NearestScatterSurface Class

public sealed class NearestScatterSurface : Surface

Public NotInheritable Class NearestScatterSurface
	Inherits Surface

public ref class NearestScatterSurface sealed : public Surface

[<SealedAttribute>]
type NearestScatterSurface = 
    class
        inherit Surface
    end

Inheritance

Object  →  Surface  →  NearestScatterSurface

The NearestScatterSurface class implements the simplest form of scattered data interpolation: for any query point x, it returns the function value fᵢ associated with the nearest sample point pᵢ.

Interpolation method: Given N sample points pᵢ ∈ ℝᴰ with values fᵢ, the interpolant is defined as:

s(x) = f_nearest, where nearest = argminᵢ ||x - pᵢ||

This produces a piecewise constant function with Voronoi-like regions around each data point. The interpolant is discontinuous at the boundaries between regions.

Properties:

• Works in any number of dimensions.
• Defined everywhere in ℝⁿ (no extrapolation concerns).
• Produces discontinuous, piecewise constant output.
• Gradient is zero almost everywhere (except at measure-zero boundaries).

Performance: The current implementation uses brute-force linear search with O(N) evaluation cost per query, where N is the number of sample points. In case of ties (multiple points at the same minimum distance), the point with the smallest index is selected.

Note: Future versions may implement spatial indexing (e.g., k-d tree) to improve query performance to O(log N).

Use cases: Nearest-neighbor interpolation is useful for:

• Categorical or discrete data where smooth interpolation is inappropriate.
• Fast lookups when continuity is not required.
• Initial prototyping or as a fallback method.
• Debugging or visualization of sample point coverage.

The NearestScatterSurface class inherits from Surface and works in arbitrary dimensions. Create instances using the ScatteredNearestInterpolator(Matrix<Double>, Vector<Double>) factory methods.

Reference