linear, cubic, and natural methods are all triangulation based. they take
the scattered points, use octave's delauney triangulation, then calculate
local interpolants within the triangles. linear (actually bilinear i guess)
is simply a weighted some of triangle areas (the interpolation point
creates three sub-triangles within the mesh triangle, and value is a
weighted projection inversely proportional to sub-triangle size, where a
big sub-triangle has you more strongly weighted toward the point not
associated with that sub-triangle). the v4 method does not triangulate,
and does a weighted interpolation over the entire mesh. that can get slow
and memory intensive, but it's currently the only 'smooth' interpolation
function Octave has implemented (sort of).