Euclidean Allocation
Euclidean allocation produces a grid where each empty cell is assigned to the source it is nearest to. The nearest source is determined by Euclidean distance. Sources are all of the cells with a value, including zero. Empty cells are cells with no value.

Euclidean distance is the assumption that the distance between two points is a straight line: d = sqrt( (x1-x0)^2 + (y1-y0)^2 )

A maximum proximity distance can be assigned to allocate a cell to the source. The code to use in ArcView Spatial Analyst for proximity mapping is Grid.EucAllocation. (Reference: ESRI GIS)

Inverse Distance Weighted Interpolation
Inverse distance weighted interpolation is a method used for interpolation of scatter points and assumes that the interpolating surface should be more heavily influenced by nearby points than distant ones. It determines cell values using a linearly weighted combination of a set of points. The weight is a function of inverse distance. (Reference: National Center for Geographic Information and Analysis)

Triangulated Irregular Network (TIN)
A TIN model represents a surface as a set of continuous, non-overlapping triangles. The surface within each triangle is a plane. The triangles are made from mass points, which can occur at any location (do not have to be evenly spaced). Carefully selected mass points provide a more accurate surface model. Mass points should occur where there is a major change in the surface shape.

The best triangulation method is Delauney triangulation. It requires that a circle drawn through three nodes of a triangle will contain no other node. (Reference: Ianko's GIS Website)