Nearest Neighbor in Interpolations

Interpolation of data is needed in IRIS products that include a cross-section (XSECT). The HCLASS data are interpolated with a rule of the nearest neighbor.

In its simplest form, the HCLASS value in any point X along a straight line between the points A and B, in which the HCLASS data values are HCLASS(A) and HCLASS(B), is obtained in the parametrization:

$\vec{X} (t) = \vec{A x} (t) + \vec{B} x (1 - t)$ , when $t \in [0, 1]$

$H C L A S S (\vec{X}) = H C L A S S (\vec{A})$ , when $t \leq 0.5$

$H C L A S S (\vec{X}) = H C L A S S (\vec{B})$ , when $t \geq 0.5$

This approach generalizes to interpolating in the N-dimensional data grid:

H C L A S S (\vec{X}) = H C L A S S (\vec{A_{i}})

where $\vec{A_{i}}$ has the shortest distance to the data point $\vec{X}$

r_{i} = | \vec{X} - {\vec{A}}_{i} | = \min {r_{j} = | \vec{X} - {\vec{A}}_{j} |, w h e n A_{j} \in p r o x i m a t e d a t a}