
+ -1.0382749146578347
+ -0.4631499529505209
+  0.08274258979323065
+```