Date: 09/23/07 (Algorithms)    Keywords: no keywords

I need to come up with an algorithm and general formula for using bilinear interpolation onto a regularly-spaced 2-D grid (x,y) from starting observations that are irregularly spaced. I know how to do bilinear interpolation when going from one regular grid to another, but my starting points are irregular, so I'm not sure how to alter it. The regular form I've used is:

f(x,y) = [f(x1,y1)/(x2-x1)(y2-y1)](x2-x)(y2-y) + [f(x2,y1)/(x2-x1)(y2-y1)](x-x1)(y2-y) + [f(x1,y2)/(x2-x1)(y2-y1)](x2-x)(y-y1) + [f(x2,y2)/(x2-x1)(y2-y1)](x-x1)(y-y1)

where (x1,y1) is in the lower-left, (x1,y2) is the upper-left, (x2,y1) lower-right, and (x2,y2) upper-right with (x,y) in the middle of that rectangle. The problem I have now is that my known points aren't on a rectangle. Suggestions? Thanks in advance!

(Crossposted to math_help.)

Source: http://community.livejournal.com/algorithms/92551.html