ScatteredInterpolation.jl

Interpolation of scattered data in Julia

ScatteredInterpolation.jl interpolates scattered data in arbitrary dimensions.

• ScatteredInterpolation.jl
• Example Usage
• Supported methods
• Radial Basis Functions
• Inverse Distance Weighting
• Nearest Neighbor
• API
• Functions
• Types

Example Usage

Interpolate data defined on the vertices and in the center of a square using a multiquadratic radial basis function:

julia> using ScatteredInterpolation

julia> samples = [0.0; 0.5; 0.5; 0.5; 1.0];

julia> points = [0.0 0.0; 0.0 1.0; 1.0 0.0; 0.5 0.5; 1.0 1.0]';

julia> itp = interpolate(Multiquadratic(), points, samples);

julia> interpolated = evaluate(itp, [0.6; 0.6])
1-element Vector{Float64}:
 0.6105

If we instead want to use nearest neighbor interpolation:

julia> itp = interpolate(NearestNeighbor(), points, samples);

julia> interpolated = evaluate(itp, [0.6; 0.6])
1×1 Matrix{Float64}:
 0.5000

Gridding of data

A common use case for scattered interpolation is gridding of data, i.e. interpolation of scattered data to a grid. Using the same data as above, we can interpolate it to a 5x5 grid

n = 5
x = range(0, stop = 1, length = n)
y = range(0, stop = 1, length = n)
X = repeat(x, n)[:]
Y = repeat(y', n)[:]
gridPoints = [X Y]'

itp = interpolate(Multiquadratic(), points, samples)
interpolated = evaluate(itp, gridPoints)
gridded = reshape(interpolated, n, n)

# output

5×5 Matrix{Float64}:
 -0.0000  0.1081  0.2365  0.3703  0.5000
  0.1081  0.2263  0.3615  0.4975  0.6246
  0.2365  0.3615  0.5000  0.6356  0.7582
  0.3703  0.4975  0.6356  0.7688  0.8868
  0.5000  0.6246  0.7582  0.8868  1.0000