Approximation Examples

The 400 x 300 pixel RGB color image (a photograph taken by myself during a visit to Barcelona, Spain) used as source function in the approximation examples below. The image was sampled at 1,600 random positions, and reconstructed using several "classic" scattered data methods.
Reconstruction using Shepard's global method.
Reconstruction using Shepard's local method, using one closest sample. In this case, Shepard's local method degenerates to a piecewise constant-valued Voronoi diagram of the sample points.
Reconstruction using Shepard's local method, using 10 closest samples.
Reconstruction using Shepard's local method, using 100 closest samples.
Reconstruction using Hardy's global method, using parameters R = 1.0 and a = 0.5.
Reconstruction using Hardy's global method, using parameters R = 10.0 and a = 0.5.
Reconstruction using Hardy's global method, using parameters R = 100.0 and a = 0.5.
Reconstruction using Hardy's global method, using parameters R = 1.0 and a = 0.1.
Reconstruction using Hardy's local method, using 10 closest neighbours and parameters R = 1.0 and a = 0.5.
Reconstruction using Hardy's local method, using 100 closest neighbours and parameters R = 1.0 and a = 0.5.
Reconstruction using Sibson's method.
Reconstruction using piecewise linear interpolation based on a Delaunay triangulation of the sample points.
Reconstruction using piecewise linear interpolation based on an optimized triangulation of the sample points.