Nearest-neighbor interpolation (point sampling)

Characteristics

• Simple rule: value at query = value at nearest sample.
• Produces a Voronoi tessellation of the domain: each sample controls the surrounding cell.
• Result is piecewise constant with discontinuities at cell boundaries.
• Preserves original sampled values (it does not invent new intermediate values).
• Computationally cheap and easy to implement.

Because it assigns one sample's value to an entire neighborhood, nearest-neighbor interpolation is well suited for categorical or label data where mixing values would be meaningless (for example land-cover classes in raster GIS). It is also used in digital imaging when a fast, non-smoothing upscaling is desired, though the visual result can be blocky and aliased.

Algorithm sketch

1. For each target point, compute distances to known samples (or use a spatial index).
2. Select the sample with minimum distance (ties resolved by a fixed rule).
3. Return the selected sample's value as the interpolated value.
4. Optionally accelerate with spatial data structures (k-d tree, grid).

Typical alternatives include bilinear or bicubic interpolation (which produce smooth transitions) and inverse-distance weighting or k-nearest methods (which combine multiple neighbors). Nearest-neighbor stands out when preserving exact original values is important or when input data are categorical. It is unreliable where continuity or gradient fidelity matters, since it introduces sharp boundaries aligned with the Voronoi cells.

Practical notes: many libraries provide nearest-neighbor resampling for raster and point data; implementations differ in tie-breaking and distance metric choices. Its minimal computation and exact-value property make it a persistent choice for fast resampling and label-preserving workflows.