Sorry if this is a basic problem but I don't know where to start looking (mainly because being an outsider I don't know the terms and nomenclature).
Imagine two perpendicular lines ("profiles") in a "T" spatial arrangement. The lines are arbitrary (empirical functions should I say?) in the sense that they don't follow any simple formula (but I have the data of each line. Each line is a velocity profile along a transect. One line is parallel to the X axis, the other is parallel to the Y axis. These lines have one point in common, ie there a point i where Xi=Yi.
I would like to interpolate between them to guess how the velocity distribution would look in the area defined by these two lines (eg the containing rectangle?). So I want to go from 2 known lines (1D) to a surface (2D).
I imagine that I need a function Z=f(X,Y) such as when plotting this function I can have a 2D representation of the surface containing both lines ("profiles")
The lines are perpendicular. The lines are NOT straight lines (except when viewed from above). Imagine you measure velocity over two lines: one from A to B, another from C to D. When viewed from above, these lines are perpendicular and they have a point in common: they look like this: https://www.dropbox.com/s/1ju2hzmkvijlz2j/1d.lines.vel.jpg
Note that the point they have in common is the beginning of one line, and the middle of the 2nd line.
Now, what I need is an algorithm which allows me to "guess" the "surface" (2D velocity vector field) defined by these two lines. I would think on a simple interpolation, but how? I need to obtain this: https://www.dropbox.com/s/3is8zzetps4coq3/surface.png
I am sure this must be a VERY common problem in many many fields... But I don't know the math world.. Could you please provide some keywords so I start looking??
Thanks very very much!!!